Ternary Semigroups Research Articles

On Relations between Some Types of (α,β)-Intuitionistic Fuzzy Ideals of Ternary Semigroups

On Relations between Some Types of (α,β)-Intuitionistic Fuzzy Ideals of Ternary Semigroups

Ternary semigroups of topological transformations

A ternary semigroup is a nonempty set with a ternary operation which is associative. The purpose of the present paper is to give a characterization of open sets of finite-dimensional Euclidean spaces by ternary semigroups of pairs of homeomorphic transformations and extend to ternary semigroups certain results of L.M. Gluskin concerned with semigroups of homeomorphic transformations of finite-dimensional Euclidean spaces.

A New Generalization of Hesitant and Interval-Valued Fuzzy Ideals of Ternary Semigroups

A New Generalization of Hesitant and Interval-Valued Fuzzy Ideals of Ternary Semigroups

Characterizations of Some Regularities in Ordered Ternary Semigroups in Terms of Fuzzy Subsets

Characterizations of some classes of ordered ternary semigroups; left (resp., right) lightly regular and generalized regular are given in terms of fuzzy left ideals, fuzzy right ideals, fuzzy lateral ideals, and fuzzy ideals of ordered ternary semigroups.

Soft ideals of soft ternary semigroups

In this paper, we introduce the notions of certain classes of soft ideals in soft ternary semigroups and study some inter-relations between different types of soft ideals in a soft ternary semigroup. We also characterize completely regular soft ternary semigroups with the help of these soft ideals of soft ternary semigroups.

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Let n be a fixed natural number. Menger algebras of rank n, which was introduced by Menger, K., can be regarded as the suitable generalization of arbitrary semigroups. Based on this knowledge, an interesting question arises: what a generalization of ternary semigroups is. In this article, we first introduce the notion of ternary Menger algebras of rank n, which is a canonical generalization of arbitrary ternary semigroups, and discuss their related properties. In the second part, we establish the so-called a diagonal ternary semigroup which its operation is induced by the operation on ternary Menger algebras of rank n and then investigate their interesting properties. Moreover, we introduce the concept of homomorphism and congruences on ternary Menger algebras of rank n. These lead us to study the quotient ternary Menger algebras of rank n and to investigate the homomorphism theorem for ternary Menger algebra of rank n with respect to congruences. Furthermore, the characterization of reduction of ternary Menger algebra into Menger algebra is presented.

Bir üçlü monoidin Bruck-Reilly genişlemesi

In this study, Bruck-Reilly extension of a ternary monoid is defined. Additionally, some results about this construction are given which belongs to one of the classes of ternary semigroups; regular, inverse, orthodox and strongly regular.

Classifications and Properties of (α, β)-Fuzzy Ideals in Ternary Semigroups

Classifications of (α, β)-fuzzy left (right and lateral) ideals of ternary semigroup s are discussed. Relations between (2,2 _ q)-fuzzy left (right and lateral) ideals and (q,2_ q)-fuzzy left (right and lateral) ideals are established. Giv en special sets, so called t-q-set and t-2_ q-set, conditions for the t-q-set and t-2_ q-set to be left (right and lateral) ideals are considered. Co nditions for a fuzzy set to be an (2, q)-fuzzy left (right and lateral) ideals, a (q,2)-fuzzy left (right and lateral)ideals and a (q,2_ q)-fuzzy left (right and lateral) ideals are considered. Some new characterizations of weakly regular ternary semigroups are also established. Finally, the implication-based fuzzy ideals are discussed.

A New Generalization of Fuzzy Ideals of Ternary Semigroups

A New Generalization of Fuzzy Ideals of Ternary Semigroups

On Interval-Valued Fuzzy Soft Set Theory Applied To Ternary Semigroups

In this paper, we focus on combining the theories of interval-valued fuzzy soft sets over ternary semigroups, and establishing a new framework for interval-valued fuzzy soft ternary semigroups. The aim of this manuscript is to apply interval-valued fuzzy soft set for dealing with several kinds of theories in ternary semigroups. First, we present the concepts of interval-valued fuzzy soft sets, interval-valued fuzzy soft ternary semigroups and interval-valued fuzzy soft ideals. Meanwhile, some illustrative examples are given to show the rationality of the definitions introduced in this paper. Second, several new kinds of generalized fuzzy soft sets over ternary semigroups are proposed, and related properties and mutual relationships are also investigated. Finally, our goal is to establish a relation between different types of ternary subsemigroups (left ideal, right ideal, lateral ideal, two-sided ideal, ideal) of a ternary semigroup and interval-valued fuzzy soft subsemigroups (interval-valued fuzzy soft left ideal, interval-valued fuzzy soft right ideal, interval-valued fuzzy soft lateral ideal, interval-valued fuzzy soft two-sided ideal, interval-valued fuzzy soft two-sided ideal) over a ternary semigroup and also characterize these notions in terms of soft sets in ternary semigroups.

