Bipolar fuzzy soft hyperideals of ordered -hypersemigroups

2013

We introduced and study fuzzy Γ-hypersemigroups, according to fuzzy semihypergroups as previously defined [33] and prove that results in this respect. In this regard first we introduce fuzzy hyperoperation and then study fuzzy Γ-hypersemigroup. We will proceed by study fuzzy Γ-hyperideals and fuzzy Γ-bihyperideals. Also we study the relation between the classes of fuzzy Γ-hypersemigroups and Γ-semigroups. Precisely, we associate a Γ-hypersemigroup to every fuzzy Γ-hypersemigroup and vice versa. Finally, we introduce and study fuzzy Γ-hypersemigroups regular and fuzzy strongly regular relations of fuzzy Γ-hypersemigroups.

Malaysian Journal of Fundamental and Applied Sciences

A fuzzy subset A defined on a set X is represented as A = {(x, A (x), where x ∈ X}. It is not always possible for membership functions of type λA : X → [0,1] to associate with each point x in a set X a real number in the closed unit interval [0,1] without the loss of some useful information. The importance of the ideas of “belongs to” (∈) and “quasi coincident with” (q) relations between a fuzzy point and fuzzy set is evident from the research conducted during the past two decades. Ordered Γ-semigroup (generalization of ordered semigroups) play an important role in the broad study of ordered semigroups. In this paper, we provide an extension of fuzzy generalized bi Γ-ideals and introduce (∈,∈∨qk)-fuzzy generalized bi Γ-ideals of ordered Γ-semigroup. The purpose of this paper is to link this new concept with ordinary generalized bi Γ-ideals by using level subset and characteristic function.

2016

A fuzzy subset A defined on a set X is represented as     X x x x A A   where , ) ( , . It is not always possible for membership functions of type ] 1 , 0 [ :  X A  to associate with each point x in a set X a real number in the closed unit interval ( ] 1 , 0 [ ) without the loss of some useful information. The importance of the ideas of “belongs to” () and “quasi coincident with” ( q ) relations between a fuzzy point and fuzzy set is evident from the research conducted during the past two decades. Ordered  -semigroup (generalization of ordered semigroups) play an important role in the broad study of ordered semigroups. In this paper we provide an extension of fuzzy generalized bi  -ideals and introduce ) , ( k q    -fuzzy generalized bi  -ideals of ordered  -semigroup. The purpose of this paper is to link this new concept with ordinary generalized bi  -ideals by using level subset and characteristic function.

Information Sciences, 2011

In this paper, we introduce the concept of (α, β)-bipolar fuzzy generalized bi-ideal in ordered semigroup, which is a generalization of bipolar-fuzzy generalized bi-ideal in ordered semigroup. Using this concept, we provide some characterization theorems. We prove that in regular ordered semigroup, the concept of (∈, ∈ ∨q)-bipolar fuzzy generalized bi-ideal and (∈, ∈ ∨q)-bipolar fuzzy bi-ideal coincide. We also introduce the upper/lower parts of (∈, ∈ ∨q)-bipolar fuzzy generalized bi-ideals and characterize the regular ordered semigroups in terms of lower part of (∈, ∈ ∨q)-bipolar fuzzy left (resp. right or two sided) ideals and (∈, ∈ ∨q)-bipolar fuzzy generalized bi-ideals.

Jurnal Teknologi, 2013

2021

The aim of this article is to study ordered semihypergroups in the framework of (M,N)-int-soft bi-hyperideals. In this paper, we introduce the notion of (M,N)-int-soft bi-hyperideals of ordered semihypergroups. Some properties of (M,N)-int-soft bi-hyperideals in ordered semihypergroups are provided. We show that every int-soft bi-hyperideal is an (M,N)-int-soft bi-hyperideals of S over U but the converse is not true which is shown with help of an example. We characterize left (M,N) simple and completely regular ordered semihypergroups by means of (M,N)-int-soft bi-hyperideals.

Neural Computing and Applications, 2012

In Jun et al. (Bull Malays Math Sci Soc 32 :391-408, 2009), (a, b)-fuzzy bi-ideals are introduced and some characterizations are given. In this paper, we generalize the concept of (a, b)-fuzzy bi-ideals and define (2; 2 _q k )-fuzzy bi-ideals in ordered semigroups, which is a generalization of the concept of an (a, b)-fuzzy bi-ideal in an ordered semigroup. Using this concept, some characterization theorems of regular, left (resp. right) regular and completely regular ordered semigroups are provided. In the last section, we give the concept of upper/lower parts of an (2; 2 _q k )-fuzzy bi-ideal and investigate some interesting results of regular and intra-regular ordered semigroups.

In several applied disciplines like control engineering, computer sciences, error-correcting codes and fuzzy automata theory , the use of fuzzified algebraic structures especially ordered semi-groups and their fuzzy subsystems play a remarkable role. In this paper, we introduce the notion of (∈, ∈ ∨q k)-fuzzy subsystems of ordered semigroups namely (∈, ∈ ∨q k)-fuzzy generalized bi-ideals of ordered semigroups. The important milestone of the present paper is to link ordinary generalized bi-ideals and (∈, ∈ ∨q k)-fuzzy generalized bi-ideals. Moreover, different classes of ordered semi-groups such as regular and left weakly regular ordered semigroups are characterized by the properties of this new notion. Finally, the upper part of a (∈, ∈ ∨q k)-fuzzy generalized bi-ideal is defined and some characterizations are discussed.

Soft Computing, 2017

Molodtsov's soft set theory is a new mathematical model for dealing with uncertainty from a parameterization point of view. In soft set theory, the problem of setting the membership function does not arise, which makes the theory easily applied to many different fields. In this paper, we discuss a new approach to soft sets and compare soft sets to the related concepts of ordered semihypergroups. We define int-soft generalized bi-hyperideals in ordered semihypergroups and characterize regular and left weakly regular ordered semihypergroups by the properties of their int-soft generalized bi-hyperideals. Keywords Soft set • Regular • Left weakly regular ordered semihypergroups • Left (resp., right, bi-and generalized bi-)hyperideals • Int-soft left (resp., right, bi-and generalized bi-)hyperideals in ordered semihypergroups 1 Introduction Algebraic hyperstructures represent a natural extension of classical algebraic structures, and they were originally proposed in 1934 by a French mathematician Marty (1934), at Communicated by V. Loia.

Hacettepe Journal of Mathematics and Statistics, 2012

In this paper, the concepts of ∈-soft set and q-soft set are introduced and some interesting properties are investigated. Using the notion of generalized fuzzy bi-ideals in a semigroup, characterizations for an ∈soft set and a q-soft set to be bi-idealistic soft semigroups are established.