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 An improvised similarity measure for generalized fuzzy numbers

2019 ◽  
Vol 8 (4) ◽  
pp. 1232-1238
Author(s):  
Daud Mohamad ◽  
Noorlisa Sara Adlene Ramlan ◽  
Sharifah Aniza Sayed Ahmad
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Numbers ◽  
Geometric Mean ◽  
Similarity Measures ◽  
Jaccard Index ◽  
Fuzzy Environment ◽  
Distance Methods ◽  
Generalized Fuzzy Numbers

Similarity measure between two fuzzy sets is an important tool for comparing various characteristics of the fuzzy sets. It is a preferred approach as compared to distance methods as the defuzzification process in obtaining the distance between fuzzy sets will incur loss of information. Many similarity measures have been introduced but most of them are not capable to discriminate certain type of fuzzy numbers. In this paper, an improvised similarity measure for generalized fuzzy numbers that incorporate several essential features is proposed. The features under consideration are geometric mean averaging, Hausdorff distance, distance between elements, distance between center of gravity and the Jaccard index. The new similarity measure is validated using some benchmark sample sets. The proposed similarity measure is found to be consistent with other existing methods with an advantage of able to solve some discriminant problems that other methods cannot. Analysis of the advantages of the improvised similarity measure is presented and discussed. The proposed similarity measure can be incorporated in decision making procedure with fuzzy environment for ranking purposes.

scholarly journals Similarity measures for Fermatean fuzzy sets and its applications in group decision-making

2022 ◽  
Vol 11 (2) ◽  
pp. 167-180
Author(s):  
Laxminarayan Sahoo
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Future Research ◽  
Uncertain Information

The intention of this paper is to propose some similarity measures between Fermatean fuzzy sets (FFSs). Firstly, we propose some score based similarity measures for finding similarity measures of FFSs and also propose score based cosine similarity measures between FFSs. Furthermore, we introduce three newly scored functions for effective uses of Fermatean fuzzy sets and discuss some relevant properties of cosine similarity measure. Fermatean fuzzy sets introduced by Senapati and Yager can manipulate uncertain information more easily in the process of multi-criteria decision making (MCDM) and group decision making. Here, we investigate score based similarity measures of Fermatean fuzzy sets and scout the uses of FFSs in pattern recognition. Based on different types of similarity measures a pattern recognition problem viz. personnel appointment is presented to describe the use of FFSs and its similarity measure as well as scores. The counterfeit results show that the proposed method is more malleable than the existing method(s). Finally, concluding remarks and the scope of future research of the proposed approach are given.

Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making

2021 ◽  
Vol 10 (1) ◽  
pp. 64-93
Author(s):  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Extended Family ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Optimal Point ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

scholarly journals New Entropy-Based Similarity Measure between Interval-Valued Intuitionstic Fuzzy Sets

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 73 ◽  
Author(s):  
Saida Mohamed ◽  
Areeg Abdalla ◽  
Robert John
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
New Approach ◽  
Interval Valued

In this paper, we propose a new approach to constructing similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiveness of the proposed formula. Finally, we use the new proposed similarity measure to develop a new approach for solving problems of pattern recognition and multi-criteria fuzzy decision-making.

Selection of an alternative based on interval-valued hesitant picture fuzzy sets

2021 ◽  
pp. 1-11
Author(s):  
Tabasam Rashid ◽  
M. Sarwar Sindhu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Multiple Criteria Decision Making ◽  
Similarity Measures ◽  
Hesitant Fuzzy Sets ◽  
Ambiguous Information ◽  
Cosine Similarity Measures ◽  
Picture Fuzzy Sets ◽  
Interval Valued ◽  
Selection Of

Motivated by interval-valued hesitant fuzzy sets (IVHFSs) and picture fuzzy sets (PcFSs), a notion of interval-valued hesitant picture fuzzy sets (IVHPcFSs) is presented in this article. The concept of IVHPcFSs is put forward and some operational rules are developed to deal with it. The cosine similarity measures (SMs) are modified for IVHPcFSs to deal with interval-valued hesitant picture fuzzy (IVHPcF) data and the linear programming (LP) methodology is used to find out the criteria’s weights. A multiple criteria decision making (MCDM) approach is then developed to tackle the vague and ambiguous information involved in MCDM problems under the framework of IVHPcFSs. For the validation and strengthen of the proposed MCDM approach a practical example is put forward to select the educational expert at the end.

scholarly journals n-Valued Refined Neutrosophic Soft Sets and their Applications in Decision Making Problems and Medical Diagnosis

2018 ◽  
Vol 8 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Ayman A. Hazaymeh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Numerical Example

Abstract In this work we use the concept of a ‘n’-valued refined neutrosophic soft sets and its properties to solve decision making problems, Also a similarity measure between two ‘n’-valued refined neutrosophic soft sets are proposed. A medical diagnosis (MD) method is established for ‘n’-valued refined neutrosophic soft set setting using similarity measures. Lastly a numerical example is given to demonstrate the possible application of similarity measures in medical diagnosis (MD).

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

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