Fuzzy Hyper Research Articles

On Intuitionistic Fuzzy Implicative Hyper GR-ideals

The influx of researches on hyperstructure theory has encouraged many researchers to introduce new algebras. Notable among these is the work of Indangan and Petalcorin who introduced hyper GR-algebra and that of Macodi and Petalcorin who studied fuzzification of hyper GR-algebra. Macodi extended the fuzzification of hyper GR-algebra into intuitionistic fuzzification and introduced the concept of an intuitionistic fuzzy hyper GR-ideal. Following the works of Macodi and Petalcorin, this paper established an intuitionistic fuzzy implicative hyper GR-ideal and obtained its characterization using level subsets. Moreover, some properties of intuitionistic fuzzy implicative hyper GR-ideals are presented.

On Fuzzy Subhypernear-Ring

In this study, two main goals were achieved. In near-ring N, we have proven that, the level set is a subnear-ring of N if and only if the fuzzy set is the fuzzy subnear-ring of N. Similarly, in hyper near-ring R, it has been proven that, a fuzzy set is a fuzzy hypernear-ring if and only if level set is a sub-hypernear-ring of R. A direct proof method was used to reach these results, which will contribute to expanding the field of study on fuzzy near-ring and fuzzy hyper near-rings.

A new representation of fundamental relations on fuzzy hyperrings

A new representation of fundamental relations on fuzzy hyperrings

Constructing Symmetric Equality Algebras

In this paper, we introduce the notion of strong fuzzy filter on hyper equality algebras and investigate some equivalence definitions of it. Then by using this notion we constructed a symmetric equality algebra and define a special form of classes. By using these, we define the concept of a fuzzy hyper congruence relation on hyper equality algebra and we prove that the quotient is made by it is an equality algebra. Also, by using a fuzzy equivalence relation on hyper equality, we introduce a fuzzy hyper congruence relation and prove that this fuzzy hyper congruence is regular and finally we prove that the quotient structure that is made by it is a symmetric hyper equality algebra.

ON ALMOST CONTRA-SOMEWHAT FUZZY CONTINUOUS FUNCTIONS

In this paper, a new notion of fuzzy contra-continuity, called almost contra-somewhat fuzzy continuity between fuzzy topological spaces,is introduced. Several characterizations of these functions are obtained and it is shown that fuzzy almost contra-semi continuous functions are almost contra-somewhat fuzzy continuous functions. The conditions under which fuzzy hyper connected spaces become the fuzzy Baire spaces, fuzzy second category spaces and fuzzy almost irresolvable spaces, are obtained by means of almost contra-somewhat fuzzy continuous functions.

Bipolar picture fuzzy hypersoft set-based performance analysis of abrasive textiles for enhanced quality control

Abrasive textiles have widespread industrial applications in the fields of polishing, finishing, deburring, and cleaning of various surfaces. Effective decision making and performance analysis are crucial in the development and manufacturing of abrasive textiles, as it enables manufacturers to evaluate and optimize the performance of these materials for specific applications and to make informed decisions about their production processes. For that purpose, this work aims to introduce an innovative bipolar picture fuzzy hypersoft set (BPFHSS) which is composed of two picture fuzzy hyper soft sets; one of them gives us the positive information, and the other gives us the negative information, for each membership degree, neutral membership, and non-membership degree. The properties of the designed structure and discussed alongside a thorough discussion on the De-Morgan's laws. Also, the bipolar picture fuzzy hypersoft weighted geometric (BPFHSWG) operator is defined for the BPFHSS framework to aggregate bipolar picture fuzzy hypersoft numbers (BPFHSN) information. This research highlights the importance of considering inconsistent, bipolar, and multiple sub-attribute information in decision-making processes by using the defined operators to develop an algorithm for a multi-attribute analysis for quality control of manufacture of abrasive textiles.

Characterization of Derived Nilpotent (Engel) Lie Ring of Fuzzy Hyperrings by Using Fuzzy Strongly Regular Relations

In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation (). Moreover, we proved that for a fuzzy hyperring S, the quotient () was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.

Construction of Fuzzy Hyper BCI-Algebras Using Fuzzy Hypergroupoid

In this paper, by considering the notion of fuzzy hyperoperation, we define the concept of fuzzy hyper [Formula: see text]-algebras as a generalization of [Formula: see text]-algebras and study related properties. Moreover, we introduce the notions of fuzzy hyper [Formula: see text]-ideal and weak (strong) fuzzy hyper [Formula: see text]-ideal, and then examine the relations among them. Finally, we investigate the relation between fuzzy hyper [Formula: see text]-algebras with fuzzy hypersemigroup, fuzzy hypergroup and hyper [Formula: see text]-algebras.

Fuzzy Sets in Hyper UP-algebra

In this paper, we apply the concept of fuzzy set to hyper UP-subalgebras. We introduce the notions of fuzzy hyper UP-subalgebra and fuzzy hyper UP-filter and establish some of their properties. Furthermore, some properties of hyper homomorphism in relation to fuzzy hyper UP-subalgebras and fuzzy hyper UP-filter are also presented.

