Perceptual reasoning based solution methodology for linguistic
  optimization problems
  Decision making in real-life scenarios may often be modeled as an
optimization problem. It requires the consideration of various attributes like
human preferences and thinking, which constrain achieving the optimal value of
the problem objectives. The value of the objectives may be maximized or
minimized, depending on the situation. Numerous times, the values of these
problem parameters are in linguistic form, as human beings naturally understand
and express themselves using words. These problems are therefore termed as
linguistic optimization problems (LOPs), and are of two types, namely single
objective linguistic optimization problems (SOLOPs) and multi-objective
linguistic optimization problems (MOLOPs). In these LOPs, the value of the
objective function(s) may not be known at all points of the decision space, and
therefore, the objective function(s) as well as problem constraints are linked
by the if-then rules. Tsukamoto inference method has been used to solve these
LOPs; however, it suffers from drawbacks. As, the use of linguistic information
inevitably calls for the utilization of computing with words (CWW), and
therefore, 2-tuple linguistic model based solution methodologies were proposed
for LOPs. However, we found that 2-tuple linguistic model based solution
methodologies represent the semantics of the linguistic information using a
combination of type-1 fuzzy sets and ordinal term sets. As, the semantics of
linguistic information are best modeled using the interval type-2 fuzzy sets,
hence we propose solution methodologies for LOPs based on CWW approach of
perceptual computing, in this paper. The perceptual computing based solution
methodologies use a novel design of CWW engine, called the perceptual reasoning
(PR). PR in the current form is suitable for solving SOLOPs and, hence, we have
also extended it to the MOLOPs.
