in this paper the class of n-ary hypergroups is introduced and several properties are found andexamples are presented. n-ary hypergroups are a generalization of hypergroups in the sense of marty. on theother hand, we can consider n-ary hypergroups as a good generalization of n-ary groups. we define thefundamental relation β* on an n-ary hypergroup h as the smallest equivalence relation such tha...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

The concept of algebraic hyperstructures introduced by Marty as a generalization of ordinary algebraic structures. In an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. The concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper‌rings and a generalizat...

The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introdu...

in this paper, we define the concepts of a complex fuzzy subset and a complex fuzzy finite state automaton. then we extend the notion of a complex fuzzy finite state automaton and introduce the notion of a general complex fuzzy automaton. after that we define the concept of a max- min general complex fuzzy automaton and construct some equivalence relations and some congruence relations in a max...

in a recent paper, de baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. in this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. the reasoninglargely ...

the main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. in this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

The main goal of the present paper is to extend classical results from the measure theory and dynamical systems to the fuzzy subset setting. In this paper, the notion of  dynamic equivalence relation is introduced and then it is proved that this relation is an equivalence relation. Also, a new metric on the collection of all equivalence classes is introduced and it is proved that this metric is...

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...

The main tools in the theory of n-ary hyperstructures are the fundamental relations. The fundamental relation on an n-ary hypersemigroup is defined as the smallest equivalence relation so that the quotient would be the n-ary semigroup. In this paper we study neutral elements in n-ary hypersemigroups and introduce a new strongly compatible equivalence relation on an n-ary hypersemigroup so that ...