A Note on le-Ternary Semigroups

Petraq Petro, Kostaq Hila, and Jani Dine given several properties in le- Γ - semigroups and especially in every Q-class satisfying the Green’s condition. Rabah Kellil studied Green's Relations on Ternary Semigroups in 2013 and Parinyawat Choosuwa, Ronnason Chinram the notion of the quasi-ideals in ternary semigroups. In this paper we study that the characterizations of le–ternary semigroups and In particular we proved that the quasi-ideal element q of an le–ternary semigroup T has the intersection property if and only if q = l(q) ∧ m(q) ∧ r(q)

M-ideals and its generators of ternary semigroups

The purpose of this paper is to introduce some new classes of m-bi ideals and m-quasi ideals in ternary semigroups and give some characterizations in terms of bi ideals and quasi ideals. Let U1 be the m-bi ideal of T and U2 be the m-bi ideal of U1 such that U3 2 = U2, shown that U2 is a m-bi ideal of T. Let U1, U2 and U3 be the three ternary subsemigroups of T, it has been shown that U1U2U3 is a t-bi ideal if at least one of U1, U2, U3 is l-RI or m-LATI or n-LI of T. Also we discuss m-bi ideal generated by B is < B > sub>m= B ∪ P finite

Some characterizations of ternary semigroups by bi-ideals

Some characterizations of ternary semigroups by bi-ideals

INTUITIONISTIC FUZZY IDEALS AND INTUITIONISTIC FUZZY FILTERS OF TERNARY SEMIGROUPS

In this paper, we consider the intuitionistic fuzzification of ternary sub semigroups (left ideals, right ideals, lateral ideals, ideals) and intuitionistic fuzzification of left filters (right filters, lateral filters, filters) of ternary semigroups and investigate some of their basic properties.

A Note on Ideals and Regularity in Ternary Semigroups

A Note on Ideals and Regularity in Ternary Semigroups

Green’s relations on ternary semihypergroups and crossed hyperproduct of hypergroups

In this paper, we introduce all Green’s relations on the ternary semihypergroup and study some properties of these equivalence relations in view of those obtained in binary and ternary semigroups. We also define crossed hyperproduct of two hypergroups.

Stuctures of Ternary Semigroup of Mappings

We first consider the ternary semigroup of mappings between two nonempty sets $$X$$ and $$Y$$ , that is $$T[X,Y]$$ . Then we characterize different types of elements in $$T[X,Y]$$ . In particular, we provide some necessary and sufficient conditions for an element of $$T[X,Y]$$ to become a left regular, a right regular, a completely regular and an idempotent element of the ternary semigroup $$T[X,Y]$$ . Our results enrich the structure of the ternary semigroup of mappings.

Note on topological ternary semigroup

In this paper, we have discussed various topological properties of (Hausdörff) topological ternary semigroup and topological ternary group. We have proved that the Cartesian product of an arbitrary family of topological ternary semigroups is again a topological ternary semigroup. We have investigated the existence of identity and idempotent in a topological ternary semigroup and discussed a method to topologize a ternary semigroup (group) with a compatible topology using some family of pseudometrics. Finally, we have proved that a compact topological ternary semigroup contains a ternary subgroup.

Intuitionistic Fuzzy Ideals and Fuzzy Filters Of Ternary Semigroups

Intuitionistic Fuzzy Ideals and Fuzzy Filters Of Ternary Semigroups

Applications of hesitant fuzzy sets to ternary semigroups

The aim of this paper is to introduce a new concept of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals on ternary semigroups. We extend the concept of fuzzy bi-ideals and fuzzy interior ideals to the context of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals, respectively. Some characterizations of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals are obtained. Moreover, we investigate relationships between hesitant fuzzy ideals and hesitant fuzzy interior ideals on ternary semigroups. Finally, we obtain necessary and sufficient conditions of hesitant fuzzy interior ideal in order to be a hesitant fuzzy ideal.