In this paper we investigate some properties of congruences on ternary semigroups. We also define the notion of congruence on a ternary semigroup generated by a relation and we determine the method of obtaining a congruence on a ternary semigroup T from a relation R on T. Furthermore we study the lattice of congruences on a ternary semigroup and we show that this lattice is not generally modular...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

We introduce the concept of interval-valued fuzzy congruences on a semigroup S and we obtain some important results: First, for any interval-valued fuzzy congruence R on a group G, the interval-valued congruence class Re is an interval-valued fuzzy normal subgroup of G. Second, for any interval-valued fuzzy congruence R on a groupoid S, we show that a binary operation ∗ an S/R is well-defined a...

Revealed preference theory was initiated by Samuelson [8] as a way of defining the rational behaviour of a consumer in terms of a preference relation associated with a demand function. This topic has been axiomatically treated by Arrow (1959), Richter (1966), Sen (1971) and many others. Papers Banerjee (1995), Georgescu (2004; 2005) attempt at developing a theory of revealed preference for fuzz...

BL-algebras have been invented by P. Hájek [3] in order to provide an algebraic proof of the completeness theorem of “Basic Logic” (BL, for short) arising from the continuous triangular norms, familiar in the fuzzy logic framework. The above notion is generalized to an algebraic system in which the required conditions are fulfilled (Definition 2.1). Filters in BL-algebras are also defined. A fi...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

Abstract Fuzzy set (FS) theory and rough sets (RSs) are constructed to accommodate the data uncertainty. In contrast, bipolar FS (BFS) can tackle uncertainty bipolarity of in different circumstances. This article aims introduce idea fuzzy ideals semigroup (SG), which is a generalization concept BFSs (RBFSs) an SG. We also investigate roughness subsemigroup (BF-SSG) with help congruence relation...

This paper deenes a congruence relation on Gamma programs. Based on this congruence relation, laws for transforming programs are derived. We deene an axiomatic semantics for Gamma based on Brookes' transition assertions. The deenition of the congruence is in terms of provable satissability of such assertions. We consider the relationship between our congruence and other orderings that have been...

The definition of open bisimilarity on the χ-processes does not give rise to a sensible relation on the χ-processes with the mismatch operator. The paper proposes ground open congruence as a principal open congruence on the χ-processes with the mismatch operator. The algebraic properties of the ground congruence is studied. The paper also takes a close look at barbed congruence. This relation i...