Special Fuzzy Boolean Ring

The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Abstract— The aim of this article is to study the behaviour of the fuzzy Boolean algebras formed by the fuzzy subsets of a finite set. The properties of homomorphism, isomorphism and automorphism of the fuzzy Boolean algebras have been investigated. Further, the ideal and filter of the fuzzy Boolean algebras have also been observed with their characteristics.

The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. ABSTRACT It has been established that the fuzzy sets do not hold the Complement laws of Boolean algebra. The aim of this article is to introduce and study a kind of family of fuzzy subsets of a finite set which holds the Complement laws. The complement operation has redefined for this purpose. Further, it has been established that the introduced fuzzy subsets can form Boolean lattice and also Boolean algebra. Keywords fuzzy subset, membership value, the complement operation, the complement laws, Boolean lattice, subsets of a fuzzy subset, fuzzy power set.

International Journal of Computer Applications, 2013

It has been established that the fuzzy sets do not hold the Complement laws of Boolean algebra. The aim of this article is to introduce and study a kind of family of fuzzy subsets of a finite set which holds the Complement laws. The complement operation has redefined for this purpose. Further, it has been established that the introduced fuzzy subsets can form Boolean lattice and also Boolean algebra.

Archive for Mathematical Logic, 2007

In this study, by the use of Yuan and Lee's definition of the fuzzy group based on fuzzy binary operation we give a new kind of fuzzy ring. The concept of fuzzy subring, fuzzy ideal and fuzzy ring homomorphism are introduced, and we make a theoretical study their basic properties analogous to those of ordinary rings.

The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.

Fuzzy Sets and Systems, 1992

The classical theory of fuzzy sets has been developed within the Cantorian framework, as a simple generalization of the indicator or characteristic function and thus as a generalization of the membership property only, paying no attention to the equality relation. The nonstandard approach to fuzzy sets on the contrary is based on a non-Cantorian framework, which essentially amounts to viewing the eternally constant Cantorian-Platonic universe through two observers: the absolute Cantorian and the local non-Cantorian [5]. The construction of such a theory is based on a generalization of both equality and membership relations and technically is based on the theory of Boolean powers and a Boolean generalization of Nonstandard Analysis based on them [5, 6, 8, 15]. For Nonstandard Analysis see [1, 13]. In this paper, which is a continuation of [5], we give some new results for the basic concepts of fuzzy sets from our point of view, along with interpretations which are more interesting to fuzzy theorists.

International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2023

This article proposes some important theoretic aspects of L-fuzzy power set of a finite set. Here, we take a non-empty finite set E and an ordered subset M of the closed interval   0,1 , then the set of mappings from E to M denoted by F is defined as L-fuzzy power set. Considering the disjunctive union '    ' operations between fuzzy subsets of F , the structure   , F  forms a groupoid, which is defined as special fuzzy groupoid. Later, we try to introduce the product of special fuzzy groupoids and their properties.

Ibn Al-Haitham Journal For Pure And Applied Science, 2022

This paper introduces the concept of fuzzy σring as a generalization of fuzzy σ −algebra and basic properties; examples of this concept have been given. As the first result, it has been proved that every fuzzy σ-algebra over a fuzzy set * is a fuzzy σ-ring over a fuzzy set * and construct their converse by example. Furthermore, the fuzzy ring concept has been studied to generalize fuzzy algebra and its relation. Investigating that the concept of fuzzy σring is a stronger form of a fuzzy ring that is every fuzzy σ-ring over a fuzzy set * is a fuzzy ring over a fuzzy set * and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied as well. Finally, the main goal of this paper is to study these concepts and give basic properties, examples, characterizations and relationships between them.

In this paper, we studied the theory of fuzzy rings, the concept of fuzzy ring with operators, fuzzy ideal and anti-fuzzy ideal with operators, fuzzy homomorphism with operators etc., and their some elementary properties.

Indonesian Journal of Electrical Engineering and Computer Science, 2021

In this paper, we define the-fuzzy subring and discussed various fundamental aspects of-fuzzy subrings. We introduce the concept of-level subset of this new fuzzy set and prove that-level subset of-fuzzy subring form a ring. We define-fuzzy ideal and show that set of all-fuzzy cosets form a ring. Moreover, we investigate the properties of homomorphic image of-fuzzy subring.