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9789_0	The Atlas der Neederlanden, or Atlas of the Netherlands, is a composite atlas which was presumably collected and composed by the publishing company Covens and Mortier in Amsterdam. The maps are gathered in nine volumes and show how the Low Countries, including Belgium and the former colonies of the Netherlands, have developed over the course of about two decades. The atlas contains more than 600 printed and manuscript maps and is preserved by the Special Collections of the University of Amsterdam. Composite atlas
9789_1	The Atlas der Neederlanden is an atlas factice, also known as composite atlas. These atlases were composed by wealthy people who collected maps concerning a specific region or topic. In some cases rich buyers contracted the publisher to collect the maps for them. These maps were then bound together in one or more volumes by a book binder in the typical “atlas-binding”. Each composite atlas contains a different collection of maps and is therefore unique in its composition. There are different composite atlases preserved, for example the Atlas Blaeu-Van der Hem in the Austrian National Library in Vienna and the Atlas Van der Hagen, which was made earlier than the Atlas der Neederlanden, around 1690, and has been in the possession of the National Library of the Netherlands since 1887. History
9789_2	Who the collector of the Atlas der Neederlanden was or for whom it was made remains unclear. At some point in the 19th century the book found its way to the University of Amsterdam where it is now part of the Special Collections of its University Library. It is assumed that the atlas was composed by Covens and Mortier. The publisher is mentioned at the frontispieces of eight of the nine volumes with the following text: Table des cartes etc: de I. Cóvens et C. Mortier contenues dans ce volume. Also, most of the maps in the atlas were published by Covens and Mortier.
9789_3	When the last volume of the atlas was finished around 1816, the publishing house was led by Cornelis Covens (1764-1825). He worked for his family’s firm from 1790 until 1825, bringing it innovation and success. Covens and Mortier published many new maps but also kept the old stock, which ensured that the firm had a large fund of maps. Within the field of commercial and government cartography Covens and Mortier became the leading publishing company at the beginning of the 19th century.
9789_4	Around 1816 the last volume of the atlas was finished. The largest part of the map collection dates from the 18th century. A few maps originate from the 17th century, like the Leo Belgicus dating from 1611 and a map of the Netherlands created by Frederik de Wit in 1670. Most of the 18th century maps are collected in volumes 1-8. Volume 9 contains maps from the 17th century and a few maps dating from the beginning of the 19th century. This volume doesn’t have a frontispiece of the publisher. The most recent maps in the atlas are to be found in volume 9 and date from 1816. Map collection
9789_5	The Atlas der Neederlanden contains maps of large sizes. Most atlases from the 17th and 18th century don’t have large maps because these didn’t fit in the bound volumes. The Atlas der Neederlanden forms an exception. The large-scale maps were folded to fit in the atlas and several wall maps of 4, 12 and 25 sheets were bound separately. The multi-sheet wall maps were popular decorations and therefore rarely preserved well. Because the separate sheets were bound and kept in the atlas, they remained in good condition with their lively colours still preserved.
9789_6	The atlas has nine volumes. Each volume is about a different part of the Netherlands: Volume I: Gelderlandt, Utrecht & Over Yssel (Gelderland, Utrecht and Overijssel) Volume II: Holland 1. Zuid-Holland (South Holland) Volume III: Holland 2. Zuid-Holland (South Holland) Volume IV: Holland 3. Zuid-Holland (South Holland) Volume V: Holland 4. Noord-Holland (North Holland) Volume VI: Zeeland (Zeeland) Volume VII: Vriesland, Groningen & Drenthe (Friesland, Groningen and Drenthe) Volume VIII: Belgiën (Belgium) Volume IX: Algemeene kaarten & Coloniën (General maps and colonies) Restoration In 2011 the atlas was restored and digitized. A facsimile edition has been made of the nine volumes. This facsimile was presented at the celebration of the 200 year commemoration of the Kingdom of the Netherlands in 2013. The facsimile was published together with the book De Atlas der Neederlanden: Kaarten van de Republiek en het prille Koninkrijk met 'Belgiën' en 'Coloniën’.
9789_7	Maps on Wikimedia Commons Look at the Wikimedia Commons page Atlas der Neederlanden. The Special Collections of the University of Amsterdam has made all the scans of the Atlas der Neederlanden'' available on Wikimedia Commons. See also Early modern Netherlandish cartography References External links Video of the Atlas der Neederlanden. (in Dutch) Website Atlas der Neederlanden. (in Dutch) Report and photos the restoration project. All geo-referenced maps online Atlases History of the Netherlands Geography of the Netherlands
9790_0	The Hungarian minority of Romania (; ) is the largest ethnic minority in Romania, consisting of 1,227,623 people and making up 6.1% of the total population, according to the 2011 census. Most ethnic Hungarians of Romania live in areas that were, before the 1920 Treaty of Trianon, parts of Hungary. Encompassed in a region known as Transylvania, the most prominent of these areas is known generally as Székely Land (; ), where Hungarians comprise the majority of the population. Transylvania also includes the historic regions of Banat, Crișana and Maramureș. There are forty-one counties of Romania; Hungarians form a large majority of the population in the counties of Harghita (85.21%) and Covasna (73.74%), and a large percentage in Mureș (38.09%), Satu Mare (34.65%), Bihor (25.27%), Sălaj (23.35%) and Cluj (15.93%) counties.
9790_1	There also is a community of Hungarians living mostly in Moldavia, known as the Csángós. These live in the so-called region of Csángó Land in Moldavia but also in parts of Transylvania and in a village of Northern Dobruja known as Oituz. History Historical background The Hungarian tribes originated in the vicinity of the Ural Mountains and arrived in the territory formed by present-day Romania during the 9th century from Etelköz or Atelkuzu (roughly the space occupied by the present day Southern Ukraine, the Republic of Moldova and the Romanian province of Moldavia). Due to various circumstances (see Honfoglalás), the Magyar tribes crossed the Carpathians around 895 AD and occupied the Carpathian Basin (including present-day Transylvania) without significant resistance from the local populace. The precise date of the conquest of Transylvania is not known; the earliest Magyar artifacts found in the region are dated to the first half of the 10th century.
9790_2	In 1526, at the Battle of Mohács, the forces of the Ottoman Empire annihilated the Hungarian army and in 1571 Transylvania became an autonomous state, under the Ottoman suzerainty. The Principality of Transylvania was governed by its princes and its parliament (Diet). The Transylvanian Diet consisted of three Estates (Unio Trium Nationum): the Hungarian nobility (largely ethnic Hungarian nobility and clergy); the leaders of Transylvanian Saxons-German burghers; and the free Székely Hungarians.
9790_3	With the defeat of the Ottomans at the Battle of Vienna in 1683, the Habsburg Monarchy gradually began to impose their rule on the formerly autonomous Transylvania. From 1711 onward, after the conclusion of Rákóczi's War for Independence, Habsburg control over Transylvania was consolidated, and the princes of Transylvania were replaced with Habsburg imperial governors. In 1765 the Grand Principality of Transylvania was proclaimed, consolidating the special separate status of Transylvania within the Habsburg Empire, established by the Diploma Leopoldinum in 1691. The Hungarian historiography sees this as a mere formality. Within the Habsburg Empire, Transylvania was administratively part of Kingdom of Hungary.
