Cubic Set Structure and Its Applications

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 5448

Special Issue Editor


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Guest Editor
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea
Interests: BCK/BCI algebras and related systems; fuzzy algebraic structures; soft and rough set theory in algebraic structures; fuzzy hyper structures; cubic algebraic structures
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Special Issue Information

Dear Colleagues,

Fuzzy set theory was initiated by L. A. Zadeh in 1965, and fuzzy sets and some generalizations have been considered in a variety of fields. Fuzzy sets are somewhat similar to sets whose elements have degrees of membership. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition—an element either belongs or does not belong to the set. In contrast, fuzzy set theory enables the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval [0, 1]. Fuzzy sets generalize classical sets, because the indicator functions of classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values of “0” or “1”. In fuzzy set theory, classical bivalent sets are usually called crisp sets. Fuzzy sets greatly contribute to solving several problems involving uncertainty.  Problems involving uncertainty appear in various forms; therefore, hybrid structures are emerging at a time when it is necessary to develop tools to solve them. At this point, Y.B. Jun et al. implemented a cubic set, which is a combination of a fuzzy set with an interval-valued fuzzy set.

The aim of this Special Issue is to establish a collection of high-quality and original theoretical and applied research papers on “Cubic Set Structure and Its Applications”.

Potential topics include, but are not limited to:

  • Cubic sets;
  • Cubic relations;
  • Cubic bipolar sets;
  • Cubic hesitant fuzzy sets;
  • Cubic picture fuzzy sets;
  • Cubic Pythagorean fuzzy sets;
  • Cubic vague sets;
  • Cubic graphs;
  • Cubic soft sets;
  • Cubic rough sets;
  • Crossing cubic structures;
  • Cubic algebraic structures;
  • Cubic hyper structures;
  • Cubic topological spaces;
  • N-cubic sets;
  • Neutrosophic cubic set;
  • Plithogenic cubic sets;
  • Spherical cubic sets;
  • Generalization of cubic sets;
  • Applications of cubic sets.

Prof. Dr. Young Bae Jun
Guest Editor

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Published Papers (3 papers)

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Research

29 pages, 423 KiB  
Article
A Study on Groupoids, Ideals and Congruences via Cubic Sets
by Jeong-Gon Lee, Samy M. Mostafa, Jong-Il Baek, Sang-Hyeon Han and Kul Hur
Axioms 2022, 11(9), 443; https://doi.org/10.3390/axioms11090443 - 30 Aug 2022
Viewed by 1294
Abstract
The inclusion, the intersection and the union between cubic sets are each defined in two ways. From this point of view, we introduce the concepts of cubic subgroupoids, cubic ideals, cubic subgroups, and cubic congruences as two types, respectively, and discuss their various [...] Read more.
The inclusion, the intersection and the union between cubic sets are each defined in two ways. From this point of view, we introduce the concepts of cubic subgroupoids, cubic ideals, cubic subgroups, and cubic congruences as two types, respectively, and discuss their various properties. In particular, we give a relationship between the set of all cubic normal subgroups of a group and all cubic congruences on the group. Full article
(This article belongs to the Special Issue Cubic Set Structure and Its Applications)
23 pages, 385 KiB  
Article
Neighborhood Structures and Continuities via Cubic Sets
by Jeong-Gon Lee, Güzide Şenel, Jong-Il Baek, Sang Hyeon Han and Kul Hur
Axioms 2022, 11(8), 406; https://doi.org/10.3390/axioms11080406 - 16 Aug 2022
Cited by 4 | Viewed by 1233
Abstract
Cubic sets are a very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of [0, 1] and a number from [0, 1]. In this article, we first highlight some of the claims made in the [...] Read more.
Cubic sets are a very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of [0, 1] and a number from [0, 1]. In this article, we first highlight some of the claims made in the previous article about cubic sets. Then, the concept of semi-coincidence in cubic sets, cubic neighborhood system according to cubic topology, and cubic bases and subbases are introduced. This article deals with a cubic closure and a cubic interior and how to obtain their various properties. In addition, cubic compact spaces and their properties are defined and a useful example is given. We mainly focus on the concept of cubic continuities and deepen our research by finding its characterization. One of the most important discoveries of this paper is determining that there is a cubic product topology induced by the projection mappings, and discovering sufficient conditions for the projection mappings to be cubic open. Full article
(This article belongs to the Special Issue Cubic Set Structure and Its Applications)
16 pages, 337 KiB  
Article
Semigroup Structures and Commutative Ideals of BCK-Algebras Based on Crossing Cubic Set Structures
by Mehmet Ali Öztürk, Damla Yılmaz and Young Bae Jun
Axioms 2022, 11(1), 25; https://doi.org/10.3390/axioms11010025 - 9 Jan 2022
Cited by 2 | Viewed by 1793
Abstract
First, semigroup structure is constructed by providing binary operations for the crossing cubic set structure. The concept of commutative crossing cubic ideal is introduced by applying crossing cubic set structure to commutative ideal in BCK-algebra, and several properties are investigated. The relationship between [...] Read more.
First, semigroup structure is constructed by providing binary operations for the crossing cubic set structure. The concept of commutative crossing cubic ideal is introduced by applying crossing cubic set structure to commutative ideal in BCK-algebra, and several properties are investigated. The relationship between crossing cubic ideal and commutative crossing cubic ideal is discussed. An example to show that crossing cubic ideal is not commutative crossing cubic ideal is given, and then the conditions in which crossing cubic ideal can be commutative crossing cubic ideal are explored. Characterizations of commutative crossing cubic ideal are discussed, and the relationship between commutative crossing cubic ideal and crossing cubic level set is considered. An extension property of commutative crossing cubic ideal is established, and the translation of commutative crossing cubic ideal is studied. Conditions for the translation of crossing cubic set structure to be commutative crossing cubic ideal are provided, and its characterization is processed. Full article
(This article belongs to the Special Issue Cubic Set Structure and Its Applications)
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