Fuzzy Hyperstructures Research Articles

Fuzzy Degree and Intuitionistic Fuzzy Degree for Chemical Hyperstructures

The notion of hyperstructures first introduced by Marty in 1934 as a generalization of algebraic structures. Next, by associating fuzzy sets, Corsini introduced new notion in hyperstructures, that is fuzzy hyperstructures. After fuzzy hyperstructures introduced by Corsini, Cristea introduced the notion of intuitionistic fuzzy hyperstructures as a generalization of fuzzy hyperstructures. In 2023, Violeta-Fotea related the notion of fuzzy hyperstructures with genetic inheritance. Inspired by this research, this paper aims to find relation between fuzzy and intuitionistic fuzzy hyperstructures with chemical hyperstructures, that is to finding the fuzzy degree and intuitionistic fuzzy degree on chemical hyperstructures such as redox reactions, electrochemical cells, equilibrium reactions, and acid rain reactions.

A systematic study in the applications of fuzzy hyperlattice

In the last few decennium, the acquaintance between algebraic hyperstructures and fuzzy sets have been considered for its theoretical as well as applications in various fields. Fuzzy hyperstructures are fascinating research topic and substantial amount of researches have been undergoing as of now. As a consequence, fuzzy hyperlattice was introduced by Pengfei He, Xiaolong Xin. But the applications on fuzzy hyperlattice are not defined so far. By scrutinizing the fuzzy hyperlattice, our objective is to present some applications of fuzzy hyperlattice in Biological and Physical Sciences. We find the first and second applications in dihybrid cross of Drosophila melanogaster (housefly) and Pisum sativum (Peas), respectively. Third application is in particle Physics (Elementary particles interaction).

Sustainable goals in combating human trafficking: Analysis by mathematics of uncertainty

We use mathematics of uncertainty to analyze the relationship between the sustainable development goals and human trafficking. Thiscomes about naturally due to the use of multiplication in the determination of metrics in scoring categories by the Stakeholder Forum.We develop a method for ranking the members of the Organizationfor Economic Cooperation and Development in their achievement ofthe sustainable development goals that are pertinent to traffickingin humans. This method includes linear equations involving ten ofthe SDGs. SGD 5 (Gender Equality), 8 (Decent Work and EconomicGrowth), and 16 (Peace, Justice, and Strong Institutions) carry themost weight in determining these rankings. We found that Denmark,Finland, Iceland, and Sweden rank the highest in achieving the sustainable development goals pertinent to human trafficking. We discuss how our methods can be placed in a setting of fuzzy hyperstructures.

Certain fuzzy hyperstructures from a fuzzy set

Fuzzy set theory and also the hypergroups in the sense of Marty are both generalizations of some existing mathematical concepts which are used for modeling many real life situations. The main purpose of this paper is the study of the link between fuzzy sets and fuzzy hypergroups and fuzzy semihypergroups. As a matter of fact, some commutative fuzzy hypergroups and fuzzy semihypergroups have been constructed from fuzzy set and some of their properties were investigated.

Some properties of fuzzy HX group

In this paper, we investigate some properties of fuzzy hyperstructures generated on a group quotient by some kind of fuzzy cosets and some kind of fuzzy middle cosets. It was established that some kind of fuzzy middle coset generates the same fuzzy hyperstructures as some fuzzy cosets do. Besides, it was also established that when a group is quotient by the class of its t-level subgroups, it generates a HX group on the group.

Generalized fuzzy hypergraphs and hypergroupoids

This article first generalizes the ordinary fuzzy hypergraphs to generalized fuzzy hypergraphs and it makes a connection between generalized fuzzy hypergraphs and fuzzy hyperstructures. We construct a partial fuzzy hypergroupoid associated with it, giving some properties of the associated fuzzy hyperstructure. Moreover, we construct higher order fuzzy hypergroupoids and study their properties. Finally, by considering a regular equivalence relation on a (g-f)p-hypergroupoid, we define a quotient (g-f)phypergroupoid and we investigate some relationships between diagonal product of hypergroupoids and p-product of (g-f)-hypergraphs.

Lattice structure on some fuzzy algebraic systems

In this paper, we study the lattice structure of some fuzzy algebraic systems such as (G-)fuzzy groups, some fuzzy ordered algebras and fuzzy hyperstructures. We prove that under suitable conditions, these structures form a distributive or modular lattice.