The variety generated by the truth value algebra of type-2 fuzzy sets

Authors:
John Harding;Carol Walker;Elbert Walker
Affiliations:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA;Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA;Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA
Venue:
Fuzzy Sets and Systems
Year:
2010

Citing 7
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Abstract

This paper addresses some questions about the variety generated by the algebra of truth values of type-2 fuzzy sets. Its principal result is that this variety is generated by a finite algebra, and in particular is locally finite. This provides an algorithm for determining when an equation holds in this variety. It also sheds light on the question of determining an equational axiomatization of this variety, although this problem remains open.