In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.

As mentioned in the Introduction, it has the following goals: to develop the main topics of revealed preference theory (rationality, revealed preference, congruence, consistency) for a large class of fuzzy choice functions, to explore new topics (degree of dominance, similarity, indicators of rationality) specific to a fuzzy approach to choice functions and to show the manner in which some prob...

To a fuzzy choice function C we assign the indicators of revealed preference WAFRP (C), SAFRP (C) and the indicators of congruence WFCA(C), SFCA(C). These indicators measure the degree to which the fuzzy choice function C verifies the axioms of revealed preference WAFRP , SAFRP and of congruenceWFCA and SFCA, respectively.

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) ...

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule 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...

We develop the commutator theory for fuzzy congruence relations of general universal algebras. In particular, algebras in modular varieties, we characterize congruences using Day’s terms.

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...

In this paper we study relations which are congruences with respect to ∧ and ⊔p, where ⊔pis the p-cut of the L-fuzzy hyperoperation ⊔. The main idea is to start from an equivalence relation R1 which is a congruence with respect to ∧ and ⊔1and, for each p ∈ X , construct an equivalence relation Rp which is a congruence with respect to ∧ and ⊔p. Furthermore, for each x ∈ Rp we construct a quotien...

In this paper, we establish the idea of fuzzy congruences on Abel-Grassmann's group (AG-group). We investigate different outcomes fuzzy-congruences AG-groups in detail and give some examples to illustrate newly established results. develop relation between congruence normal subgroup. end, also provide results homomorphism AG-groups.

Starting with the underlying motivation of developing a general theory of L-fuzzy sets where L is a multilattice (a particular case of non-deterministic algebra), we study the relationship between the crisp notions of congruence, homomorphism and substructure on some non-deterministic algebras which have been used in the literature, i.e. hypergroups, and join spaces. Moreover, we provide suitab...