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...

Fuzzy control has achieved numerous successful industrial applications. However, stability analysis for fuzzy control systems remains a difficult problem, and most of the critical comments on fuzzy control are due to the lack of a general method for its stability analysis. Although significant research efforts have been made in the literature, appropriate tools for this issue have yet to be fou...

On the basis of the concept of interval valued intuitionistic fuzzy set introduced by K. Atanassov [3], the notion of interval valued intuitionistic fuzzy subsemigroup (ideal, bi-ideal, (1, 2)-ideal) of a semigroup 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 o...

We consider the monoid T with the presentation 〈a, b; aab = aba〉 which is “close” to trace monoids. We prove two different types of results. First, we give a combinatorial description of the lexicographically minimum and maximum representatives of their congruence classes in the free monoid {a, b}∗ and solve the classical equations, such as commutation and conjugacy in T. Then we study the clos...

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems proved by authors in 2017. In this study, homomorphism between algebras is defined, function examined then congruence relations are defined algebra. First third isomorphism introduced.

The purpose of this note is to show that O. Ore's general formulation of the Jordan-Holder theorems in partially ordered sets [3] yields the Jordan-Holder theorems for loops [ l ] which have recently been obtained by A. A. Albert [2]. We shall assume that the reader is familiar with the papers [l, 2, 3] of O. Ore and of A. A. Albert. We begin with an examination of certain congruence relations ...

In this paper we develop the method of diagrams for fuzzy predicate logics and give a characterization of different kinds of preserving mappings in terms of diagrams. Our work is a contribution to the modeltheoretic study of equality-free fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts bei...

We clarify the explicit structure of the Hurwitz quaternion order, which is of fundamental importance in Riemann surface theory and systolic geometry. We present some properties of the associated congruence subgroups. Namely, we show that a Hurwitz group defined by a congruence subgroup associated with an odd ideal, is necessarily defined by a principal congruence subgroup. All such Hurwitz gro...