scholarly journals A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 436
Author(s):  
Ruirui Zhao ◽  
Minxia Luo ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Distance Measures ◽  
Numerical Comparison ◽  
Mathematical Tool ◽  
Practical Applications ◽  
Fuzzy Point ◽  
Point Operator ◽  
The Difference ◽  
Picture Fuzzy Sets

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

Some Measures of Picture Fuzzy Sets and Their Application

2017 ◽  
Vol 3 (2) ◽  
pp. 35
Author(s):  
Nguyen Van Dinh ◽  
Nguyen Xuan Thao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Dissimilarity Measure ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
The Difference ◽  
Picture Fuzzy Sets

To measure the difference of two fuzzy sets (FSs) / intuitionistic sets (IFSs), we can use the distance measure and dissimilarity measure between fuzzy sets/intuitionistic fuzzy set. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide  the formulas for determining these values. We also present an application of dissimilarity measures in the sample recognition problems, can also be considered a decision-making problem.

Medical Diagnosis Based on Distance Measures Between Picture Fuzzy Sets

2018 ◽  
Vol 7 (4) ◽  
pp. 15-36 ◽  
Author(s):  
Palash Dutta
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Partial Information ◽  
Distance Measures ◽  
Medical Decision ◽  
Mathematical Tool ◽  
Membership Degree ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets

This article describes how most frequently uncertainty arises due to vagueness, imprecision, partial information, etc., are encountered in medical diagnosis. To deal with this type of uncertainty, initially fuzzy set theory (FST) was explored and accordingly, medical decision making became one of the most important and interesting areas of applications of FST. Interval valued fuzzy sets (IVFSs) and intuitionistic fuzzy sets (IFS's) were developed and successfully applied in different areas including medical diagnosis. Although, IFS forms a membership degree and a non-membership degree separately in such a way that sum of the two degrees must not exceed one, but one of the important and integral part i.e., degree of neutrality is not taken into consideration in IFS, which is generally occurred in medical diagnosis. In such circumstances, picture fuzzy set (PFS) can be considered as a strong mathematical tool, which adequate in situations when human opinions involved more answers of type: yes, abstain, no. For this purpose, this article, proposes some distance measures on PFS and studies some of its properties. Also, an attempt has been made to carry out medical diagnosis via the proposed distance measures on PFSs and exhibit the technique with a suitable case study. It is found that the distance measures make it possible to introduce weights of all symptoms and consequently patient can be diagnosed directly.

scholarly journals A Consistency Check Method for Trusted Hesitant Fuzzy Sets with Confidence Levels Based on a Distance Measure

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Huimin Xiao ◽  
Meiqi Wang ◽  
Xiaoning Xi
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Consistency Check ◽  
Hesitant Fuzzy Sets ◽  
Numerical Examples ◽  
Confidence Levels ◽  
Check Method ◽  
The Difference

This paper proposes a consistency check method for hesitant fuzzy sets with confidence levels by employing a distance measure. Firstly, we analyze the difference between each fuzzy element and its corresponding attribute comprehensive decision value and then obtain a comprehensive distance measure for each attribute. Subsequently, by taking the relative credibility as the weight, we assess the consistency of hesitant fuzzy sets. Finally, numerical examples are put forward to verify the effectiveness and reliability of the proposed method.

scholarly journals A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 142 ◽  
Author(s):  
Qianli Zhou ◽  
Hongming Mo ◽  
Yong Deng
Keyword(s):  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Distance Measure ◽  
Belief Function ◽  
Intuitionistic Fuzzy Sets ◽  
Divergence Measure ◽  
Pythagorean Fuzzy Sets ◽  
Practical Applications ◽  
Intuitionistic Fuzzy ◽  
Jensen Shannon Divergence

As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

scholarly journals A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers

2010 ◽  
Vol 2010 ◽  
pp. 1-25 ◽  
Author(s):  
Debashree Guha ◽  
Debjani Chakraborty
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Theoretical Development ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Intuitionistic Fuzzy

The objective of this paper is to introduce a distance measure for intuitionistic fuzzy numbers. Firstly the existing distance measures for intuitionistic fuzzy sets are analyzed and compared with the help of some examples. Then the new distance measure for intuitionistic fuzzy numbers is proposed based on interval difference. Also in particular the type of distance measure for triangle intuitionistic fuzzy numbers is described. The metric properties of the proposed measure are also studied. Some numerical examples are considered for applying the proposed measure and finally the result is compared with the existing ones.

