Towards Efficient Algorithms for Approximating a Fuzzy Relation by Fuzzy Rules: Case When "And"- and "Or"-Operation are Distributive

Authors

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

Publication Date

5-2014

Comments

Technical Report: UTEP-CS-14-25a

Published in Proceedings of the 2014 Annual Conference of the North American Fuzzy Information Processing Society NAFIPS'2014, Boston, Massachusetts, June 24-26, 2014.

Abstract

A generic fuzzy relation often requires too many parameters to represent -- especially when we have a relation between many different quantities x1, ..., xn. There is, however, a class of relations which require much fewer parameters to describe - namely, relations which come from fuzzy rules. It is therefore reasonable to approximate a given relation by fuzzy rules. In this paper, we explain how this can be done in an important case when "and"- and "or"-operation are distributive -- and we also explain why this case is important.