9790_4	After quashing the 1848 revolution, the Austrian Empire imposed a repressive regime on Hungary and ruled Transylvania directly through a military governor and abolished the Unio Trium Nationum and granted citizenship to ethnic Romanians. Later, the compromise of 1867 established the Austria-Hungary and Transylvania became integral part of the Kingdom of Hungary again, with Hungarian becoming the official language, as well the policy of Magyarization affected the region. Following defeat in World War I, Austria-Hungary disintegrated. The ethnic Romanian elected representatives of Transylvania, Banat, Crișana and Maramureș proclaimed Union with Romania on 1 December 1918.
9790_5	With the conclusion of World War I, the Treaty of Trianon (signed on 4 June 1920) defined the new border between the states of Hungary and Romania. As a result, the more than 1.5 million Hungarian minority of Transylvania found itself becoming a minority group within Romania. Also after World War I, a group of Csángó families founded a village in Northern Dobruja known as Oituz, where Hungarians still live today.
9790_6	In August 1940, during the Second World War, the northern half of Transylvania was returned to Hungary by the second Second Vienna Award. Historian Keith Hitchins summarizes the situation created by the award: Some 1,150,000 to 1,300,000 Romanians, or 48 per cent to over 50 per cent of the population of the ceded territory, depending upon whose statistics are used, remained north of the new frontier, while about 500,000 Hungarians (other Hungarian estimates go as high as 800,000, Romanian as low as 363,000) continued to reside in the south. The Treaty of Paris (1947) after the end of the Second World War overturned the Vienna Award, and the territory of northern Transylvania was returned to Romania. The post-World War II borders with Hungary agreed on at the Treaty of Paris were identical with those set out in 1920.
9790_7	After the war, in 1952, a Magyar Autonomous Region was created in Romania by the communist authorities. The region was dissolved in 1968, when a new administrative organization of the country (still in effect today) replaced regions with counties. The communist authorities, and especially after Nicolae Ceaușescu's regime came to power, restarted the policy of Romanianization. Today, "Transylvania proper" (bright yellow on the accompanying map) is included within the Romanian counties (județe) of Alba, Bistrița-Năsăud, Brașov, Cluj, Covasna, Harghita, Hunedoara, Mureș, Sălaj (partially) and Sibiu. In addition to "Transylvania proper", modern Transylvania includes Crișana and part of the Banat; these regions (dark yellow on the map) are in the counties of Arad, Bihor, Caraș-Severin, Maramureș, Sălaj (partially), Satu Mare, and Timiș. Post-communist era
9790_8	In the aftermath of the Romanian Revolution of 1989, ethnic-based political parties were constituted by both the Hungarians, who founded the Democratic Union of Hungarians in Romania, and by the Romanian Transylvanians, who founded the Romanian National Unity Party. Ethnic conflicts, however, never occurred on a significant scale, even though some violent clashes, such as the Târgu Mureș events of March 1990, did take place shortly after the fall of Ceaușescu regime. In 1995, a basic treaty on the relations between Hungary and Romania was signed. In the treaty, Hungary renounced all territorial claims to Transylvania, and Romania reiterated its respect for the rights of its minorities. Relations between the two countries improved as Romania and Hungary became EU members in the 2000s.
9790_9	Politics The Democratic Union of Hungarians in Romania (UDMR) is the major representative of Hungarians in Romania, and is a member of the Unrepresented Nations and Peoples Organization. The aim of the UDMR is to achieve local government, cultural and territorial autonomy and the right to self-determination for Hungarians. UDMR is a member of the European Democrat Union (EDU) and the European People's Party (EPP). Since 1996, the UDMR has been a member or supporter of every governmental coalition.
9790_10	Political agreements have brought the gradual implementation of Hungarian language in everyday life: Public administration Law 215/2002 stipulates "the use of national minority languages in public administration in settlements where minorities exceed 20% of the population"; minority ethnics will receive a copy of the documents in Romanian language and a translation in their language; however, official documents are preserved by the local administration in Romanian only; local administration will provide inscriptions for the names of localities and public institutions under their authority, and display public interest announcements in the native language of the citizens of the respective ethnic minority under the same 20% rule.
9790_11	Even though Romania co-signed the European laws for protecting minorities' rights, the implementation has not proved satisfactory to all members of Hungarian community. There is a movement by Hungarians both for an increase in autonomy and distinct cultural development. Initiatives proposed by various Hungarian political organizations include the creation of an "autonomous region" in the counties that form the Szekler region (Székelyföld), roughly corresponding to the territory of the former Hungarian Autonomous Province as well as the historical Szekler land that had been abolished by the Hungarian government in the second half of the 19th century, and the re-establishment of an independent state-funded Hungarian-language university.
