Linguistic optimization problems: solution methodology using perceptual reasoning

Abstract

A number of real-life scenarios involving decision making may be modelled as optimization problems. In these optimization problems, the human preferences and thinking constrain achieving the optimal value of the problem objective(s). If there is a single objective, then the optimization problems are called single objective optimization problems (SOOPs) else the multi-objective optimization problems (MOOPs). Various solution methodologies have been proposed for SOOPs and MOOPs, which are useful, as long as the SOOPs and MOOPs involve the numeric data. However, the data is generally in linguistic form (or words), when elicited by the human beings. Therefore, the SOOPs and MOOPs are referred as single objective linguistic optimization problems (SOLOPs) and multiobjective linguistic optimization problems (MOLOPs), respectively, in such situations, to emphasize the existence of linguistic information in optimization problems. 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 through if- then rules. Previously, the Tsukamoto’s inference method was used to solve these types of LOPs; however, it suffers from drawbacks. As, the use of linguistic information inevitably calls for the utilization of computing with words (CWW), hence, in this paper, we discuss the solution methodologies for LOPs based on the perceptual reasoning (PR). PR is a novel CWW engine design for the CWW approach of perceptual computing. We also demonstrate the applicability of PR based solution methodology for LOPs to the case study of car purchase modelled as LOP.