A Study on Intuitionistic Fuzzy Maximal Ideals in Gamma Near-Rings | Chapter 3 | Mathematics and Computer Science: Research Updates Vol. 1

This paper introduces the concepts of intuitionistic fuzzy maximal ideals and complete normal intuitionistic fuzzy ideals within the framework of Γ-near-rings. We investigate and analyse various properties related to these newly defined ideals, including their structural characteristics and relationships. This study aims to extend the understanding of intuitionistic fuzzy theory in algebraic structures, providing insights into the behavior of maximal and normal ideals under intuitionistic fuzziness. Furthermore, we examine the implications of these ideals in Γ-near-rings, offering a foundation for further research on fuzzy algebraic structures.

 

Author (s) Details

 

Ezhilmaran Devarasan
School of Advanced Sciences, Vellore Institute Technology, Vellore - 632 014, Tamil Nadu, India.

 

N. Palaniappan
School of Mathematics, Alagappa University, Karaikudi – 630 003, Tamil Nadu, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v1/3068

A Case Study for Engineering Students: Intuitionistic Fuzzy Set and Its Application in Selecting Specialization | Chapter 1 | Current Topics on Mathematics and Computer Science Vol. 4

The intuitionistic fuzzy set (IFS) is a useful model for elaborating on the uncertainty and ambiguity inherent in decision making. The idea of defining an intuitionistic fuzzy set as a generalised fuzzy set is intriguing and beneficial in a variety of settings. In this work, the notion of IFS was studied, and a proposal for its use in specialised selection was made. A case study for engineering students is discussed in detail. From supplied data, we describe a method for computing membership and non-membership degrees. The strategy provided here can be used to a wide range of similar real-world scenarios.

Author (S) Details

A. M. Kozae
Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt.

Assem Elshenawy
Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.

Manar Omran
Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, Tanta, Egypt.

View Book :- https://stm.bookpi.org/CTMCS-V4/article/view/2276

On Applications of Fuzzy Soft and Intuitionistic Fuzzy Soft Sets in Dimension Reduction and Medical Diagnosis | Chapter 7 | New Ideas Concerning Science and Technology Vol. 8

 In our everyday lives, we are often confronted with a variety of issues relating to data with a high dimensionality. Irrelevant and superfluous data, as well as valuable data, are present in such problems. As a result, dimensionality reduction has a broad range of applications in data processing and analysis. In recent years, the problem of dimensionality reduction in a fuzzy situation has gotten a lot of attention from researchers. They have developed different methods and hypotheses to solve these types of problems. Some of these approaches are based on a probabilistic approach, while others are not. Fuzzy soft set theory is gaining popularity for seeking coherent and logical solutions to a variety of real-world problems involving complexity, imprecision, and vagueness. A theoretical analysis of intuitionistic fuzzy soft has been developed recently. When ambiguity due to vagueness is more complicated, the combination of intuitionistic fuzzy set and intuitionistic fuzzy soft set is more useful from an application standpoint. The definition of fuzzy soft set is described in this chapter as a hybridization of fuzzy set and soft set theory. A new technique for converting a soft set table into a fuzzy soft set table is proposed, which can be used in big data dimension reduction. As a hybridization of fuzzy set and soft set theory, fuzzy soft set and intuitionistic fuzzy soft set are described. Following Sanchez's approach, new methods of applying fuzzy soft and intuitionistic soft sets are also defined in Medical Diagnosis.

Author (s) Details

Prof. D. S. Hooda
Former PVC, Kurukshetra University, Department of Mathematics, G. J. University of Science and Technology, Hisar- 125001, India.

View Book :- https://stm.bookpi.org/NICST-V8/issue/view/45