9790_12	However, the situation of the Hungarian minority in Romania has been seen by some as a model of cultural and ethnic diversity in the Balkan area: In an address to the American people, President Clinton asked in the midst of the air war in Kosovo: Who is going to define the future of this part the world... Slobodan Milošević, with his propaganda machine and paramilitary forces which compel people to give up their country, identity, and property, or a state like Romania which has built a democracy respecting the rights of ethnic minorities? Notable Hungarians of Romania
9790_13	Sports Several ethnic Hungarians<ref></ref</ref> have won Olympic medals for Romania. Iolanda Balaș (Jolanda Balázs) (2G) High-jump 1960 and 1964. Ileana Silai (Ilona Gergely) (S) 800m 1968 Ecaterina Szabo (Katalin Szabó) (3G-individual, 1G-team 1S-individual) Gymnastics 1984 Emilia Eberle (Hungarian-German) (1S-individual, 1S-team) Gymnastics 1980 Gabriela Szabo (1G, 1S, 1B) 1996, 2000 (father Hungarian) Corneliu Oros (B) Team-volleyball Noemi Lung (Noemi Ildikó Lung) (S, B) Swimming 1984 Elena Horvat (Ilona Horvath) (G) team-rowing 1984 Viorica Ioja (Ibolya Jozsa) (G, S) Team-rowing 84 Aneta Mihaly (S) Team-rowing 1984 Herta Anitaș (S, B) Team-rowing 1988 Eniko Barabas (Enikö Barabás)(B) Team-rowing 2008 Elisabeta Lazăr (Erzsébet Lázár) (B) Team-rowing76 Ladislau Lovrenschi (László Lavrenszki) ( B) Team-rowing 72 (S) 88 Ioan Pop (János Pap) (2B) Team-sabre (B) 76, (B) 84 Alexandru Nilca (Sándor Nyilka) Team-sabre (B) 76
9790_14	Vilnos Szabo (Vilmos Szabó) (B) Team-Sabre 1984 Monika Weber-Koszto (S) Team-foil 1984 (+ 1S, 2B for Germany) Marcela Zsak (S) Team-foil 1984´ Rozalia Oros (Rozália Orosz)(S) Team-foil 1984 Olga Orban-Szabo (Olga Orbán Szabó) (2B) Team women's´foil 1968,1972 (1S) Women's Foil Individual 1956 Ileana Gyulai-Drimba (Ilona Gyulai) (2B) Team-women's foil 1968,1972 Ecaterina Stahl-Iencic (Katalin Jencsik) (2B) Team-women's foil 1968,1972 Reka Zsofia Lazar-Szabo(1S, 1B) Team Women's´foil 1992, 1996 Simona Pop Stefan Birtalan (István Bertalan) (1S, 2B) Team-Handball 1972, 1976,1980 Gabriel Kicsid (1S, 1B) Team-Handball 1972,1976 Iosif Boros (J´zsef Boros)(2B) Team-handball 1980 and 1984. Stefan Tasnadi (István Tasnádi) (S) weightlifting 1984 Valentin Silaghi (B) boxing 1980 Ladislau Simon (László Simon) (B) wrestling 1976 Francisc Horvat (Ferenc Horvát) (B) wrestling 1956
9790_15	Olympic chess players Janos Balogh Stefan Erdélyi (István Erdélyi) Alexandru Tyroler (Sándor Tyroler) Miklós Bródy Szidonia Vajda Science Albert-László Barabási (network scientist) Classical music Sandor Vegh (violinist) Sándor Veress (composer) György Ligeti (composer) György Kurtág (composer) Péter Eötvös (composer/conductor) György Selmeczi (composer) Péter Csaba Emil Telmányi István Ruha (violinist) Johanna Martzy (violinist) Júlia Várady (soprano) Literature Attila Bartis (writer) Miklós Bánffy (writer, politician) Ádám Bodor (writer) György Dragomán (writer) András Ferenc Kovács (poet) Sándor Kányádi (poet) Benő Karácsony (writer) Béla Markó (poet, politician) András Sütő (writer, playwright) Csaba Székely (playwright, screenwriter) János Székely (writer, poet, playwright) Domokos Szilágyi (poet) István Szilágyi (writer) Áron Tamási (writer) Actors of Hungarian descent Rick Moranis Béla Lugosi Subgroups Székelys
9790_16	The Székely people are Hungarians who mainly live in an area known as Székely Land (Ținutul Secuiesc in Romanian), and who maintain a different set of traditions and different identity from that of other Hungarians in Romania. Based on the latest Romanian statistics (2011 Romanian census, 532 people declared themself "Székelys" rather than "Hungarians.". The three counties of the unofficial Székely Land – Harghita, Covasna, and Mureș – have a combined ethnic Hungarian population of 609,033. Csángós
9790_17	The Csángós (, ) are people of Roman Catholic faith, some speaking a Hungarian dialect and some Romanian. They live mainly in the Bacău, Neamț and Iași counties, Moldavia region. Their homeland in Moldavia is known as Csángó Land. Some also live in Transylvania (around the Ghimeș-Palanca Pass and in the so-called Seven Villages) and in Oituz at Northern Dobruja. The Csango settled there between the 13th and 15th centuries and today, they are the only Hungarian-speaking ethnic group living to the east of the Carpathians.
9790_18	The ethnic background of Csango is nevertheless disputed, since, due to its active connections to the neighboring Polish kingdom and to the Papal States, the Roman Catholic faith persisted in Moldavia throughout medieval times, long after Vlachs living in other Romanian provinces, closer to the Bulgarian Empire, had been completely converted to Eastern-Rite Christianity. Some Csango claim having Hungarian ancestry while others claim Romanian ancestry. The Hungarian-speaking Csangos have been subject to some violations of basic minority rights: Hungarian-language schools have been closed down over time, their political rights have been suppressed and they have even been subject to slow, forced nationalisation by various Romanian governments over the years, because the Romanian official institutions deem Csangos as a mere Romanian population that was Magyarized in certain periods of time. Culture
9790_19	The number of Hungarian social and cultural organizations in Romania has greatly increased after the fall of communism, with more than 300 being documented a few years ago. There are also several puppet theatres. Professional Hungarian dancing in Romania is represented by the Maros Folk Ensemble (formerly State Szekler Ensemble) in Târgu Mureș, the Hargita Ensemble, and the Pipacsok Dance Ensemble. Other amateur popular theaters are also very important in preserving the cultural traditions.
9790_20	While in the past the import of books was hindered, now there are many bookstores selling books written in Hungarian. Two public TV stations, TVR1 and TVR2, broadcast several Hungarian programs with good audiences also from Romanians. This relative scarcity is partially compensated by private Hungarian-language television and radio stations, like DUNA-TV which is targeted for the Hungarian minorities outside Hungary, particularly Transylvania. A new TV station entitled "Transylvania" is scheduled to start soon, the project is funded mostly by Hungary but also by Romania and EU and other private associations. There are currently around 60 Hungarian-language press publications receiving state support from the Romanian Government. While their numbers dropped as a consequence of economic liberalisation and competition, there are many others private funded by different Hungarian organizations. The Székely Region has many touristic facilities that attract Hungarian and other foreign
9790_21	tourists.
9790_22	Education According to Romania's minority rights law, Hungarians have the right to education in their native language, including as a medium of instruction. In localities where they make up more than 20% of the population they have the right to use their native language with local authorities. According to the official data of the 1992 Romanian census, 98% of the total ethnic Hungarian population over the age of 12 has had some schooling (primary, secondary or tertiary), ranking them fourth among ethnic groups in Romania and higher than the national average of 95.3%. On the other hand, the ratio of Hungarians graduating from higher education is lower than the national average. The reasons are diverse, including a lack of enough native-language lecturers, particularly in areas without a significant proportion of Hungarians.
9790_23	At Babeș-Bolyai University Cluj-Napoca, the largest state-funded tertiary education institution in Romania, more than 30% of courses are held in the Hungarian language. There is currently a proposal by local Hungarians, supported by the Democratic Alliance of Hungarians in Romania (RMDSZ), to separate the Hungarian-language department from the institution, and form a new, Hungarian-only Bolyai University. The former Bolyai University was disbanded in 1959 by Romanian Communist authorities and united with the Romanian Babeș University to form the multilingual Babeș-Bolyai University that continues to exist today. Other universities that offer study programs in Hungarian are the University of Medicine, Pharmacy, Science and Technology of Târgu Mureș (public), Târgu Mureș University of Arts (public), Sapientia University (private) in Cluj-Napoca, Miercurea Ciuc and Târgu Mureș, Partium Christian University (private) in Oradea and Protestant Theological Institute of Cluj (private).
9790_24	Identity and citizenship Many Hungarians living in Transylvania were disconcerted when the referendum held in Hungary in 2004 on the issue of giving dual-citizenship to ethnic Hungarians living abroad failed to receive enough electoral attendance and the vote was uncertain. Some of them complain that when they are in Hungary, they are perceived as half-Romanians, and are considered as having differences in language and behaviour. However, a large proportion of Transylvanian Hungarians currently work or study in Hungary, usually on a temporary basis. After 1996, Hungarian-Romanian economic relations boomed, and Hungary is an important investor in Transylvania, with many cross-border firms employing both Romanians and Hungarians.
