scholarly journals Analysis of medical diagnosis based on variation co-efficient similarity measures under picture hesitant fuzzy sets and their application

2022 ◽  
Vol 19 (1) ◽  
pp. 855-872
Author(s):  
Zeeshan Ali ◽  
◽  
Tahir Mahmood ◽  
Hussain AlSalman ◽  
Bader Fahad Alkhamees ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Hesitant Fuzzy Sets ◽  
Flexible Parts ◽  
The Stability ◽  
Vague Data

<abstract> <p>One of the most dominant and feasible technique is called the PHF setting is exist in the circumstances of fuzzy set theory for handling intricate and vague data in genuine life scenario. The perception of PHF setting is massive universal is compared to these assumptions, who must cope with two or three sorts of data in the shape of singleton element. Under the consideration of the PHF setting, we utilized some SM in the region of the PHF setting are to diagnose the PHFDSM, PHFWDSM, PHFJSM, PHFWJSM, PHFCSM, PHFWCSM, PHFHVSM, PHFWHVSM and demonstrated their flexible parts. Likewise, a lot of examples are exposed under the invented measures based on PHF data in the environment of medical diagnosis to demonstrate the stability and elasticity of the explored works. Finally, the sensitive analysis of the presented works is also implemented and illuminated their graphical structures.</p> </abstract>

Reliability Analysis for Environment Systems Using Dual Hesitant Fuzzy Set

2019 ◽  
pp. 162-173 ◽  
Author(s):  
Akshay Kumar ◽  
Mangey Ram
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Reliability Function ◽  
Hesitant Fuzzy Set ◽  
Electronic Systems ◽  
Hesitant Fuzzy Sets ◽  
Fuzzy Reliability ◽  
Dual Hesitant Fuzzy Set

In this chapter, we deal with dual hesitant fuzzy set theory and compute the fuzzy reliability with lifetime components of different electronic systems, such as series and parallel systems from a Markov chain technique. In dual hesitant fuzzy sets, we have membership and non-membership degree function whereas hesitant fuzzy sets only have membership function. In this chapter we also discuss the Weibull distribution and reliability function of the proposed systems. A numerical example is also given in the end of proposed algorithm.

scholarly journals Index Number of Multi Fuzzy Sets

2019 ◽  
Vol 8 (4) ◽  
pp. 2873-2876
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Medical Diagnosis ◽  
Index Number ◽  
Political Leaders ◽  
Diagnosis System ◽  
Medical Diagnosis System ◽  
Diagnosis Of Diseases

Multi fuzzy set theory is an extension of fuzzy set theory. In this paper we developing the theory of Index number of multi fuzzy sets. This theory is applied to medical diagnosis system and will help doctors to select the effective symptoms and could make diagnosis of diseases concern. This theory also helps in selecting right political leaders.

scholarly journals An Improved Correlation Coefficient of Intuitionistic Fuzzy Sets

2019 ◽  
Vol 28 (2) ◽  
pp. 231-243 ◽  
Author(s):  
Han-Liang Huang ◽  
Yuting Guo
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Abstract The intuitionistic fuzzy set is a useful tool to deal with vagueness and uncertainty. Correlation coefficient of the intuitionistic fuzzy sets is an important measure in intuitionistic fuzzy set theory and has great practical potential in a variety of areas, such as decision making, medical diagnosis, pattern recognition, etc. In this paper, an improved correlation coefficient of the intuitionistic fuzzy sets is defined, and it can overcome some drawbacks of the existing ones. The properties of this correlation coefficient are discussed. Then, the generalization of the coefficient of interval-valued intuitionistic fuzzy sets is also introduced. Finally, two examples about the application of the proposed correlation coefficient of the intuitionistic fuzzy sets in medical diagnosis and clustering are shown to illustrate the advantages over the existing methods.

