Author :
Harding, John ; Walker, Carol ; Walker, Elbert
Author_Institution :
Dept. of Math. Sci., New Mexico State Univ., Las Cruces, NM, USA
Abstract :
This paper is a study of a variety of algebras that arise in the investigation of the truth value algebra of type-2 fuzzy sets. The variety generated by the truth value algebra of type-2 fuzzy sets with only its two semilattice operations in its type is generated by a four-element algebra that has a particularly simple form, which we call a bichain. Our initial goal is to understand the equational properties of this particular bichain, and thus of the truth value algebra of type-2 fuzzy sets. We outline the progress on this goal, and then concentrate on some results on our study of bichains in general.
Keywords :
algebra; fuzzy set theory; bichains; four-element algebra; truth value algebra; type-2 fuzzy sets; Equations; Fuzzy logic; Fuzzy sets; Generators; Lattices; System-on-a-chip;
Conference_Titel :
Fuzzy Information Processing Society (NAFIPS), 2011 Annual Meeting of the North American
Conference_Location :
El Paso, TX
Print_ISBN :
978-1-61284-968-3
Electronic_ISBN :
Pending
DOI :
10.1109/NAFIPS.2011.5752043
