Tense Operators on BL-algebras and Their Applications

Abstract

In this paper, the notions of tense operators and tense filters in BL-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense BL-algebras, tense MV-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a BL-algebra is complete sublattice of F(L) of all filters of BL-algebra L. Also, maximal tense filters and simple tense BL-algebras and the relation between them are studied. Finally, the notions of tense congruence relations in tense BL-algebras and strict tense BL-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided.

Keywords

• (simple) tense bl-algebra
• tense operators
• tense filter
• tense congruence