A new multi-criteria decision making algorithm for medical diagnosis and classification problems using divergence measure of picture fuzzy sets

2019 ◽  
Vol 37 (6) ◽  
pp. 7785-7796 ◽  
Author(s):  
Nguyen Xuan Thao ◽  
Mumtaz Ali ◽  
Le Thi Nhung ◽  
Hemant Kumar Gianey ◽  
Florentin Smarandache
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Multi Criteria Decision Making ◽  
Divergence Measure ◽  
Classification Problems ◽  
Diagnosis And Classification ◽  
Picture Fuzzy Sets

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 DISSIMILARITY MEASURES ON PICTURE FUZZY SETS AND APPLICATIONS

2018 ◽  
Vol 34 (3) ◽  
pp. 219-231 ◽  
Author(s):  
Nhung Thi Le ◽  
Dinh Van Nguyen ◽  
Chau Minh Ngoc ◽  
Thao Xuan Nguyen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Supplier Selection ◽  
Intuitionistic Fuzzy Sets ◽  
Multi Criteria Decision Making ◽  
Dissimilarity Measures ◽  
Selection Problems ◽  
Mcdm Method ◽  
Picture Fuzzy Sets

The dissimilarity measures between fuzzy sets/intuitionistic fuzzy sets/picture fuzzy sets are studied and applied in various matters. In this paper, we propose some new dissimilarity measures on picture fuzzy sets. This new dissimilarity measures overcome the restrictions of all existing dissimilarity measures on picture fuzzy sets. After that, we apply these new measures to the pattern recognition problems. Finally, we introduce a multi-criteria decision making (MCDM) method that used the new dissimilarity measures and apply them in the supplier selection problems.

scholarly journals Unified Fuzzy Divergence Measures with Multi-Criteria Decision Making Problems for Sustainable Planning of an E-Waste Recycling Job Selection

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 90 ◽  
Author(s):  
Pratibha Rani ◽  
Kannan Govindan ◽  
Arunodaya Raj Mishra ◽  
Abbas Mardani ◽  
Melfi Alrasheedi ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Waste Recycling ◽  
Multi Criteria Decision Making ◽  
Divergence Measure ◽  
Divergence Measures ◽  
Job Selection ◽  
Sustainable Planning ◽  
Control Decision ◽  
Fuzzy Divergence

In the literature of information theory and fuzzy set doctrine, there exist various prominent measures of divergence; each possesses its own merits, demerits, and disciplines of applications. Divergence measure is a tool to compute the discrimination between two objects. Particularly, the idea of divergence measure for fuzzy sets is significant since it has applications in several areas viz., process control, decision making, image segmentation, and pattern recognition. In this paper, some new fuzzy divergence measures, which are generalizations of probabilistic divergence measures are introduced. Next, we review two different generalizations of the following measures. Firstly, directed divergence (Kullback–Leibler or Jeffrey invariant) and secondly, Jensen difference divergence, based on these measures, we develop a class of unified divergence measures for fuzzy sets (FSs). Then, a method based on divergence measure for fuzzy sets (FSs) is proposed to evaluate the multi-criteria decision-making (MCDM) problems under the fuzzy atmosphere. Lastly, an illustrative example of the recycling job selection problem of sustainable planning of the e-waste is presented to demonstrate the reasonableness and usefulness of the developed method.

A new multi-criteria decision-making method utilizing power heronian operators with picture hesitant fuzzy information

2021 ◽  
pp. 1-22
Author(s):  
Baolin Li ◽  
Lihua Yang ◽  
Jie Qian
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Distance Measure ◽  
Multi Criteria Decision Making ◽  
Comparison Analysis ◽  
Fuzzy Information ◽  
Hesitant Fuzzy Sets ◽  
Novel Method ◽  
Picture Fuzzy Sets

In practice, picture hesitant fuzzy sets (PHFSs) combining the picture fuzzy sets (PFSs) and hesitant fuzzy sets (HFSs) are suitable to represent more complex multi-criteria decision-making (MCDM) information. The power heronian (PH) operators, which have the merits of power average (PA) and heronian mean (HM) operators, are extended to the environment of PHFSs in this article. First, some algebraic operations of picture hesitant fuzzy numbers (PHFNs), comparative functions and distance measure are introduced. Second, two novel operators, called as picture hesitant fuzzy weighted power heronian (PHFWPH) operator and picture hesitant fuzzy weighted geometric power heronian (PHFWGPH) operator, are defined. Meanwhile, some desirable characteristics and special instances of two operators are investigated as well. Third, a novel MCDM approach applying the proposed PH operators to handle PHFNs is explored. Lastly, to indicate the effectiveness of this novel method, an example regarding MCDM problem is conducted, as well as sensitivity and comparison analysis.

scholarly journals A Novel Multi-Criteria Decision Making Method for Evaluating Water Reuse Applications under Uncertainty

2019 ◽  
Vol 1 (3) ◽  
pp. 230-239
Author(s):  
Nhung Thi Le ◽  
Thao Xuan Nguyen
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Water Reuse ◽  
Dissimilarity Measure ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Dissimilarity Measures ◽  
The World ◽  
Picture Fuzzy Sets ◽  
Selection Of

There are currently many places in the world where water is scarce. Therefore, water reuse has been mentioned by many researchers. Evaluation of water reuse applications is the selection of the best water reuse application of the existing options; it is also one of the applications of multi-criteria decision making (MCDM). In this paper, we introduce a new dissimilarity measure of picture fuzzy sets. This new measure overcomes the restriction of other existing dissimilarity measures of picture fuzzy sets. Then, we apply it to the multi-criteria decision making. Finally, we refer to a new method for selecting the best water reuse application of the available options by using the picture fuzzy MCDM.

Multi-criteria decision-making methods based on q-rung picture fuzzy information

2021 ◽  
pp. 1-26
Author(s):  
Muhammad Akram ◽  
Shumaiza
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Industrial Robot ◽  
Multi Criteria Decision Making ◽  
Compromise Solution ◽  
Fuzzy Information ◽  
Topsis Method ◽  
Vikor Method ◽  
Ideal Solutions ◽  
Picture Fuzzy Sets

 The q-rung picture fuzzy sets serve the fuzzy set theory as a competent, broader and accomplished extension of q-rung orthopair fuzzy sets and picture fuzzy sets which exhibit excellent performance in modeling the obscure data beyond the limits of existing approaches owing to the parameter q and three real valued membership functions. The accomplished strategy of VIKOR method is established on the major concepts of regret measure and group utility measure to specify the compromise solution. Further, TOPSIS method is another well established multi-criteria decision-making strategy that finds out the best solution with reference to the distances from ideal solutions. In this research study, we propose the innovative and modified versions of VIKOR and TOPSIS techniques using the numerous advantages of q-rung picture fuzzy information for obtaining the compromise results and rankings of alternatives in decision-making problems with the help of two different point-scales of linguistic variables. The procedure for the entropy weighting information is adopted to compute the normal weights of attributes. The q-rung picture fuzzy VIKOR (q-RPF VIKOR) method utilizes ascending order to rank the alternatives on the basis of maximum group utility and minimum individual regret of opponent. Moreover, a compromise solution is established by scrutinizing the acceptable advantage and the stability of decision. In the case of TOPSIS technique, the distances of alternatives to ideal solutions are determined by employing the Euclidean distance between q-rung picture fuzzy numbers. The TOPSIS method provides the ranking of alternatives by considering the descending order of closeness coefficients. For explanation, the presented methodologies are practiced to select the right housing society and the suitable industrial robot. The comparative results of the proposed techniques with four existing approaches are also presented to validate their accuracy and effectiveness.

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