Likert-Scale Fuzzy Uncertainty from a Traditional Decision Making Viewpoint: It Incorporates Both Subjective Probabilities and Utility Information

Authors

Joe Lorkowski, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

3-2013

Comments

Technical Report: UTEP-CS-13-11a

To appear in Proceedings of the joint World Congress of the International Fuzzy Systems Association and Annual Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS'2013, Edmonton, Canada, June 24-28, 2013.

Abstract

One of the main methods for eliciting the values of the membership function μ(x) is to use the Likert scales, i.e., to ask the user to mark his or her degree of certainty by an appropriate mark k on a scale from 0 to n and take μ(x)=k/n. In this paper, we show how to describe this process in terms of the traditional decision making. Our conclusion is that the resulting membership degrees incorporate both probability and utility information. It is therefore not surprising that fuzzy techniques often work better than probabilistic techniques -- which only take into account the probability of different outcomes.