Search

Humanity's efforts are manifested in the creation of novel solutions to complex problems in diverse fields. Traditional mathematical methods fail to solve real-world problems due to their complexity. Researchers have come up with new mathematical theories like fuzzy set theory and rough set theory to help them figure out how to model the uncertainty in these fields. Soft set theory is a novel approach to real-world problem solving that does not require the membership function to be specified. This aids in the resolution of a wide range of issues, and significant progress has recently been made. After Jun et al. came up with a hybrid system that combined fuzzy and soft set concepts, many people came up with hybrid ideas in different algebraic structures. In this paper, we introduce the concepts of subsystem and strong subsystem of a hybrid finite state machine (HFSM) and investigate a portion of their significant properties. We also provide an example that shows that every subsystem does not need to be a strong subsystem. Additionally, we study the cyclic subsystem of HFSMs and also obtain their equivalent results and examples. Finally, we define the notions of homomorphism of subsystems and strong subsystems of HFSMs. [ABSTRACT FROM AUTHOR]

An essential and quite different class of functions is the triangular norm and its related operators (uninorms, nullnorms, and associative copulas). They are used widely in many disciplines, including fuzzy set theory, probability and statistics, decision sciences, and others. This paper proposes the notion of hybrid Ξ -norm and defines the concepts of Ξ -hybrid ideals, Ξ -hybrid h -ideals in a hemiring . Some equivalent conditions are obtained for a hybrid structure to be a Ξ -hybrid left h -ideal, and it is proved that every imaginable Ξ -hybrid left h -ideal of hemiring is a hybrid left h -ideal, but not conversely by an example. [ABSTRACT FROM AUTHOR]

In a right regular L A -semigroup, the hybrid ideals, hybrid interior ideals, hybrid (1,2)-ideals, hybrid generalized bi-ideals, and hybrid quasi-ideals are all introduced in this work. A right regular L A -semigroup has also been described in terms of its hybrid right and hybrid left ideals. Moreover, we obtain some equivalent conditions in terms of hybrid two-sided ideal, hybrid bi- (respectively, generalized bi-)ideal, hybrid quasi-ideal, hybrid interior ideal and hybrid (1 , 2) -ideal over right regular L A -semigroups. [ABSTRACT FROM AUTHOR]

The fuzzy set is a fantastic tool for expressing hesitancy and dealing with uncertainty in real-world circumstances. Soft set theory has recently been developed to deal with practical problems. The soft and fuzzy sets were combined by Jun et al. to generate hybrid structures. The idea of hybrid ideals on a distributive lattice is discussed in this work. The relation between hybrid congruences and hybrid ideals on a distributive lattice is also examined. In addition, the product of hybrid ideals and its numerous results are discussed. [ABSTRACT FROM AUTHOR]

We are completely aware of the fact that ternary algebraic structures in some way naturally occur in diverse fields of theoretical and mathematical physics, computer science, especially in ternary operators in Java and Python, ternary logic applied for digital signal processing, and musical systems for song composition. The primary aim of this research is to examine ternary semigroups in the context of hybrid quasi-ideals and hybrid A-ideals. Different features of hybrid quasi-ideals and hybrid A-ideals in the ternary semigroup are discussed. In addition, the idea of minimal hybrid A-ideals of ternary semigroups is defined. [ABSTRACT FROM AUTHOR]

Our aim is to explore the idea of neutrosophic N−ideals in near-subtraction semigroups in this article and obtain some outcomes that are equivalent to them. We also illustrate the notion of a neutrosophic κ− intersection. Additionally, in a near-subtraction semigroup, we examine the term homomorphism of a neutrosophic κ− structure and establish some conclusions based on a homomorphic neutrosophic κ− structure preimage of a neutrosophic κ− left (respectively, right) ideal. [ABSTRACT FROM AUTHOR]

This article explores the concept of hybrid interior ideals and the hybrid characteristic interior ideals of a ternary semigroup. We establish some equivalent requirements for a hybrid structure to be a hybrid interior ideal of a ternary semigroup. Also, we show that for a regular semigroup and an intra-regular semigroup, hybrid interior ideals and hybrid ideals coincide. Furthermore, the notion of a hybrid bi-ideal of a ternary semigroup is introduced, and some of its key characteristics are explored. [ABSTRACT FROM AUTHOR]

An AG-groupoid is the midway between commutative semigroup and groupoid. The core structure of Flock theory is an AG-groupoid, which focuses on motion replication and distance optimization and has numerous applications in physics and biology. Unfortunately, in many cases, modelling real-world problems in domains like computer science, operations research, artificial intelligence, control engineering, and robotics can be risky. Different theories, such as fuzzy sets, intuitionistic fuzzy sets, probability, soft sets, neutrosophic sets, and others, have been created to deal with similar situations. In this paper, We define the notions of neutrosophic κ-ideal structures in an AG-groupoid and investigate their properties. We also obtain equivalent assertion of neutrosophic κ-ideals and product of neutrosophic κ-structures in AG-groupoid. [ABSTRACT FROM AUTHOR]

