scholarly journals Novel concepts of $ m $-polar spherical fuzzy sets and new correlation measures with application to pattern recognition and medical diagnosis

2021 ◽  
Vol 6 (10) ◽  
pp. 11346-11379
Author(s):  
Muhammad Riaz ◽  
◽  
Maryam Saba ◽  
Muhammad Abdullah Khokhar ◽  
Muhammad Aslam ◽  
...  
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Real Life ◽  
Hybrid Structure ◽  
Fuzzy Environment ◽  
Life Problems ◽  
Correlation Measures ◽  
Relationship Of

<abstract><p>In this paper, we introduce the notion of $ m $-polar spherical fuzzy set ($ m $-PSFS) which is a hybrid notion of $ m $-polar fuzzy set ($ m $-PFS) and spherical fuzzy set (SFS). The purpose of this hybrid structure is to express multipolar information in spherical fuzzy environment. An $ m $-PSFS is a new approach towards computational intelligence and multi-criteria decision-making (MCDM) problems. We introduce the novel concepts of correlation measures and weighted correlation measures of $ m $-PSFSs based on statistical notions of covariances and variances. Correlation measures estimate the linear relationship of the two quantitative objects. A correlation may be positive or negative depending on the direction of the relation between two objects and its value lies the interval $ [-1, 1] $. The same concept is carried out towards $ m $-polar spherical fuzzy ($ m $-PSF) information. We investigate certain properties of covariances and the correlation measures to analyze that these concepts are extension of crisp correlation measures. The main advantage of proposed correlation measures is that these notions deal with uncertainty in the real-life problems efficiently with the help of $ m $-PSF information. We discuss applications of $ m $-polar spherical fuzzy sets and their correlation measures in pattern recognition and medical diagnosis. To discuss the superiority and efficiency of proposed correlation measures, we give a comparison analysis of proposed concepts with some existing concepts.</p></abstract>

scholarly journals Correlation Measures for Cubic m-Polar Fuzzy Sets with Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Harish Garg ◽  
Muhammad Riaz ◽  
Muhammad Abdullah Khokhar ◽  
Maryam Saba
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
New Correlation ◽  
Robust Model ◽  
Operational Laws ◽  
Correlation Measures

A cubic m -polar fuzzy set (CmPFS) is a new hybrid extension of m -polar fuzzy set and cubic set. A CmPFS is a robust model to express multipolar information in terms of m fuzzy intervals representing membership grades and m fuzzy numbers representing nonmembership grades. In this article, we explore some new operational laws of CmPFSs, produce some related results, and discuss their consequences. We propose relative informational coefficients and relative noninformational coefficients for CmPFSs. These coefficients are analyzed to investigate further properties of CmPFSs. Based on these coefficients, we introduce new correlation measures and their weighted versions for CmPFSs. The value of proposed correlation measures is symmetrical and lies between −1 and 1. Moreover, the applications of the proposed correlation in pattern recognition and medical diagnosis are developed. The feasibility and efficiency of suggested correlation measures is determined by respective illustrative examples.

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 New Similarity Measure between Intuitionistic Fuzzy Multisets based on Tangent Function and its Application in Medical Diagnosis

2019 ◽  
Vol 8 (2S3) ◽  
pp. 161-165 ◽  
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Tangent Function

In recent years, Intuitionistic fuzzy set is very useful in decision making problems such as medical diagnosis, pattern recognition, clustering etc., which deals with vagueness and uncertainty. Similarity measure is a tool used to find the closeness of the intuitionistic fuzzy sets by considering the membership, nonmembership and hesitation function. In this paper, we propose an effective similarity measure based on tangent function for intuitionistic fuzzy multi sets in which membership, nonmembership, hesitation function occurs more than once and also we apply this measure in medical diagnosis and pattern recognition.

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.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

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.

Fuzzy sets in modeling of patient’s disease states

2019 ◽  
Vol 0 (9/2019) ◽  
pp. 5-11
Author(s):  
Andrzej Ameljańczyk
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Medical Diagnostics ◽  
Medical Data ◽  
Medical Decisions ◽  
Disease States ◽  
Definition Of ◽  
Disease Unit

The paper concerns the mathematical modeling of patient’s disease states and disease unit patterns for the needs of algorithms supporting medical decisions. Due to the specificity of medical data and assessments in the modeling of patient’s disease states as well as diseases, the fuzzy set methodology was used. The paper presents a number of new characteristics of fuzzy sets allowing to assess the quality of medical diagnosis. In addition, a definition of a multi-aspect fuzzy set is presented, which may be useful in supporting medical diagnostics based on multi-criteria similarity models. The presented results can be used in the construction of algorithms for assessing the patient's state of health and mainly in the construction of algorithms for supporting diagnostic processes.

scholarly journals A Dynamic Interval-Valued Intuitionistic Fuzzy Sets Applied to Pattern Recognition

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Zhenhua Zhang ◽  
Min Wang ◽  
Yong Hu ◽  
Jingyu Yang ◽  
Youpei Ye ◽  
...  
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Recognition Accuracy ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Simulation Results ◽  
Interval Valued

We present dynamic interval-valued intuitionistic fuzzy sets (DIVIFS), which can improve the recognition accuracy when they are applied to pattern recognition. By analyzing the degree of hesitancy, we propose some DIVIFS models from intuitionistic fuzzy sets (IFS) and interval-valued IFS (IVIFS). And then we present a novel ranking condition on the distance of IFS and IVIFS and introduce some distance measures of DIVIFS satisfying the ranking condition. Finally, a pattern recognition example applied to medical diagnosis decision making is given to demonstrate the application of DIVIFS and its distances. The simulation results show that the DIVIFS method is more comprehensive and flexible than the IFS method and the IVIFS method.

scholarly journals A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yafei Song ◽  
Xiaodan Wang ◽  
Lei Lei ◽  
Aijun Xue
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Axiomatic Definition

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

scholarly journals Jaccard and Dice Similarity Measures Based on Novel Complex Dual Hesitant Fuzzy Sets and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Tahir Mahmood ◽  
Ubaid Ur Rehman ◽  
Zeeshan Ali ◽  
Ronnason Chinram
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Real Life ◽  
Similarity Measures ◽  
Hesitant Fuzzy Set ◽  
The Novel ◽  
Dual Hesitant Fuzzy Set ◽  
Life Problems ◽  
Novel Approach ◽  
Operational Laws

Complex dual hesitant fuzzy set (CDHFS) is a combination of two modifications, called complex fuzzy set (CFS) and dual hesitant fuzzy set (DHFS). CDHFS makes two degrees, called membership valued and nonmembership valued in the form of a finite subset of a unit disc in the complex plane, and is a capable method to solve uncertain and unpredictable information in real-life problems. The goal of this study is to describe the notion of CDHFS and its operational laws. The novel approach of the complex interval-valued dual hesitant fuzzy set (CIvDHFS) and its fundamental laws are also described and defended with the help of an example. Further, the vector similarity measures (VSMs), weighted vector similarity measures (WVSMs), hybrid vector similarity measure, and weighted hybrid vector similarity measure are additionally explored. These similarity measures (SM) are applied to the environment of pattern recognition and medical diagnosis to assess the capability and feasibility of the interpreted measures. We additionally solved some numerical examples utilizing the established measures. We examine the dependability and validity of the proposed measures by comparing them with some existing measures. The advantages, comparative analysis, and graphical portrayal of the investigated interpreted measures and existing measures are additionally described in detail.

Sign in / Sign up

Export Citation Format

Share Document