In Alsina et al. Derivation of Min-Max Fuzzy Logic from Distributivity, All Conditions Are Necessary: A Proof

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Ildar Batyrshin, Instituto Politecnico Nacional, MexicoFollow
Nailya Kubysheva, Kazan Federal University

Publication Date

7-2019

Comments

Technical Report: UTEP-CS-19-79

Abstract

In their 1983 paper, C. Alsina, E. Trillas, and L. Valverde proved that distributivity, monotonicity, and boundary conditions imply that the "and"-operation is min and the "or"-operation is max. In this paper, we show that all these conditions are necessary for Alsina et al. result to be true.