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Decision making in real-life scenarios may often be modeled as anoptimization problem. It requires the consideration of various attributes likehuman preferences and thinking, which constrain achieving the optimal value ofthe problem objectives. The value of the objectives may be maximized orminimized, depending on the situation. Numerous times, the values of theseproblem parameters are in linguistic form, as human beings naturally understandand express themselves using words. These problems are therefore termed aslinguistic optimization problems (LOPs), and are of two types, namely singleobjective linguistic optimization problems (SOLOPs) and multi-objectivelinguistic optimization problems (MOLOPs). In these LOPs, the value of theobjective function(s) may not be known at all points of the decision space, andtherefore, the objective function(s) as well as problem constraints are linkedby the if-then rules. Tsukamoto inference method has been used to solve theseLOPs; however, it suffers from drawbacks. As, the use of linguistic informationinevitably calls for the utilization of computing with words (CWW), andtherefore, 2-tuple linguistic model based solution methodologies were proposedfor LOPs. However, we found that 2-tuple linguistic model based solutionmethodologies represent the semantics of the linguistic information using acombination of type-1 fuzzy sets and ordinal term sets. As, the semantics oflinguistic information are best modeled using the interval type-2 fuzzy sets,hence we propose solution methodologies for LOPs based on CWW approach ofperceptual computing, in this paper. The perceptual computing based solutionmethodologies 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 havealso extended it to the MOLOPs.

Perceptual reasoning based solution methodology for linguistic optimization problems