Computing with words for multi-objective linguistic optimization problems

Abstract

Linguistic information is encountered frequently in the real-life situations, especially those involving human beings. The linguistic information is vague and imprecise; however, human beings compute seamlessly using it. Use of linguistic information inevitably requires the use of computing with words (CWW) methodology for its processing, in a manner similar to a computer. In a number of recent works, it was shown that the CWW approach of perceptual computing (Per-C) is better at processing the linguistic information and generation of unique recommendations, in comparison to other CWW approaches. Furthermore, in another work, a formulation of Per-C was used to propose a novel solution methodology for the multi-objective linguistic optimization problems (MOLOPs), where a novel design of Per-C’s CWW engine was used called the perceptual reasoning (PR). In this PR based solution methodology for MOLOPs, the codebook was generated using the process of data collection. However, we fell that there can be scenarios, where it is not possible to collect the data for construction of the codebook. Therefore, in this paper, we propose to use the linguistic terms with symmetric membership functions and distributed uniformly on the information representation scale for such scenarios. Furthermore, the uniqueness of this work is that only the middle term’s location from the linguistic term set needs to be established initially. Other linguistic terms are generated using the various operations of the linguistic hedges. We have also demonstrated the applicability of the PR based solution methodology for MOLOPs (based on symmetric term sets), to the case study of pollution routing problem, modeled as a MOLOP.