9790_25	A proposal supported by the RMDSZ to grant Hungarian citizenship to Hungarians living in Romania but without meeting Hungarian-law residency requirements was narrowly defeated at a 2004 referendum in Hungary (the referendum failed only because there were not enough votes to make it valid). After the failed vote, the leaders of the Hungarian ethnic parties in the neighboring countries formed the HTMSZF organization in January 2005, as an instrument lobbying for preferential treatment in the granting of Hungarian citizenship.
9790_26	In 2010 some amendments were passed in Hungarian law facilitating an accelerated naturalization process for ethnic Hungarians living abroad; among other changes, the residency-in-Hungary requirement was waived. According to a RMDSZ poll conducted that year, over 85 percent of Romania's ethnic Hungarians were eager to apply for Hungarian citizenship. Romania's President Traian Băsescu declared in October 2010 that "We have no objections to the adoption by the Hungarian government and parliament of a law making it easier to grant Hungarian citizenship to ethnic Hungarians living abroad." Between 2011 and 2012, 200,000 applicants took advantage of the new, accelerated naturalization process; there were another 100,000 applications pending in the summer of 2012. As of February 2013, the Hungarian government has granted citizenship to almost 400,000 Hungarians 'beyond the borders'. In April 2013, the Hungarian government announced that 280,000 of these were Romanian citizens.
9790_27	Population 2011 census The remaining 4,973 (0.4%) ethnic Hungarians live in the other counties of Romania, where they make up less than 0.1% of the total population. Religion In 2002, 46.5% of Romania's Hungarians were Reformed, 41% Roman Catholic, 4.5% Unitarian and 2% Romanian Orthodox. A further 4.7% belonged to various other Christian denominations. In 2011, 45.9% of Romania's Hungarians were Reformed, 40.8% Roman Catholic, 4.5% Unitarian and 2.1% Romanian Orthodox. A further 5.8% belonged to various other Christian denominations. Around 0.25 percent of the Hungarians were atheist. Hungarian Heritage in Transylvania, Romania See also Romanians in Hungary List of towns in Romania by ethnic Hungarian population Romanian Hearth Union Hungarian Cultural Days of Cluj Transylvanianism References Further reading
9790_28	External links Multiculturalism debated Editorial about the Hungarian University in Cluj (Nine o'Clock English Language Daily [e]Newspaper) The Hungarian National Theater in Cluj, one of the most prestigious Hungarian theaters in Transylvania Democratic Alliance of Hungarians in Romania, the main Hungarian ethnic party website Romania Ethnic groups in Romania Ethnic groups in Transylvania
9791_0	A fuzzy concept is a concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether. It has a definite meaning, which can be made more precise only through further elaboration and specification - including a closer definition of the context in which the concept is used. The study of the characteristics of fuzzy concepts and fuzzy language is called fuzzy semantics. The inverse of a "fuzzy concept" is a "crisp concept" (i.e. a precise concept).
9791_1	A fuzzy concept is understood by scientists as a concept which is "to an extent applicable" in a situation. That means the concept has gradations of significance or unsharp (variable) boundaries of application. A fuzzy statement is a statement which is true "to some extent", and that extent can often be represented by a scaled value. The term is also used these days in a more general, popular sense – in contrast to its technical meaning – to refer to a concept which is "rather vague" for any kind of reason.
9791_2	In the past, the very idea of reasoning with fuzzy concepts faced considerable resistance from academic elites. They did not want to endorse the use of imprecise concepts in research or argumentation. Yet although people might not be aware of it, the use of fuzzy concepts has risen gigantically in all walks of life from the 1970s onward. That is mainly due to advances in electronic engineering, fuzzy mathematics and digital computer programming. The new technology allows very complex inferences about "variations on a theme" to be anticipated and fixed in a program.
9791_3	New neuro-fuzzy computational methods make it possible to identify, measure and respond to fine gradations of significance with great precision. It means that practically useful concepts can be coded and applied to all kinds of tasks, even if ordinarily these concepts are never precisely defined. Nowadays engineers, statisticians and programmers often represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets. Origins Problems of vagueness and fuzziness have probably always existed in human experience. From ancient history, philosophers and scientists have reflected about those kinds of problems.
9791_4	Sorites paradox The ancient Sorites paradox first raised the logical problem of how we could exactly define the threshold at which a change in quantitative gradation turns into a qualitative or categorical difference. With some physical processes this threshold is relatively easy to identify. For example, water turns into steam at 100 °C or 212 °F (the boiling point depends partly on atmospheric pressure, which decreases at higher altitudes). With many other processes and gradations, however, the point of change is much more difficult to locate, and remains somewhat vague. Thus, the boundaries between qualitatively different things may be unsharp: we know that there are boundaries, but we cannot define them exactly. According to the modern idea of the continuum fallacy, the fact that a statement is to an extent vague, does not automatically mean that it is invalid. The problem then becomes one of how we could ascertain the kind of validity that the statement does have.
9791_5	Loki's wager The Nordic myth of Loki's wager suggested that concepts that lack precise meanings or precise boundaries of application cannot be usefully discussed at all. However, the 20th-century idea of "fuzzy concepts" proposes that "somewhat vague terms" can be operated with, since we can explicate and define the variability of their application, by assigning numbers to gradations of applicability. This idea sounds simple enough, but it had large implications. Precursors The intellectual origins of the species of fuzzy concepts as a logical category have been traced back to a diversity of famous and less well-known thinkers, including (among many others) Eubulides, Plato, Cicero, Georg Wilhelm Friedrich Hegel, Karl Marx and Friedrich Engels, Friedrich Nietzsche, Hugh MacColl, Charles S. Peirce, Max Black, Jan Łukasiewicz, Emil Leon Post, Alfred Tarski, Georg Cantor, Nicolai A. Vasiliev, Kurt Gödel, Stanisław Jaśkowski and Donald Knuth.
9791_6	Across at least two and a half millennia, all of them had something to say about graded concepts with unsharp boundaries. This suggests at least that the awareness of the existence of concepts with "fuzzy" characteristics, in one form or another, has a very long history in human thought. Quite a few logicians and philosophers have also tried to analyze the characteristics of fuzzy concepts as a recognized species, sometimes with the aid of some kind of many-valued logic or substructural logic.
9791_7	An early attempt in the post-WW2 era to create a theory of sets where set membership is a matter of degree was made by Abraham Kaplan and Hermann Schott in 1951. They intended to apply the idea to empirical research. Kaplan and Schott measured the degree of membership of empirical classes using real numbers between 0 and 1, and they defined corresponding notions of intersection, union, complementation and subset. However, at the time, their idea "fell on stony ground". J. Barkley Rosser Sr. published a treatise on many-valued logics in 1952, anticipating "many-valued sets". Another treatise was published in 1963 by Aleksandr A. Zinov'ev and others In 1964, the American philosopher William Alston introduced the term "degree vagueness" to describe vagueness in an idea that results from the absence of a definite cut-off point along an implied scale (in contrast to "combinatory vagueness" caused by a term that has a number of logically independent conditions of application).
