Likert-Type Fuzzy Uncertainty From A Traditional Decision Making Viewpoint: How Symmetry Helps Explain Human Decision Making (Including Seemingly Irrational Behavior)

Authors

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

Publication Date

10-2014

Comments

Technical Report: UTEP-CS-14-48a

Published in Applied and Computational Mathematics, 2014, Vol. 13, No. 3, pp. 275-298.

Abstract

One of the main methods for eliciting the values of the membership function μ(x) is to use the Likert-type 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, and we conclude 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). We also show how symmetry helps explain human decision making, including seemingly irrational behavior.