We introduce the concepts of pre-implication algebra and implication algebra based on orthosemilattices which generalize the concepts of implication algebra, orthoimplication algebra defined by J.C. Abbott [2] and orthomodular implication algebra introduced by the author with his collaborators. For our algebras we get new axiom systems compatible with that of an implication algebra. This unifie...

This paper aims to introduce fuzzy congruence relations over Heyting algebras (HA) and give constructions of quotient Heyting algebras induced by fuzzy congruence relations on HA. The Fuzzy First, Second and Third Isomorphism Theorems of HA are established. MSC: 06D20, 06D72, 06D75.

In this work we introduce the notion of fuzzy congruence relation on an ndgroupoid and study conditions on the nd-groupoid which guarantee a complete lattice structure on the set of fuzzy congruence relations. The study of these conditions allowed to construct a counterexample to the statement that the set of fuzzy congruences on a hypergroupoid is a complete lattice.

The AGM postulates [4], [1] are widely regarded to have captured much of what is involved in the process of rational belief revision. Recently however, Parikh [7] observed that despite their success, the AGM postulates are rather liberal in their treatment of the notion of relevance. More precisely, Parikh argues that during belief revision a rational agent does not change her entire belief cor...

EQ-algebras introduced by Novák are algebras of truth values for a higher-order fuzzy logic (fuzzy type theory). In this paper, the compatibility of multiplication w.r.t. the fuzzy equality in an arbitrary EQ-algebra is examined. Particularly, an example indicates that the compatibility axiom does not always hold, and then a class of EQ-algebras satisfying the compatibility axiom is characteriz...

In this paper, the notion of an interval valued intuitionistic fuzzy subsemiring (ideal) of a semiring with respect to t−norm T and s−norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on semirings, new interval valued intuitionistic (S, T )−fuzzy subsemirings (ideals) ...

The Arrow index of a fuzzy choice function C is a measure of the degree to which C satisfies the Fuzzy Arrow Axiom, a fuzzy version of the classical Arrow Axiom. The main result of this paper shows that A(C) characterizes the degree to which C is full rational. We also obtain a method for computing A(C). The Arrow index allows to rank the fuzzy choice functions with respect to their rationality...