9791_8	The German mathematician published a German-language paper on fuzzy sets in 1965, but he used a different terminology (he referred to "many-valued sets", not "fuzzy sets"). Two popular introductions to many-valued logic in the late 1960s were by Robert J. Ackermann and Nicholas Rescher respectively. Rescher's book includes a bibliography on fuzzy theory up to 1965, which was extended by Robert Wolf for 1966–1974. Haack provides references to significant works after 1974. Bergmann provides a more recent (2008) introduction to fuzzy reasoning.
9791_9	Lotfi Zadeh The Iranian-born American computer scientist Lotfi A. Zadeh (1921-2017) is usually credited with inventing the specific idea of a "fuzzy concept" in his seminal 1965 paper on fuzzy sets, because he gave a formal mathematical presentation of the phenomenon that was widely accepted by scholars. It was also Zadeh who played a decisive role in developing the field of fuzzy logic, fuzzy sets and fuzzy systems, with a large number of scholarly papers. Unlike most philosophical theories of vagueness, Zadeh's engineering approach had the advantage that it could be directly applied to computer programming. Zadeh's seminal 1965 paper is acknowledged to be one of the most-cited scholarly articles in the 20th century. In 2014, it was placed 46th in the list of the world's 100 most-cited research papers of all time. Since the mid-1960s, many scholars have contributed to elaborating the theory of reasoning with graded concepts, and the research field continues to expand.
9791_10	Definition The ordinary scholarly definition of a concept as "fuzzy" has been in use from the 1970s onward. Criteria Radim Bělohlávek explains:
9791_11	Hence, a concept is generally regarded as "fuzzy" in a logical sense if: defining characteristics of the concept apply to it "to a certain degree or extent" (or, more unusually, "with a certain magnitude of likelihood"). or, the boundaries of applicability (the truth-value) of a concept can vary in degrees, according to different conditions. or, the fuzzy concept itself straightforwardly consists of a fuzzy set, or a combination of such sets.
9791_12	The fact that a concept is fuzzy does not prevent its use in logical reasoning; it merely affects the type of reasoning which can be applied (see fuzzy logic). If the concept has gradations of meaningful significance, it is necessary to specify and formalize what those gradations are, if they can make an important difference. Not all fuzzy concepts have the same logical structure, but they can often be formally described or reconstructed using fuzzy logic or other substructural logics. The advantage of this approach is, that numerical notation enables a potentially infinite number of truth-values between complete truth and complete falsehood, and thus it enables - in theory, at least - the greatest precision in stating the degree of applicability of a logical rule.
9791_13	Probability Petr Hájek, writing about the foundations of fuzzy logic, sharply distinguished between "fuzziness" and "uncertainty": In metrology (the science of measurement), it is acknowledged that for any measure we care to make, there exists an amount of uncertainty about its accuracy, but this degree of uncertainty is conventionally expressed with a magnitude of likelihood, and not as a degree of truth. In 1975, Lotfi A. Zadeh introduced a distinction between "Type 1 fuzzy sets" without uncertainty and "Type 2 fuzzy sets" with uncertainty, which has been widely accepted. Simply put, in the former case, each fuzzy number is linked to a non-fuzzy (natural) number, while in the latter case, each fuzzy number is linked to another fuzzy number. Applications
9791_14	Philosophy
9791_15	In philosophical logic and linguistics, fuzzy concepts are often regarded as vague concepts which in their application, or formally speaking, are neither completely true nor completely false, or which are partly true and partly false; they are ideas which require further elaboration, specification or qualification to understand their applicability (the conditions under which they truly make sense). The "fuzzy area" can also refer simply to a residual number of cases which cannot be allocated to a known and identifiable group, class or set if strict criteria are used. The collaborative written works of French philosopher Gilles Deleuze and French psychoanalyst Félix Guattari refer occasionally to fuzzy sets in conjunction with their idea of multiplicities. In A Thousand Plateaus, they note that "a set is fuzzy if its elements belong to it only by virtue of specific operations of consistency and consolidation, which themselves follow a special logic", and in What Is Philosophy?, a work
9791_16	dealing with the functions of concepts, they write that concepts as a whole are "vague or fuzzy sets, simple aggregates of perceptions and affections, which form within the lived as immanent to a subject".
9791_17	Sciences In mathematics and statistics, a fuzzy variable (such as "the temperature", "hot" or "cold") is a value which could lie in a probable range defined by some quantitative limits or parameters, and which can be usefully described with imprecise categories (such as "high", "medium" or "low") using some kind of scale or conceptual hierarchy. Fuzzy logic
9791_18	In mathematics and computer science, the gradations of applicable meaning of a fuzzy concept are described in terms of quantitative relationships defined by logical operators. Such an approach is sometimes called "degree-theoretic semantics" by logicians and philosophers, but the more usual term is fuzzy logic or many-valued logic. The novelty of fuzzy logic is, that it "breaks with the traditional principle that formalisation should correct and avoid, but not compromise with, vagueness". The basic idea of fuzzy logic is that a real number is assigned to each statement written in a language, within a range from 0 to 1, where 1 means that the statement is completely true, and 0 means that the statement is completely false, while values less than 1 but greater than 0 represent that the statements are "partly true", to a given, quantifiable extent. Susan Haack comments:
9791_19	"Truth" in this mathematical context usually means simply that "something is the case", or that "something is applicable". This makes it possible to analyze a distribution of statements for their truth-content, identify data patterns, make inferences and predictions, and model how processes operate. Petr Hájek claimed that "fuzzy logic is not just some "applied logic", but may bring "new light to classical logical problems", and therefore might be well classified as a distinct branch of "philosophical logic" similar to e.g. modal logics.
9791_20	Machinery and analytics Fuzzy logic offers computationally-oriented systems of concepts and methods, to formalize types of reasoning which are ordinarily approximate only, and not exact. In principle, this allows us to give a definite, precise answer to the question, "To what extent is something the case?", or, "To what extent is something applicable?". Via a series of switches, this kind of reasoning can be built into electronic devices. That was already happening before fuzzy logic was invented, but using fuzzy logic in modelling has become an important aid in design, which creates many new technical possibilities. Fuzzy reasoning (i.e., reasoning with graded concepts) turns out to have many practical uses. It is nowadays widely used in: The programming of vehicle and transport electronics, household appliances, video games, language filters, robotics, and driverless vehicles. Fuzzy logic washing machines are gaining popularity.
9791_21	All kinds of control systems that regulate access, traffic, movement, balance, conditions, temperature, pressure, routers etc. Electronic equipment used for pattern recognition, surveying and monitoring (including radars, satellites, alarm systems and surveillance systems). Cybernetics research, artificial intelligence, virtual intelligence, machine learning, database design and soft computing research. "Fuzzy risk scores" are used by project managers and portfolio managers to express financial risk assessments. Fuzzy logic has been applied to the problem of predicting cement strength.