New distance and similarity measures for hesitant fuzzy sets and their application in hierarchical clustering

2020 ◽  
Vol 39 (3) ◽  
pp. 4349-4360
Author(s):  
Kamran Rezaei ◽  
Hassan Rezaei
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
The Other ◽  
Hesitant Fuzzy Set ◽  
Membership Degree ◽  
Hesitant Fuzzy Sets ◽  
Variation Range

The hesitant fuzzy sets (HFSs) are an extension of the classical fuzzy sets. The membership degree of each element in a hesitant fuzzy set can be a set of possible values in the interval [0,1]. On the other hand, distance and similarity measures are important tools in several applications such as pattern recognition, clustering, medical diagnosis, etc. Hence, numerous studies have focused on investigating distance and similarity measures for HFSs. In this paper, some improved distance and similarity measures are introduced for the HFSs, considering the variation range as a hesitance degree for these sets. Comparing the proposed measures to some available distance and similarity measures indicated the better results of the proposed measures. Finally, the application of the proposed measures was investigated in the clustering.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

2021 ◽  
pp. 1-17
Author(s):  
Changlin Xu ◽  
Juhong Shen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
New Method ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

scholarly journals A method for classification of red, blue, and green galaxies using fuzzy set theory

2020 ◽  
Vol 499 (1) ◽  
pp. L31-L35
Author(s):  
Biswajit Pandey
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Sloan Digital Sky Survey ◽  
Sky Survey ◽  
Blue Galaxies ◽  
Boundary Sets ◽  
Red Galaxies

ABSTRACT Red and blue galaxies are traditionally classified using some specific cuts in colour or other galaxy properties, which are supported by empirical arguments. The vagueness associated with such cuts are likely to introduce a significant contamination in these samples. Fuzzy sets are vague boundary sets that can efficiently capture the classification uncertainty in the absence of any precise boundary. We propose a method for classification of galaxies according to their colours using fuzzy set theory. We use data from the Sloan Digital Sky Survey (SDSS) to construct a fuzzy set for red galaxies with its members having different degrees of ‘redness’. We show that the fuzzy sets for the blue and green galaxies can be obtained from it using different fuzzy operations. We also explore the possibility of using fuzzy relation to study the relationship between different galaxy properties and discuss its strengths and limitations.

Fuzzy Logic in the Broad Sense

2017 ◽  
Author(s):  
Radim Bělohlávek ◽  
Joseph W. Dauben ◽  
George J. Klir
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Human Reasoning ◽  
Human Beings ◽  
Real Numbers ◽  
New Directions ◽  
Gradual Development

The chapter begins by introducing the important and useful distinction between the research agendas of fuzzy logic in the narrow and the broad senses. The chapter deals with the latter agenda, whose ultimate goal is to employ intuitive fuzzy set theory for emulating commonsense human reasoning in natural language and other unique capabilities of human beings. Restricting to standard fuzzy sets, whose membership degrees are real numbers in the unit interval [0,1], the chapter describes how this broad agenda has become increasingly specific via the gradual development of standard fuzzy set theory and the associated fuzzy logic. An overview of currently recognized nonstandard fuzzy sets, which open various new directions in fuzzy logic, is presented in the last section of this chapter.

scholarly journals Fuzzy Set Theory and Topos Theory

1986 ◽  
Vol 29 (4) ◽  
pp. 501-508 ◽  
Author(s):  
Michael Barr
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Topos Theory

AbstractThe relation between the categories of Fuzzy Sets and that of Sheaves is explored and the precise connection between them is explicated. In particular, it is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant categories are indeed toposes.

FUZZY SETS AND FUZZY RELATIONAL STRUCTURES AS CHU SPACES

2000 ◽  
Vol 08 (04) ◽  
pp. 471-479 ◽  
Author(s):  
BASIL K. PAPADOPOULOS ◽  
APOSTOLOS SYROPOULOS
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Linear Logic ◽  
Relational Structure ◽  
Mathematical Structures ◽  
Relational Structures ◽  
Chu Spaces

Chu spaces, which derive from the Chu construct of *-autonomous categories, can be used to represent most mathematical structures. Moreover, the logic of Chu spaces is linear logic. Most efforts to incorporate fuzzy set theory into the realm of linear logic are based on the assumption that fuzzy and linear negation are identical operations. We propose an incorporation based on the opposite assumption and we provide an interpretation of some linear connectives. Furthermore, we show that it is possible to represent any fuzzy relational structure as a Chu space by means of the functor G.

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