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How to Take All Available Information into Account in Fuzzy Decision Making: Beyond Traditional "And" - and "Or" - Operations

In the traditional fuzzy logic, we can use “and”-operations (also known as t-norms) to estimate the expert’s degree of confidence in a composite statement A & B based on his/her degrees of confidence d ( A ) and d ( B ) in the corresponding basic statements A and B . But what if we want to estimate the degree of confidence in A & B & C in situations when, in addition to the degrees of estimate d ( A ) , d ( B ) , and d ( C ) of the basic statements, we also know the expert’s degrees of confidence in the pairs d ( A & B ) , d ( A & C ) , and d ( B & C ) ? Traditional “and”-operations can provide such an estimate – but only by ignoring some of the available information. In this paper, we show that, by going beyond the traditional “and”- and “or”-operations, we can find a natural estimate that takes all available information into account – and thus, hopefully, leads to a more accurate estimate.