9791_22	It looks like fuzzy logic will eventually be applied in almost every aspect of life, even if people are not aware of it, and in that sense fuzzy logic is an astonishingly successful invention. The scientific and engineering literature on the subject is constantly increasing. Community Originally lot of research on fuzzy logic was done by Japanese pioneers inventing new machinery, electronic equipment and appliances (see also Fuzzy control system). The idea became so popular in Japan, that the English word entered Japanese language (ファジィ概念). "Fuzzy theory" (ファジー理論) is a recognized field in Japanese scientific research.
9791_23	Since that time, the movement has spread worldwide; nearly every country nowadays has its own fuzzy systems association, although some are larger and more developed than others. In some cases, the local body is a branch of an international one. In other cases, the fuzzy systems program falls under artificial intelligence or soft computing. The main international body is the International Fuzzy Systems Association (IFSA). The Computational Intelligence Society of the Institute of Electrical and Electronics Engineers, Inc. (IEEE) has an international membership and deals with fuzzy logic, neural networks and evolutionary computing. It publishes the journal IEEE Transactions on Fuzzy Systems and holds international conferences. The conference on Fuzzy Systems and Data Mining (FSDM) chose Bangkok for its 4th international conference in November 2018.
9791_24	The interdisciplinary Japan Society for Fuzzy Theory and Intelligent Informatics (SOFT) traces its origin back to 1972 and publishes two journals. The original Korea Fuzzy System Society founded in 1991 is now known as the Korean Institute of Intelligent Systems (KIIS) to make it more inclusive. In mainland China, there is the Fuzzy Mathematics and Fuzzy systems Association of China, and there exists also an important Taiwan Fuzzy Systems Association. The North American Fuzzy Information Processing Society (NAFIPS) was founded in 1981. In Europe, there is a European Society for Fuzzy Logic and Technology (EUSFLAT) which includes the Working Group on Mathematical Fuzzy Logic.
9791_25	In 2002, the Iran Fuzzy Systems Society was approved as an affiliate of the Statistics Association of Iran, and in 2005 registered as a non-commercial scientific institute. When Lotfi A. Zadeh received an honorary doctorate from the University of Teheran on 9 March 2017, a member of Iran's parliament stated that Iran now ranks third in the world with regard to the output of scientific research about fuzzy systems. In 2005, Russia's Association for Fuzzy Systems (founded in January 1990) became the Russian Association for Fuzzy Systems and Soft Computing (RAFSSoftCom). Zadeh's seminal paper on fuzzy sets was translated into Russian in 1974, and from that time Russian fuzzy research began to take off - increasingly overcoming official skepticism. In 2009, the Brazilian Applied Mathematical Society (SBMAC) created the Thematic Committee on Fuzzy Systems which inspired the First Brazilian Congress on Fuzzy Systems (CBSF I) in 2010. CBSF IV was held in Campinas in 2016.
9791_26	In India, the Center for Soft Computing Research at the Indian Statistical Institute (Kolkata) organizes and publishes research on fuzzy sets, rough sets, and applications of fuzzy logic. The Sri Lanka Association for Artificial Intelligence is a non-profit scientific association devoted to understanding the mechanisms underlying thoughts and intelligent behaviour, and their emulation in machines. The Asia Pacific Neural Network Society, founded in 1993, has board members from 13 countries: Australia, China, Hong Kong, India, Japan, Malaysia, New Zealand, Singapore, South Korea, Qatar, Taiwan, Thailand, and Turkey.
9791_27	Achievements Lotfi A. Zadeh estimated around 2014 that there were more than 50,000 fuzzy logic–related, patented inventions. He listed 28 journals at that time dealing with fuzzy reasoning, and 21 journal titles on soft computing. His searches found close to 100,000 publications with the word "fuzzy" in their titles, but perhaps there are even 300,000. In March 2018, Google Scholar found 2,870,000 titles which included the word "fuzzy". When he died on 11 September 2017 at age 96, Professor Zadeh had received more than 50 engineering and academic awards, in recognition of his work. Lattices and big data sets The technique of fuzzy concept lattices is increasingly used in programming for the formatting, relating and analysis of fuzzy data sets.
9791_28	Concept formalization According to the computer scientist Andrei Popescu at Middlesex University London, a concept can be operationally defined to consist of: an intent, which is a description or specification stated in a language, an extent, which is the collection of all the objects to which the description refers, a context, which is stated by: (i) the universe of all possible objects within the scope of the concept, (ii) the universe of all possible attributes of objects, and (iii) the logical definition of the relation whereby an object possesses an attribute. Once the context is defined, we can specify relationships of sets of objects with sets of attributes which they do, or do not share.
9791_29	Fuzzy concept lattice Whether an object belongs to a concept, and whether an object does, or does not have an attribute, can often be a matter of degree. Thus, for example, "many attributes are fuzzy rather than crisp". To overcome this issue, a numerical value is assigned to each attribute along a scale, and the results are placed in a table which links each assigned object-value within the given range to a numerical value (a score) denoting a given degree of applicability.
9791_30	This is the basic idea of a "fuzzy concept lattice", which can also be graphed; different fuzzy concept lattices can be connected to each other as well (for example, in "fuzzy conceptual clustering" techniques used to group data, originally invented by Enrique H. Ruspini). Fuzzy concept lattices are a useful programming tool for the exploratory analysis of big data, for example in cases where sets of linked behavioural responses are broadly similar, but can nevertheless vary in important ways, within certain limits. It can help to find out what the structure and dimensions are, of a behaviour that occurs with an important but limited amount of variation in a large population. Sandwich example
9791_31	Big data Coding with fuzzy lattices can be useful, for instance, in the psephological analysis of big data about voter behaviour, where researchers want to explore the characteristics and associations involved in "somewhat vague" opinions; gradations in voter attitudes; and variability in voter behaviour (or personal characteristics) within a set of parameters. The basic programming techniques for this kind of fuzzy concept mapping and deep learning are by now well-established and big data analytics had a strong influence on the US elections of 2016. A US study concluded in 2015 that for 20% of undecided voters, Google's secret search algorithm had the power to change the way they voted.
9791_32	Very large quantities of data can now be explored using computers with fuzzy logic programming and open-source architectures such as Apache Hadoop, Apache Spark, and MongoDB. One author claimed in 2016 that it is now possible to obtain, link and analyze "400 data points" for each voter in a population, using Oracle systems (a "data point" is a number linked to one or more categories, which represents a characteristic).
9791_33	However, NBC News reported in 2016 that the Anglo-American firm Cambridge Analytica which profiled voters for Donald Trump (Steve Bannon was a board member) did not have 400, but 4,000 data points for each of 230 million US adults. Cambridge Analytica's own website claimed that "up to 5,000 data points" were collected for each of 220 million Americans, a data set of more than 1 trillion bits of formatted data. The Guardian later claimed that Cambridge Analytica in fact had, according to its own company information, "up to 7,000 data points" on 240 million American voters.
