scholarly journals Improved cosine and cotangent function-based similarity measures for q-rung orthopair fuzzy sets and TOPSIS method

2021 ◽  
Author(s):  
Muhammad Jabir Khan ◽  
Poom Kumam ◽  
Nasser Aedh Alreshidi ◽  
Wiyada Kumam
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Similarity Measures ◽  
Topsis Method ◽  
Inclusion Relation ◽  
Strict Inclusion ◽  
Numerical Examples ◽  
Ideal Solutions ◽  
Relative Ideal

AbstractDespite the importance of cosine and cotangent function- based similarity measures, the literature has not provided a satisfactory formulation for the case of q-rung orthopair fuzzy set (qROFS). This paper criticizes the existing attempts in terms of respect of the basic axioms of a similarity measure and strict inclusion relation. In addition, the maximum operator-based similarity measures are criticized. Then, new improved, axiomatically supported cosine and cotangent function-based similarity measures for qROFSs are proposed. Additional properties of the new similarity measures are discussed to guarantee their good performance. Two algorithmic procedures of TOPSIS method that based on fixed and relative ideal solutions are discussed. The numerical examples are provided to support the findings

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.

A New Similarity Measure of Intuitionistic Fuzzy Sets Considering Abstention Group Influence and Its Applications

2016 ◽  
Vol 25 (2) ◽  
pp. 197-208 ◽  
Author(s):  
Bei Zhou
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Group Decision ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Group Influence ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Group A ◽  
Multicriteria Group Decision Making

AbstractThe issue of similarity measures of intuitionistic fuzzy sets (IFSs) is considered in this paper. Many existing similarity measures for two IFSs fail to take the abstention group influence into consideration and may lead to counterintuitive results in some cases. To deal with the problem, this paper first discusses the limitations of the existing similarity measures by some numerical examples, then, by considering the influence of abstention group, a new similarity measure of intuitionistic fuzzy sets is proposed, and the same numerical examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition, multicriteria group decision making, and medical diagnosis.

scholarly journals A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 441 ◽  
Author(s):  
Minxia Luo ◽  
Jingjing Liang
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

scholarly journals Distance and Similarity Measures for Spherical Fuzzy Sets and Their Applications in Selecting Mega Projects

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 519 ◽  
Author(s):  
Muhammad Jabir Khan ◽  
Poom Kumam ◽  
Wejdan Deebani ◽  
Wiyada Kumam ◽  
Zahir Shah
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Similarity Measures ◽  
Developed Countries ◽  
Distance Measures ◽  
Membership Functions ◽  
Pythagorean Fuzzy Set ◽  
Picture Fuzzy Set

A new condition on positive membership, neutral membership, and negative membership functions give us the successful extension of picture fuzzy set and Pythagorean fuzzy set and called spherical fuzzy sets ( SFS ) . This extends the domain of positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measure and application in data mining, medical diagnosis, decision making, and pattern recognition, several studies on similarity measures have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we proposed the set-theoretic similarity and distance measures. We provide some counterexamples for already proposed similarity measures in the literature and shows that how our proposed method is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for selecting mega projects in under developed countries.

scholarly journals Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

2021 ◽  
Vol 7 (3) ◽  
pp. 3866-3895
Author(s):  
Atiqe Ur Rahman ◽  
◽  
Muhammad Saeed ◽  
Hamiden Abd El-Wahed Khalifa ◽  
Walaa Abdullah Afifi ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Approximate Function

<abstract><p>Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.</p></abstract>

A New Similarity Measure of Picture Fuzzy Sets And Application in pattern recognition

2020 ◽  
pp. 5-18
Author(s):  
Ngoc Minh Chau, Nguyen Thi Lan, Nguyen Xuan Thao ◽  
Keyword(s):  
Pattern Recognition ◽  
Fault Diagnosis ◽  
Fuzzy Sets ◽  
Steam Turbine ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Similarity Measures ◽  
The Novel ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets

In this paper, we propose some novel similarity measures between picture fuzzy sets. The novel similarity measure is constructed by combining negative functions of each degree membership of picture fuzzy set. We apply them in several pattern recognition problems. Finally, we apply them to find the fault diagnosis of the steam turbine.

Novel similarity measures and multi-expert TOPSIS method using picture m-polar fuzzy sets

2021 ◽  
pp. 1-16
Author(s):  
Dliouah Ahmed ◽  
Binxiang Dai
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Alternative Solution ◽  
Topsis Method ◽  
Numerical Example ◽  
Picture Fuzzy Sets

In this paper, we give a new notion of the picture m-polar fuzzy sets (Pm-PFSs) (i.e, combination between the picture fuzzy sets (PFSs) and the m-polar fuzzy sets (m-PFSs)) and study several of the structure operations including subset, equal, union, intersection, and complement. After that, the basic definitions, theorems, and examples on Pm-PFSs are explained. Also, the certain distance between two Pm-PFSs and a novel similarity measure for Pm-PFSs based on distances are defined. MCDM is animated for Pm-PFS data that take into account the distances for the best alternative (solution) by proposed an application of similarity measure for Pm-PFSs in decision-making. Finally, we construct a new methodology to extend the TOPSIS to Pm-PFS in which capable of different objects recognizing belonging to the same family and illustrate its applicability via a numerical example.

scholarly journals New Similarity Measures of Intuitionistic Fuzzy Sets

2007 ◽  
Vol 11 (2) ◽  
pp. 202-209 ◽  
Author(s):  
Hassan Rezaei ◽  
◽  
Masao Mukaidono
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Suitable Combination ◽  
Thinking Process ◽  
Human Thinking ◽  
The Relationship

In this review of existing similarity measures of intuitionistic fuzzy sets (IFSs), we apply some numerical examples showing that not all existing similarity measures are effective and reasonable in some cases. We propose properties based on intuition and the human thinking process that should be satisfied by all dissimilarity and similarity measures, together with new similarity measures of IFSs that overcome drawbacks of existing measures. In examples, we compare the proposed similarity measures to existing measures and present two propositions on the relationship between similarity and dissimilarity measures of IFSs. We also propose that a suitable combination of similarity measures may be a similarity measure.

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 Evaluation of Investment Opportunities With Interval-Valued Fuzzy Topsis Method

2020 ◽  
Vol 5 (1) ◽  
pp. 461-474 ◽  
Author(s):  
Naiyer Mohammadi Lanbaran ◽  
Ercan Celik ◽  
Muhammed Yiğider
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Estimation Error ◽  
Fuzzy Topsis ◽  
Optimal Choice ◽  
Topsis Method ◽  
Relative Closeness ◽  
Ideal Solutions ◽  
Fuzzy Logic Theory ◽  
Interval Valued

AbstractThe purpose of this study is extended the TOPSIS method based on interval-valued fuzzy set in decision analysis. After the introduction of TOPSIS method by Hwang and Yoon in 1981, this method has been extensively used in decision-making, rankings also in optimal choice. Due to this fact that uncertainty in decision-making and linguistic variables has been caused to develop some new approaches based on fuzzy-logic theory. Indeed, it is difficult to achieve the numerical measures of the relative importance of attributes and the effects of alternatives on the attributes in some cases. In this paper to reduce the estimation error due to any uncertainty, a method has been developed based on interval-valued fuzzy set. In the suggested TOPSIS method, we use Shannon entropy for weighting the criteria and apply the Euclid distance to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s) can be selected in the decision-making process.

Sign in / Sign up

Export Citation Format

Share Document