Γ∗-Relation on Fuzzy Hyperrings and Fundamental Ring

Fundamental relation performs an important role on fuzzy algebraic hyperstructure and is considered as the smallest equivalence relation such that the quotient is a universal algebra. In this paper, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings such that the set of the quotient is a ring that is non-commutative. Also, we introduce the concept of a complete part of a fuzzy hyperring and study its principal traits. At last, we convey the relevance between the fundamental relation and complete parts of a fuzzy hyperring.

Hyper Fuzzy AT-ideals of AT-algebra

The aim of this paper is to introduce the notion of hyper fuzzy AT-ideals on hyper AT-algebra. Also, hyper fuzzy AT-subalgebras and fuzzy hyper AT-ideal of hyper AT-algebras are studied. We study on the fuzzy theory of hyper AT-subalgebras and hyper AT-ideal of hyper AT-algebras. Furthermore, the fuzzy set theory of the (weak, strong, s-weak) hyper fuzzy ATideals in hyper AT-algebras are applied and the relations among them are obtained.

Multipolar Intuitionistic Fuzzy Hyper BCK-Ideals in Hyper BCK-Algebras

In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzzy reflexive hyper BCK-ideal are introduced herein, and their relations and properties are investigated. These concepts are discussed in connection with the k-polar lower level set and the k-polar upper level set.

Fuzzy weak hyper deductive systems of hyper equality algebras and their measures

Fuzzy weak hyper deductive systems of hyper equality algebras and their measures

On Intuitionistic Fuzzy Hyper GR-ideals in Hyper GR-algebras

Let $P(H)$ be the power set of $H$. Consider $\ds P^*(H)=P(H)\setminus\{\phi\}$. A hyperoperation on a nonempty set $H$ is a function $\ds\circledast:H\times H\rightarrow P^*(H).$ A set $H$ endowed with a family $\Gamma$ of hyperoperations is called ahyperstructure. Hyperstructures have many applications to several sectors of both pure and applied sciences. One of the well developed hyperstructures is the hyper BCI-algebra. Recently, by following this hyperstructure, a new hyperstructure was created by Indangan et al., named as hyper GR-algebras. In this paper, fuzzy set and intuitionistic fuzzy set are applied to hyper GR-algebra. Particularly, the fuzzy hyper GR-ideal of type 1 and the intuitionistic fuzzy hyper GR-ideal are introduced, and a relationship between them are obtained. Moreover, some of their characterizations are established by the use of their level subsets.Â

BIPOLAR FUZZY IMPLICATIVE HYPER BCK-IDEALS IN HYPER BCK-ALGEBRAS

Bipolar-valued fuzzification of the notion of implicative hyper BCK-ideals is considered. Using the concepts of positive and negative lever sets, a characterization of a bipolar fuzzy implicative hyper BCK-ideal is provided. A relation between a bipolar fuzzy hyper BCK-ideal and a bipolar fuzzy implicative hyper BCK-ideal is established. A condition for a bipolar fuzzy hyper BCK-ideal to be a bipolar fuzzy implicative hyper BCK-ideal is given. By using a collection of implicative hyper BCK-ideals, a bipolar fuzzy implicative hyper BCK-ideal is established.

Multipolar fuzzy hyper BCK-ideals of hyper BCK-algebras

In this paper, we apply m-polar fuzzy set to hyper BCKalgebra. We introduce the notions of k-polar fuzzy hyper BCK-ideal, k-polar fuzzy weak hyper BCK-ideal, k-polar fuzzy s-weak hyper BCK-ideal, k-polar fuzzy strong hyper BCK-ideal and k-polar fuzzy reflexive hyper BCKideal, and investigate related properties and their relations. We discuss k-polar fuzzy (weak, s-weak, strong, reflexive) hyper BCK-ideal in relation to k-polar level set

Commutative rings derived from fuzzy hyperrings

The fundamental relation on a fuzzy hyperring is de-fined as the smallest equivalence relation, such that the quotient would be the ring, that is not commutative necessarily. In this pa-per, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings, where the ring is commutative with respect to both sum and product. With considering this relation on fuzzy hyperring, the set of the quotient is a commutative ring. Also, we introduce fundamental functor between the category of fuzzy hyperrings and category of commutative rings and some related properties. Even-tually, we introduce α-part in fuzzy hyperring and determine some necessary and sufficient conditions so that the relation α is transi-tive.

Doubt intuitionistic fuzzy hyper filters in hyper BE-algebras

The purpose of this study is to apply the intuitionistic fuzzy hyper filters to hyper BE -algebras and to derive the conditions for an intuitionistic fuzzy set to be a doubt intuitionistic fuzzy hyper filter in hyper BE -algebras. The findings of the

Fuzzy soft positive implicative hyper BCK-ideals in hyper BCK-algebras

Fuzzy soft positive implicative hyper BCK-ideals in hyper BCK-algebras

Bipolar Fuzzy Soft Hyperideals and Homomorphism of Gamma-Hypersemigroups

In this paper, we introduce the concept of bipolar fuzzy soft gamma hyperideals in gamma hyper semigroups. We define bipolar fuzzy soft hyper ideals, bi-ideals and interior ideals of gamma hyper semigroups and discuss some properties.