Quantification of qualitative assessments using computing with words: In framework of fuzzy set theory

Abstract

When qualitative data are collected, which is a widespread situation encountered in several disciplines ranging from social sciences to decision making to engineering as a result of dealing with ill-defined concepts or with complex tasks to assess, there is a certain need to crunch them and infer from them. Hence, quantification, namely computing with words (CW), emerges as a research area. Even though social science disciplines deal with these types of data numerically using various Likert scales, fuzzy set theory first proposed by Zadeh dealing words or sentences with mathematically oriented manner in order to create machines that mimic the reasoning of human being brings new perspectives. Since then, its applicability has expanded into various disciplines for different purposes to transform subjectivity into objectivity. In this manuscript, the effort of transformation from subjectivity into objectivity will be reviewed based on the available proposed methods in the literature. Two illustrative examples will be employed. While the first illustrative example, which consists of balanced and unbalanced linguistic term sets, is used for each reviewed method in the literature to show its computations step by step, the second of which, balanced linguistic term set, is an example used in the literature that is employed. Therefore, a comprehensive review of the proposed methods with illustrative examples is presented.