Fuzzified Likert Scales in Group Multiple-Criteria Evaluation

Likert scales have been in use since 1930s as tool for attitude expression in many fields of social science. Recently there have even been several attempts for the fuzzification of this instrument. In this chapter we explore the possibility of their use in multiple-criteria multi-expert evaluation. We focus on discrete fuzzy Likert scales, that are a generalization of the standard Likert scales. We propose a methodology that deals with the non-uniformity of the distribution of linguistic labels along the underlying ordinal evaluation scale and also with possible response bias. We also consider the analogy of Likert scales (crisp and fuzzy) on continuous universes. Likert-type evaluations of an alternative with respect to various criteria are represented using histograms. Histograms are also used to aggregate the Likert-type evaluations. A transformation of the multi-expert multiple-criteria evaluation represented by a histogram into a 3-bin histogram to control for the response bias is performed and an ideal-evaluation 3-bin histogram is defined. We propose a distance measure to assess the closeness of the overall evaluation to the ideal and suggest the use of the proposed methodology in multiple-criteria multi-expert evaluation.