9791_34	Harvard University Professor Latanya Sweeney calculated, that if a U.S. company knows just your date of birth, your ZIP code and sex, the company has an 87% chance to identify you by name – simply by using linked data sets from various sources. With 4,000–7,000 data points instead of three, a very comprehensive personal profile becomes possible for almost every voter, and many behavioural patterns can be inferred by linking together different data sets. It also becomes possible to identify and measure gradations in personal characteristics which, in aggregate, have very large effects.
9791_35	Human judgement Some researchers argue that this kind of big data analysis has severe limitations, and that the analytical results can only be regarded as indicative, and not as definitive. This was confirmed by Kellyanne Conway, Donald Trump's campaign advisor and counselor, who emphasized the importance of human judgement and common sense in drawing conclusions from fuzzy data. Conway candidly admitted that much of her own research would "never see the light of day", because it was client confidential. Another Trump adviser criticized Conway, claiming that she "produces an analysis that buries every terrible number and highlights every positive number"
9791_36	Propaganda machine In a video interview published by The Guardian in March 2018, whistleblower Christopher Wylie called Cambridge Analytica a "full-service propaganda machine" rather than a bona fide data science company. Its own site revealed with "case studies" that it has been active in political campaigns in numerous different countries, influencing attitudes and opinions. Wylie explained, that "we spent a million dollars harvesting tens of millions of Facebook profiles, and those profiles were used as the basis of the algorithms that became the foundation of Cambridge Analytica itself. The company itself was founded on using Facebook data".
9791_37	Audit
9791_38	On 19 March 2018, Facebook announced it had hired the digital forensics firm Stroz Friedberg to conduct a "comprehensive audit" of Cambridge Analytica, while Facebook shares plummeted 7 percent overnight (erasing roughly $40 billion in market capitalization). Cambridge Analytica had not just used the profiles of Facebook users to compile data sets. According to Christopher Wylie's testimony, the company also harvested the data of each user's network of friends, leveraging the original data set. It then converted, combined and migrated its results into new data sets, which can in principle survive in some format, even if the original data sources are destroyed. It created and applied algorithms using data to which - critics argue - it could not have been entitled. This was denied by Cambridge Analytica, which stated on its website that it legitimately "uses data to change audience behavior" among customers and voters (who choose to view and provide information). If advertisers can do
9791_39	that, why not a data company? Where should the line be drawn? Legally, it remained a "fuzzy" area.
9791_40	Legal issue The tricky legal issue then became, what kind of data Cambridge Analytica (or any similar company) is actually allowed to have and keep. Facebook itself became the subject of another U.S. Federal Trade Commission inquiry, to establish whether Facebook violated the terms of a 2011 consent decree governing its handing of user data (data which was allegedly transferred to Cambridge Analytica without Facebook's and user's knowledge). Wired journalist Jessi Hempel commented in a CBNC panel discussion that "Now there is this fuzziness from the top of the company [i.e. Facebook] that I have never seen in the fifteen years that I have covered it."
9791_41	Data privacy Interrogating Facebook's CEO Mark Zuckerberg before the U.S. House Energy and Commerce Committee in April 2018, New Mexico Congressman Rep. Ben Ray Luján put it to him that the Facebook corporation might well have "29,000 data points" on each Facebook user. Zuckerberg claimed that he "did not really know". Lujan's figure was based on ProPublica research, which in fact suggested that Facebook may even have 52,000 data points for many Facebook users. When Zuckerberg replied to his critics, he stated that because the revolutionary technology of Facebook (with 2.2 billion users worldwide) had ventured into previously unknown territory, it was unavoidable that mistakes would be made, despite the best of intentions. He justified himself saying that:
9791_42	In July 2018, Facebook and Instagram barred access from Crimson Hexagon, a company that advises corporations and governments using one trillion scraped social media posts, which it mined and processed with artificial intelligence and image analysis.
9791_43	Integrity
9791_44	It remained "fuzzy" what was more important to Zuckerberg: making money from user's information, or real corporate integrity in the use of personal information. Zuckerberg implied, that he believed that, on balance, Facebook had done more good than harm, and that, if he had believed that wasn't the case, he would never have persevered with the business. Thus, "the good" was itself a fuzzy concept, because it was a matter of degree ("more good than bad"). He had to sell stuff, to keep the business growing. If people did not like Facebook, then they simply should not join it, or opt out, they have the choice. Many critics however feel that people really are in no position to make an informed choice, because they have no idea of how exactly their information will or might be used by third parties contracting with Facebook; because the company legally owns the information that users provide online, they have no control over that either, except to restrict themselves in what they write
9791_45	online (the same applies to many other online services).
9791_46	After the New York Times broke the news on 17 March 2018, that copies of the Facebook data set scraped by Cambridge Analytica could still be downloaded from the Internet, Facebook was severely criticized by government representatives. When questioned, Zuckerberg admitted that "In general we collect data on people who are not signed up for Facebook for security purposes" with the aim "to help prevent malicious actors from collecting public information from Facebook users, such as names". From 2018 onward, Facebook faced more and more lawsuits brought against the company, alleging data breaches, security breaches and misuse of personal information (see criticism of Facebook). There still exists no international regulatory framework for social network information, and it is often unclear what happens to the stored information, after a provider company closes down, or is taken over by another company.
9791_47	On 2 May 2018, it was reported that the Cambridge Analytica company was shutting down and was starting bankruptcy proceedings, after losing clients and facing escalating legal costs. The reputational damage which the company had suffered or caused, had become too great.
9791_48	Speed A traditional objection to big data is, that it cannot cope with rapid change: events move faster that the statistics can keep up with. Yet the technology now exists for corporations like Amazon, Google and Microsoft to pump cloud-based data streams from app-users straight into big data analytics programmes, in real time. Provided that the right kinds of analytical concepts are used, it is now technically possible to draw definite and important conclusions about gradations of human and natural behaviour using very large fuzzy data sets and fuzzy programming – and increasingly it can be done very fast. Obviously this achievement has become highly topical in military technology, but military uses can also have spin-offs for medical applications. Controversies There have been many academic controversies about the meaning, relevance and utility of fuzzy concepts. "Fuzzy" label Lotfi A. Zadeh himself confessed that:
9791_49	However, the impact of the invention of fuzzy reasoning went far beyond names and labels. When Zadeh gave his acceptance speech in Japan for the 1989 Honda Foundation prize, which he received for inventing fuzzy theory, he stated that "The concept of a fuzzy set has had an upsetting effect on the established order." Do they exist Some philosophers and scientists have claimed that in reality "fuzzy" concepts do not exist. Frege According to The Foundations of Arithmetic by the logician Gottlob Frege, Kálmán Similarly, Rudolf E. Kálmán stated in 1972 that "there is no such thing as a fuzzy concept... We do talk about fuzzy things but they are not scientific concepts". The suggestion is that a concept, to qualify as a concept, must always be clear and precise, without any fuzziness. A vague notion would be at best a prologue to formulating a concept.
