Intuitionistic Fuzzy Soft Ideals

2020 ◽  
pp. 91-104
Author(s):  
Shuker Khalil
Keyword(s):  
Social Science ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Sets ◽  
Real Life ◽  
Soft Sets ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Sets Theory

The basic notions of soft sets theory are introduced by Molodtsov to deal with uncertainties when solving problems in practice as in engineering, social science, environment, and economics. This notion is convenient and easy to apply as it is free from the difficulties that appear when using other mathematical tools as theory of theory of fuzzy sets, rough sets, and theory of vague sets. The soft set theory has recently gaining significance for finding rational and logical solutions to various real-life problems, which involve uncertainty, impreciseness, and vagueness. The concepts of intuitionistic fuzzy soft left almost semigroups and the intuitionistic fuzzy soft ideal are introduced in this chapter, and some of their basic properties are studied.

On Theory of Multisets and Applications

2016 ◽  
pp. 1-22
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Sets ◽  
Model Uncertainty ◽  
Rough Sets ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Current Status ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Mathematics ◽  
Basic Sets

Although multiple occurrences of elements are immaterial in sets, in real life situations repetition of elements is useful. So, the notion of multisets (also called as bags) was introduced, where repetition of elements is taken into account. Fuzzy set, intuitionistic (a misnomer here as intuitionistic mathematics has nothing to do with its fuzzy counterpart) fuzzy sets, rough sets and soft sets are extensions of the basic notion of sets as they model uncertainty in data. Following this multisets have been extended to fuzzy multisets, intuitionistic fuzzy sets, rough multisets and soft multisets. Many properties of basic sets have been extended to the context of multisets, fuzzy multisets, intuitionistic fuzzy sets, rough multisets and soft multisets. Several applications of different multisets mentioned above are found in literature. In this chapter, it is our aim to introduce the different concepts of multisets, their properties, current status and highlight their applications.

scholarly journals On Complex Intuitionistic Fuzzy Soft Sets with Distance Measures and Entropies

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Tanuj Kumar ◽  
Rakesh Kumar Bajaj
Keyword(s):  
Fuzzy Sets ◽  
Real Life ◽  
Multicriteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

We introduce the concept of complex intuitionistic fuzzy soft sets which is parametric in nature. However, the theory of complex fuzzy sets and complex intuitionistic fuzzy sets are independent of the parametrization tools. Some real life problems, for example, multicriteria decision making problems, involve the parametrization tools. In order to get their new entropies, some important properties and operations on the complex intuitionistic fuzzy soft sets have also been discussed. On the basis of some well-known distance measures, some new distance measures for the complex intuitionistic fuzzy soft sets have also been obtained. Further, we have established correspondence between the proposed entropies and the distance measures of complex intuitionistic fuzzy soft sets.

A Short Primer on the Correlation Coefficient of Vague Sets

2011 ◽  
Vol 1 (2) ◽  
pp. 55-69 ◽  
Author(s):  
John Robinson P. ◽  
Henry Amirtharaj E.C.
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Real Life ◽  
Detailed Comparison ◽  
Intuitionistic Fuzzy Sets ◽  
Vague Set ◽  
Practical Applications ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Life Problems

Intuitionistic fuzzy sets and vague sets are generalizations of the concept of fuzzy sets. Various researchers have studied the vagueness of data through vague sets, and it was later demonstrated that vague sets are indeed intuitionistic fuzzy sets. Since its entry in the literature, vague set theory has received increased attention. Many real life problems involve information in the form of vague values, due to the increasing complexity of the socio-economic environment and the vagueness of the inherent subjective nature of human thinking. Instead of using point-based membership as in fuzzy sets, interval-based membership is used in a vague set. This paper presents a detailed comparison between vague sets and intuitionistic fuzzy sets, from various perspectives of algebraic properties, graphical representations, and practical applications. Methods of calculating the correlation coefficient of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are already found in the literature. This paper defines the correlation coefficient of vague sets through simple examples.

scholarly journals Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Tool ◽  
Intuitionistic Fuzzy ◽  
Rough Approximation ◽  
Soft Rough Set

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach.

Soft Sets and Its Applications

2016 ◽  
pp. 65-85 ◽  
Author(s):  
B. K. Tripathy ◽  
K. R. Arun
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Practical Applications ◽  
Set Operations ◽  
New Models ◽  
Pros And Cons

Uncertainty is an inherent characteristic of modern day databases. In order to handle such databases with uncertainty, several new models have been introduced in the literature. Some new models like fuzzy sets introduced by Zadeh (1965), rough sets invented by Z. Pawlak (1982) and intuitionistic fuzzy sets extended by K.T. Atanassov (1986). All these models have their own pros and cons. However, one of the major problems with these models is the lack of sufficient number of parameters to deal with uncertainty. In order to add adequate number of parameters, soft set theory was introduced by Molodtsov in 1999. Since then the theoretical developments on soft set theory has attracted the attention of researchers. However, the practical applications of any theory are of enough importance to make use of it. In this chapter, the basic definitions of soft set, operations and properties are discussed. Also, the aim in this chapter is to discuss on the different applications of soft sets; like decision making, parameter reduction, data clustering and data dealing with incompleteness.