In this article. we propose the idea of hybrid congruences and hybrid strong ŋ -ideals of hemirings and we build an example that every liybrid strong ŋ-ideal is an hybrid h-ideal. but not conversely. The hybrid hemiring homomorphisins and quotient rings through the hybrid strong 11-ideals are also discussed. In addition. we look into the relationship between hybrid congruence and hybrid strong [1-ideals of hemirings. [ABSTRACT FROM AUTHOR]

In general, models of universe problems in almost all fields, such as engineering, mathematics, medical sciences, computer science, physics, management sciences, artificial intelligence, and operations research, are practically full of complexities and include various types of uncertainties when dealing with them on numerous occasions. Different theories, such as probability, rough sets, fuzzy sets, soft ideals, and so on, have been created to deal with these uncertainties. An algebraic structure, AG-groupoid, is an intermediate structure between two types of structures: commutative semigroup and groupoid. This structure has a very close relationship to a commutative semigroup since a commutative AG-groupoid is always a semigroup. These structures have so many applications in flocks theory, geometry, topology, and many more. We explore several structural properties of an AG-groupoid by using hybrid structures in this paper. The main motivation behind this paper is to present the concepts of hybrid ideals, hybrid bi-ideals and hybrid interior ideals of an AG-groupoid and characterize AG-groupoid in terms of hybrid structures. Also, we show that the hybrid intersection and hybrid product structures will coincide under certain conditions. [ABSTRACT FROM AUTHOR]

Models of universe problems are brimming with complexities and uncertainties in almost every field of study, including engineering, mathematics, medical sciences, computer science, physics, management sciences, artificial intelligence, and operations research. To address these uncertainties, various theories have been developed, including probability, rough sets, fuzzy sets, soft ideals, and neutrosophic sets. Neutrosophic set theory is the focus of this paper. In this paper, we introduce the notions of neutrosophic N-filters and neutrosophic N-bi-filters in a semigroup and investigate several properties. Moreover, the relations of prime biideal subset and prime neutrosophic N-bi-ideal structure; neutrosophic N-bi-filter and neutrosophic N-bi-ideal structure; left (resp., right) filter and neutrosophic N-left (resp., right) filter; neutrosophic N-left(resp., right) filter and prime neutrosophic N-left (resp., right) ideals in semigroups are discussed. Finally we prove that: let X be a semigroup and XN be any neutrosophic structure. Then XN is a neutrosophic N-bi-filter of X if and only if XNc is a prime neutrosophic N-bi-ideal of X. [ABSTRACT FROM AUTHOR]

In general, ordered algebraic structures, particularly ordered semigroups, play an important role in fuzzification in many applied areas, such as computer science, formal languages, coding theory, error correction, etc. Nowadays, the concept of ambiguity is important in dealing with a variety of issues related to engineering modeling problems, network theory, decision-making problems in real-life situations, and so on. Several theories have been developed by various researchers to overcome the difficulties that arise from uncertainty, including fuzzy sets, intuitionistic fuzzy sets, probability, soft sets, neutrosophic sets, and many more. In this paper, we focus solely on neutrosophic set theory. In ordered semigroups, we define and investigate the properties of neutrosophic ℵ-ideals and neutrosophic ℵ-interior ideals. We also use neutrosophic K-ideals and neutrosophic ℵ-interior ideals to characterize ordered semigroups. [ABSTRACT FROM AUTHOR]

We define the concepts of neutrosophic N -interior ideal and neutrosophic N -- characteristic interior ideal structures of a semigroup. We infer different types of semigroups using neutrosophic N-interior ideal structures. We also show that the intersection of neutrosophic N-interior ideals and the union of neutrosophic N-interior ideals is also a neutrosophic N-interior ideal. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of neutrosophic ℵ-bi-ideal for a semigroup. We infer different semigroups using neutrosophic ℵ -bi-ideal structures. Moreover, for regular semigroups, neutrosophic ℵ-product and intersection of neutrosophic ℵ-ideals are identical. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the notion of prime bi-ideals and semi prime bi-ideals of Po-Γ-groupoids and explored the various properties of prime bi-ideals in Po-Γgroupoids. Also we obtained the condition for Po-Γ-groupoids to be regular. [ABSTRACT FROM AUTHOR]

In this paper, we study the notions of prime and semi prime bi-ideals in ordered ternary semirings and we obtain equivalent conditions for a bi-ideal to be a prime bi-ideal. [ABSTRACT FROM AUTHOR]

In this paper, the notion of hybrid generalized bi-ideal of a semigroup is introduced with some of their important properties investigated. We obtain some characterizations of regular and left quasiregular semigroups in terms of hybrid generalized bi-ideals. [ABSTRACT FROM AUTHOR]

In this paper, we study properties of generalized semi-ideal-based zero-divisor graph structure of poset P, with respect to minimal elements of P\I. We also investigate the interplay between the poset properties of P and the graph theoretic properties of GI(P). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define the notions of almost prime ideals in near rings and explore various properties of almost prime ideals and their generalizations in near-rings. [ABSTRACT FROM AUTHOR]