TRIPOLAR FUZZY SOFT IDEALS AND TRIPOLAR FUZZY SOFT INTERIOR IDEALS OVER Γ−SEMIRING

In this paper, we have introduced the notion of tripolar fuzzy soft $\Gamma -$subsemi-ring,tripolar fuzzy soft ideal, tripolar fuzzy soft interior ideals over $\Gamma -$semiring and also studiedsome of their algebraic properties and the relations between them

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Innovative types of fuzzy gamma ideals in ordered gamma semigroups

The fuzzification of algebraic structures plays an important role in handling many areas of multi-disciplinary research, such as computer science, control theory, information science, topological spaces and fuzzy automata to handle many real world problems. For instance, algebraic structures are particularly useful in detecting permanent faults on sequential machine behaviour. However, the idea of ordered T-semigroup as a generalization of ordered semigroup in algebraic structures has rarely been studied. In this research, a new form of fuzzy subsystem in ordered T-semigroup is defined. Specifically, a developmental platform of further characterizations on ordered T-semigroups using fuzzy subsystems properties and new fuzzified ideal structures of ordered semigroups is developed based on a detailed study of ordered T-semigroups in terms of the idea of belongs to (E) and quasicoincidence with (q) relation. This idea of quasi-coincidence of a fuzzy point with a fuzzy set played a remarkable role in obtaining several types of fuzzy subgroups and subsystems based on three contributions. One, a new form of generalization of fuzzy generalized bi T-ideal is developed, and the notion of fuzzy bi T-ideal of the form (E,E Vqk) in an ordered T-semigroup is also introduced. In addition, a necessary and sufficient condition for an ordered T-semigroup to be simple T-ideals in terms of this new form is stated. Two, the concept of (E,E Vqk)-fuzzy quasi T-ideals, fuzzy semiprime T-ideals, and other characterization in terms of regular (left, right, completely, intra) in ordered T-semigroup are developed. Three, a new fuzzified T-ideal in terms of interior T-ideal of ordered T-semigroups in many classes are determined. Thus, this thesis provides the characterizations of innovative types of fuzzy T-ideals in ordered T-semigroups with classifications in terms of completely regular, intra-regular, for fuzzy generalized bi T-ideals, fuzzy bi T-ideals, fuzzy quasi and fuzzy semiprime T-ideals, and fuzzy interior T-ideals. These findings constitute a platform for further advancement of ordered T-semigroups and their applications to other concepts and branches of algebra

New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations

This Special Issue puts forward for discussion state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, neutrosophic symmetry, and their applications in the real world. This book leads to the further advancement of the neutrosophic and plithogenic theories of NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, Neutrosophic n-SuperHyperGraph (the most general form of graph of today), Neutrosophic Statistics, Plithogenic Logic as a generalization of MultiVariate Logic, Plithogenic Probability and Plithogenic Statistics as a generalization of MultiVariate Probability and Statistics, respectively, and presents their countless applications in our every-day world

Some Linguistic Neutrosophic Cubic Mean Operators and Entropy with Applications in a Corporation to Choose an Area Supervisor

In this paper, we combined entropy with linguisti neutrosophic cubic numbers and used it in daily life problems related to a corporation that is going to choose an area supervisor, which is the main target of our proposed model