Interval-Valued Intuitionistic Fuzzy Sets based Method for Multiple Criteria Decision-Making

2016 ◽  
Vol 5 (4) ◽  
pp. 192-210 ◽  
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Due to the huge applications of fuzzy set theory, many generalizations were available in literature. Atanassov (1983) and Atanassov and Gargov (1989) introduced the notions of intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs) respectively. It is observed that IFSs and IVIFSs are more suitable tools for dealing with imprecise information and very powerful in modeling real life problems. However, many researchers made efforts to rank IVIFSs due to its importance in fusion of information. In this paper, a new ranking method is introduced and studied for IVIFSs. The proposed method is compared and illustrated with other existing methods by numerical examples. Then, it is utilized to identify the best alternative in multiple criteria decision-making problems in which criterion values for alternatives are IVIFSs. On the basis of the developed approach, it would provide a powerful way to the decision-makers to make his or her decision under IVIFSs. The validity and applicability of the proposed method are illustrated with practical examples.

Decision Making by Using Intuitionistic Fuzzy Rough Set

2017 ◽  
pp. 268-286
Author(s):  
T. K. Das
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Sets ◽  
Fuzzy Rough Set ◽  
Intuitionistic Fuzzy ◽  
Intelligent Technique

This chapter begins with a brief introduction of the theory of rough set. Rough set is an intelligent technique for handling uncertainty aspect in the data. This theory has been hybridized by combining with many other mathematical theories. In recent years, much decision making on rough set theory has been extended by embedding the ideas of fuzzy sets, intuitionistic fuzzy sets and soft sets. In this chapter, the notions of fuzzy rough set and intuitionistic fuzzy rough (IFR) sets are defined, and its properties are studied. Thereafter rough set on two universal sets has been studied. In addition, intuitionistic fuzzy rough set on two universal sets has been extensively studied. Furthermore, we would like to give an application, which shows that intuitionistic fuzzy rough set on two universal sets can be successfully applied to decision making problems.

Refined Neutrosophic Sets and Refined Neutrosophic Soft Sets

2016 ◽  
pp. 321-343 ◽  
Author(s):  
Irfan Deli
Keyword(s):  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Sets ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Formal Framework ◽  
Fuzzy Soft Sets ◽  
Intuitionistic Fuzzy Soft Sets

Refined neutrosophic sets (RNS) are a generalization of a neutrosophic sets, intuitionistic fuzzy sets, fuzzy sets, intuitionistic fuzzy multi-sets and fuzzy multi-sets. Similarly, refined neutrosophic soft sets (RNSS) are a generalization of a neutrosophic soft sets, intuitionistic fuzzy soft sets, fuzzy soft sets, intuitionistic fuzzy soft multi-sets and fuzzy soft multi-sets. These sets are a powerful general formal framework that has been proposed to present uncertainty, imprecise, incomplete, inaccurate and inconsistent information which exist in real life. This chapter will survey concept of RNS and concept of RNSS with basic definitions and will present an efficient approach for both RNS and RNSS. Also, the chapter will introduce an application of RNS in medical diagnosis problem, pattern recognition and an application of RNSS in decision making to illustrate the advantage of the proposed approach.

(α,β)-Soft Intersectional Rings and Ideals with their Applications

2019 ◽  
Vol 15 (02) ◽  
pp. 333-350 ◽  
Author(s):  
Chiranjibe Jana ◽  
Madhumangal Pal ◽  
Faruk Karaaslan ◽  
Aslihan Sezgi̇n
Keyword(s):  
Set Theory ◽  
Real Life ◽  
Ring Structure ◽  
Ring Theory ◽  
Mathematical Framework ◽  
Soft Sets ◽  
Life Problems ◽  
New Concepts ◽  
Ring Structures ◽  
Algebraic Tool

Molodtsov initiated the soft set theory, providing a general mathematical framework for handling uncertainties that we encounter in various real-life problems. The main object of this paper is to lay a foundation for providing a new soft algebraic tool for considering many problems that contain uncertainties. In this paper, we introduce a new kind of soft ring structure called [Formula: see text]-soft-intersectional ring based on some results of soft sets and intersection operations on sets. We also define [Formula: see text]-soft-intersectional ideal and [Formula: see text]-soft-intersectional subring, and investigate some of their properties using these new concepts. We obtain some results in ring theory based on [Formula: see text]-soft intersection sense and its application in ring structures. Furthermore, we provide relationships between soft-intersectional ring and [Formula: see text]-soft-intersectional ring, soft-intersectional ideal and [Formula: see text]-soft-intersectional ideal.

The Intuitionistic Fuzzy S-Rough Sets Model and Dynamic Transfer Degree

2014 ◽  
Vol 513-517 ◽  
pp. 4352-4356
Author(s):  
Jun Hong Hu ◽  
Guo Dong Gu ◽  
Fu Xian Liu
Keyword(s):  
Fuzzy Sets ◽  
Equivalence Relation ◽  
Fuzzy System ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Rough Sets Theory ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Characteristic ◽  
Sets Theory ◽  
System Movement

The Intuitionistic Fuzzy S-Rough Sets (IFS-RS) is the intuitionistic fuzzy extension of S-Rough sets theory. It has dynamic characteristic of S-Rough sets, as well as intuitionistic fuzzy characteristic of Intuitionistic Fuzzy sets. Based on S-Rough sets theory, this paper introduced the membership and non-membership concepts of Intuitionistic Fuzzy sets, builded the model of IFS-RS under general equivalence relation, put forward the rough property and transfer degree concepts of IFS-RS. By calculating the rough property and transfer degree of IFS-RS, Thus being able to describe the transformation degree of the elements in fuzzy system movement into or movement out more clearly and precisely.

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