9791_50	DIN and ISO standards There is no general agreement among philosophers and scientists about how the notion of a "concept" (and in particular, a scientific concept), should be defined. A concept could be defined as a mental representation, as a cognitive capacity, as an abstract object, etc. Edward E. Smith & Douglas L. Medin stated that “there will likely be no crucial experiments or analyses that will establish one view of concepts as correct and rule out all others irrevocably.” Of course, scientists also quite often do use imprecise analogies in their models to help understanding an issue. A concept can be clear enough, but not (or not sufficiently) precise.
9791_51	Rather uniquely, terminology scientists at the German national standards institute (Deutsches Institut für Normung) provided an official standard definition of what a concept is (under the terminology standards DIN 2330 of 1957, completely revised in 1974 and last revised in 2013; and DIN 2342 of 1986, last revised in 2011). According to the official German definition, a concept is a unit of thought which is created through abstraction for a set of objects, and which identifies shared (or related) characteristics of those objects.
9791_52	The subsequent ISO definition is very similar. Under the ISO 1087 terminology standard of the International Standards Organization (first published in October 2000, and reviewed in 2005), a concept is defined as a unit of thought or an idea constituted through abstraction on the basis of properties common to a set of objects. It is acknowledged that although a concept usually has one definition or one meaning, it may have multiple designations, terms of expression, symbolizations or representations. Thus, for example, the same concept can have different names in different languages. Both verbs and nouns can express concepts. A concept can also be thought of as "a way of looking at the world".
9791_53	Corruption Reasoning with fuzzy concepts is often viewed as a kind of "logical corruption" or scientific perversion because, it is claimed, fuzzy reasoning rarely reaches a definite "yes" or a definite "no". A clear, precise and logically rigorous conceptualization is no longer a necessary prerequisite, for carrying out a procedure, a project, or an inquiry, since "somewhat vague ideas" can always be accommodated, formalized and programmed with the aid of fuzzy expressions. The purist idea is, that either a rule applies, or it does not apply. When a rule is said to apply only "to some extent", then in truth the rule does not apply. Thus, a compromise with vagueness or indefiniteness is, on this view, effectively a compromise with error - an error of conceptualization, an error in the inferential system, or an error in physically carrying out a task.
9791_54	Kahan The computer scientist William Kahan argued in 1975 that "the danger of fuzzy theory is that it will encourage the sort of imprecise thinking that has brought us so much trouble." He said subsequently, According to Kahan, statements of a degree of probability are usually verifiable. There are standard tests one can do. By contrast, there is no conclusive procedure which can decide the validity of assigning particular fuzzy truth values to a data set in the first instance. It is just assumed that a model or program will work, "if" particular fuzzy values are accepted and used, perhaps based on some statistical comparisons or try-outs.
9791_55	Bad design In programming, a problem can usually be solved in several different ways, not just one way, but an important issue is, which solution works best in the short term, and in the long term. Kahan implies, that fuzzy solutions may create more problems in the long term, than they solve in the short term. For example, if one starts off designing a procedure, not with well thought-out, precise concepts, but rather by using fuzzy or approximate expressions which conveniently patch up (or compensate for) badly formulated ideas, the ultimate result could be a complicated, malformed mess, that does not achieve the intended goal.
9791_56	Had the reasoning and conceptualization been much sharper at the start, then the design of the procedure might have been much simpler, more efficient and effective - and fuzzy expressions or approximations would not be necessary, or required much less. Thus, by allowing the use of fuzzy or approximate expressions, one might actually foreclose more rigorous thinking about design, and one might build something that ultimately does not meet expectations. If (say) an entity X turns out to belong for 65% to category Y, and for 35% to category Z, how should X be allocated? One could plausibly decide to allocate X to Y, making a rule that, if an entity belongs for 65% or more to Y, it is to be treated as an instance of category Y, and never as an instance of category Z. One could, however, alternatively decide to change the definitions of the categorization system, to ensure that all entities such as X fall 100% in one category only.
9791_57	This kind of argument claims, that boundary problems can be resolved (or vastly reduced) simply by using better categorization or conceptualization methods. If we treat X "as if" it belongs 100% to Y, while in truth it only belongs 65% to Y, then arguably we are really misrepresenting things. If we keep doing that with a lot of related variables, we can greatly distort the true situation, and make it look like something that it isn't. In a "fuzzy permissive" environment, it might become far too easy, to formalize and use a concept which is itself badly defined, and which could have been defined much better. In that environment, there is always a quantitative way out, for concepts that do not quite fit, or which don't quite do the job for which they are intended. The cumulative adverse effect of the discrepancies might, in the end, be much larger than ever anticipated.
9791_58	Counter-argument A typical reply to Kahan's objections is, that fuzzy reasoning never "rules out" ordinary binary logic, but instead presupposes ordinary true-or-false logic. Lotfi Zadeh stated that "fuzzy logic is not fuzzy. In large measure, fuzzy logic is precise." It is a precise logic of imprecision. Fuzzy logic is not a replacement of, or substitute for ordinary logic, but an enhancement of it, with many practical uses. Fuzzy thinking does oblige action, but primarily in response to a change in quantitative gradation, not in response to a contradiction.
9791_59	One could say, for example, that ultimately one is either "alive" or "dead", which is perfectly true. Meantime though one is "living", which is also a significant truth - yet "living" is a fuzzy concept. It is true that fuzzy logic by itself usually cannot eliminate inadequate conceptualization or bad design. Yet it can at least make explicit, what exactly the variations are in the applicability of a concept which has unsharp boundaries. If one always had perfectly crisp concepts available, perhaps no fuzzy expressions would be necessary. In reality though, one often does not have all the crisp concepts to start off with. One might not have them yet for a long time, or ever - or, several successive "fuzzy" approximations might be needed, to get there.
9791_60	At a deeper level, a "fuzzy permissive" environment may be desirable, precisely because it permits things to be actioned, that would never have been achieved, if there had been crystal clarity about all the consequences from the start, or if people insisted on absolute precision prior to doing anything. Scientists often try things out on the basis of "hunches", and processes like serendipity can play a role.
9791_61	Learning something new, or trying to create something new, is rarely a completely formal-logical or linear process, there are not only "knowns" and "unknowns" involved, but also "partly known" phenomena, i.e. things which are known or unknown "to some degree". Even if, ideally, we would prefer to eliminate fuzzy ideas, we might need them initially to get there, further down the track. Any method of reasoning is a tool. If its application has bad results, it is not the tool itself that is to blame, but its inappropriate use. It would be better to educate people in the best use of the tool, if necessary with appropriate authorization, than to ban the tool pre-emptively, on the ground that it "could" or "might" be abused. Exceptions to this rule would include things like computer viruses and illegal weapons that can only cause great harm if they are used. There is no evidence though that fuzzy concepts as a species are intrinsically harmful, even if some bad concepts can cause harm if
9791_62	used in inappropriate contexts.

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