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...

The association between hyperstructures and binary relations had been intensively studied 5,6,10,11,2,4,20 . Chvalina 5,6 and Hort 2 use ordered structures for the construction of semigroups and hypergroups. Rosenberg 4 associated with any binary relation of full domain, a hypergroupoid and found conditions on , such that is a hypergroup. Corsini and Leoreanu 16 study hypergroups and binary rel...

The congruence subgroups of the classical modular group which can be defined as the automorphs modulo q of some fixed matrix are studied, and their genera determined. Let T = SL{2, Z). A congruence subgroup of T is any subgroup containing a principal congruence subgroup T^), defined as the set of elements A of T such that A = I mod q, where q is a positive integer. Of these one of the most impo...

A unifying approach is presented between similarity, consimilarity, T congruence and *congruence of a matrix A to a symmetric, to a Hermitian or to a real matrix. Also studied are similarity consimilarity, T congruence and *congruence of a matrix A to A∗, AT , and A. Attempts are made to find special (con)similarities and congruences, as well as to find connections between these classes of maps...