In Fuzzy Decision Making, General Fuzzy Sets Can Be Replaced by Fuzzy Numbers

Authors

Christian Servin, El Paso Community CollegeFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

3-2017

Comments

Technical Report: UTEP-CS-17-12a

To appear in Journal of Uncertain Systems

Abstract

In many real decision situations, for each of the alternatives, we only have fuzzy information about the consequences of each action. This fuzzy information can be described by a fuzzy number, i.e., by a membership function with a single local maximum, or it can be described by a more complex fuzzy set, with several local maxima. We show that, from the viewpoint of decision making, it is sufficient to consider only fuzzy numbers. To be more precise, the decisions will be the same if we replace each original fuzzy set with the smallest fuzzy number of all fuzzy numbers of which the original fuzzy set is a subset.