scholarly journals A Vectorial Tree Distance Measure

2021 ◽  
Author(s):  
Avner Priel ◽  
Boaz Tamir
Keyword(s):  
Phylogenetic Trees ◽  
Distance Measure ◽  
Lexicographic Order ◽  
Distance Measures ◽  
Tree Distance ◽  
Hierarchical Trees ◽  
Distance Vector ◽  
The Difference ◽  
Number Of Branches

Abstract A vectorial distance measure for trees is presented. Given two trees, we align the trees from their centers outwards, starting from the root-branches, to make the next level as similar as possible. The algorithm is recursive; condition on the alignment of the root-branches we align the sub-branches, thereafter each alignment is conditioned on the previous one. We define a minimal alignment under a lexicographic order which follows the intuition that the differences between the two trees closer to their cores dominate their differences at a higher level. Given such a minimal alignment, the difference in the number of branches calculated at any level defines the entry of the distance vector at that level. We compare our algorithm to other well-known tree distance measures in the task of clustering sets of phylogenetic trees. We use the TreeSimGM simulator for generating stochastic phylogenetic trees. The vectorial tree distance can successfully separate symmetric from asymmetric trees, and hierarchical from non-hierarchical trees.

scholarly journals A new divergence measure of interval-valued pythagorean fuzzy sets and its application

2021 ◽  
Vol 5 (2) ◽  
pp. 9-24
Author(s):  
Arthi N ◽  
Mohana K
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Evidence Theory ◽  
Belief Function ◽  
Divergence Measure ◽  
Pythagorean Fuzzy Sets ◽  
Practical Applications ◽  
Basic Probability ◽  
Jensen Shannon Divergence ◽  
Interval Valued

As the extension of the Fuzzy sets (FSs) theory, the Interval-valued Pythagorean Fuzzy Sets (IVPFS) was introduced which play an important role in handling the uncertainty. The Pythagorean fuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Interval-valued Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Interval-valued Pythagorean fuzzy sets,which is based on the belief function in Dempster–Shafer evidence theory, and is called IVPFSDM distance. It describes the Interval-Valued Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of IVPFSs, which is the step in establishing a link between the IVPFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1147-1160
Author(s):  
Yali Cheng ◽  
Yonghong Li ◽  
Jie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Linguistic Intuitionistic Fuzzy Sets ◽  
Linguistic Scale Function ◽  
Different Response

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

scholarly journals New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 429 ◽  
Author(s):  
Di Ke ◽  
Yafei Song ◽  
Wen Quan
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Research Area ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
The Difference ◽  
Atanassov’S Intuitionistic Fuzzy Sets

The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov’s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.

scholarly journals An innovative picture fuzzy distance measure and novel multi-attribute decision-making method

2021 ◽  
Author(s):  
Abdul Haseeb Ganie ◽  
Surender Singh
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Real Data ◽  
Distance Measures ◽  
Classification Problems ◽  
Data Set ◽  
The Real ◽  
Picture Fuzzy Set ◽  
Multi Attribute Decision Making

AbstractPicture fuzzy set (PFS) is a direct generalization of the fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). The concept of PFS is suitable to model the situations that involve more answers of the type yes, no, abstain, and refuse. In this study, we introduce a novel picture fuzzy (PF) distance measure on the basis of direct operation on the functions of membership, non-membership, neutrality, refusal, and the upper bound of the function of membership of two PFSs. We contrast the proposed PF distance measure with the existing PF distance measures and discuss the advantages in the pattern classification problems. The application of fuzzy and non-standard fuzzy models in the real data is very challenging as real data is always found in crisp form. Here, we also derive some conversion formulae to apply proposed method in the real data set. Moreover, we introduce a new multi-attribute decision-making (MADM) method using the proposed PF distance measure. In addition, we justify necessity of the newly proposed MADM method using appropriate counterintuitive examples. Finally, we contrast the performance of the proposed MADM method with the classical MADM methods in the PF environment.

Sign in / Sign up

Export Citation Format

Share Document