scholarly journals Fermatean Hesitant Fuzzy Sets with Medical Decision Making Application

2022 ◽  
Author(s):  
Murat Kirişci
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Decision Making ◽  
Aggregation Operators ◽  
Hesitant Fuzzy Set ◽  
Medical Decision ◽  
Multi Criteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Mcdm Method

Abstract Fermatean fuzzy set idea obtained by combining fermatean fuzzy sets and hesitant fuzzy sets can be used in practice to simplify the solution of complicated multi-criteria decision-making (MCDM) problems. Initially, the notion of fermatean hesitant fuzzy set is given and the operations related to this concept are presented. Aggregation operators according to fermatean hesitant fuzzy sets are given and basic properties of these operators are studied. To choose the best alternative in practice, a novel MCDM method that is obtained with operators has been created. Finally, an example of infectious diseases was examined to indicate the effectiveness of the suggested techniques.

Cubic Hesitant Fuzzy Sets and Their Applications to Multi Criteria Decision Making

2016 ◽  
Vol 5 (1) ◽  
pp. 19 ◽  
Author(s):  
Faisal Mehmood ◽  
Tahir Mahmood ◽  
Qaisar Khan
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Decision Making Problem

In this paper we introduced cubic hesitant fuzzy set and defined internal (external) cubic hesitant fuzzy set, P(R)-union and P(R)-intersection of cubic hesitant fuzzy sets. Furthermore we defined P(R)-addition and P(R)-multiplication of cubic hesitant fuzzy sets. By using the defined operations of cubic hesitant fuzzy sets we proved their different results. We also defined R-weighted averaging and R-weighted geometric operators for cubic hesitant fuzzy sets and practiced it in multi-criteria decision making problem.

scholarly journals Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

2021 ◽  
Author(s):  
Faruk Karaaslan ◽  
Mohammed Allaw Dawood Dawood
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Two Dimensional ◽  
Weighted Arithmetic ◽  
Mcdm Method ◽  
Dombi Operations

AbstractComplex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

Graded Soft Expert Set as a Generalization of Hesitant Fuzzy Set

2018 ◽  
Vol 29 (1) ◽  
pp. 223-236
Author(s):  
Afshan Qayyum ◽  
Tanzeela Shaheen
Keyword(s):  
Decision Making ◽  
Decision Analysis ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Vital Role ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Relative Importance ◽  
Hesitant Fuzzy Sets

Abstract Hesitant fuzzy sets play a vital role in decision analysis. Although they have been proved to be a landmark in evaluating information, there are certain deficiencies in their structure. Also, in decision analysis with the aid of hesitant fuzzy sets, the relative importance of the decision makers according to their area of expertise is ignored completely, which may be misleading in some situations. These sorts of issues have been resolved in this work by using graded soft expert (GSE) sets. The proposed structure is a modified form of soft expert sets. Some basic operations have been introduced, and certain laws satisfied by them have carefully been investigated. With the aid of GSE sets, a decision-making algorithm (accompanied with an example) has been developed in which experts have been given due weightage according to their area of expertise.

scholarly journals New Distance Measures for Dual Hesitant Fuzzy Sets and Their Application to Multiple Attribute Decision Making

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 191
Author(s):  
Wang ◽  
Li ◽  
Zhang ◽  
Han
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Attribute Weights ◽  
Multiple Attribute

Multiple attribute decision making (MADM) is full of uncertainty and vagueness due to intrinsic complexity, limited experience and individual cognition. Representative decision theories include fuzzy set (FS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) and so on. Compared with IFS and HFS, DHFS has more advantages in dealing with uncertainties in real MADM problems and possesses good symmetry. The membership degrees and non-membership degrees in DHFS are simultaneously permitted to represent decision makers’ preferences by a given set having diverse possibilities. In this paper, new distance measures for dual hesitant fuzzy sets (DHFSs) are developed in terms of the mean, variance and number of elements in the dual hesitant fuzzy elements (DHFEs), which overcomes some deficiencies of the existing distance measures for DHFSs. The proposed distance measures are effectively applicable to solve MADM problems where the attribute weights are completely unknown. With the help of the new distance measures, the attribute weights are objectively determined, and the closeness coefficients of each alternative can be objectively obtained to generate optimal solution. Finally, an evaluation problem of airline service quality is conducted by using the distance-based MADM method to demonstrate its validity and applicability.

scholarly journals Convex Aggregation Operators and Their Applications to Multi-Hesitant Fuzzy Multi-Criteria Decision-Making

Information ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 207 ◽  
Author(s):  
Ye Mei ◽  
Juanjuan Peng ◽  
Junjie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Choquet Integral ◽  
Convex Combination ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Hesitant Fuzzy Sets ◽  
Novel Approach ◽  
Ordered Weighted Average

Hesitant fuzzy sets (HFSs), which were generalized from fuzzy sets, constrain the membership degree of an element to be a set of possible values between zero and one; furthermore, if two or more decision-makers select the same value, it is only counted once. However, a situation where the evaluation value is repeated several times differs from one where the value appears only once. Multi-hesitant fuzzy sets (MHFSs) can deal effectively with a case where some values are repeated more than once in a MHFS. In this paper, the novel convex combination of multi-hesitant fuzzy numbers (MHFNs) is introduced. Some aggregation operators based on convex operation, such as generalized multi-hesitant fuzzy ordered weighted average (GMHFOWA) operator, generalized multi-hesitant fuzzy hybrid weighted average (GMHFHWA) operator, generalized multi-hesitant fuzzy prioritized weighted average (GMHFPWA) operator and generalized multi-hesitant fuzzy Choquet integral weighted average (GMHFCIWA) operator, are developed and corresponding properties are discussed in detail. Then, based on the proposed aggregation operators, a novel approach for multi-criteria decision-making (MCDM) problem is proposed for ranking alternatives. Finally, an example is provided to verify the developed approach and demonstrate its validity and feasibility and the study is supported by a sensitivity analysis and a comparison analysis.

The cross-entropy and improved distance measures for complex q-rung orthopair hesitant fuzzy sets and their applications in multi-criteria decision-making

2021 ◽  
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Cross Entropy ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Pythagorean Fuzzy Set ◽  
The Real

AbstractThe complex q-rung orthopair fuzzy set (Cq-ROFS) is the extension of complex Pythagorean fuzzy set (CPFS) in which the sum of the q-power of the real part (imaginary part) of the support for and the q-power of the real part (imaginary part) of the support against is limited by one; however, it is difficult to express the hesitant information. In this study, the conception of complex q-rung orthopair hesitant fuzzy set (Cq-ROHFS) by combining the Cq-ROFS and hesitant fuzzy set (HFS) is proposed, and its properties are discussed, obviously, Cq-ROHFS can reflect the uncertainties in structure and in detailed evaluations. Further, some distance measures (DMs) and cross-entropy measures (CEMs) are developed based on complex multiple fuzzy sets. Moreover, these proposed measures are utilized to solve a multi-criteria decision-making problem based on TOPSIS (technique for order preference by similarity to ideal solution) method. Then, the advantages and superiority of the proposed measures are explained by the experimental results and comparisons with some existing methods.

scholarly journals Multicriteria Group Decision Making by Using Trapezoidal Valued Hesitant Fuzzy Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Tabasam Rashid ◽  
Syed Muhammad Husnine
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Order Preference ◽  
Multicriteria Group Decision Making

The concept of trapezoidal valued hesitant fuzzy set is introduced. Notion for distance between any two trapezoidal valued hesitant fuzzy elements is given. Using this proposed distance measure, we extend the technique for order preference by similarity to ideal solution for trapezoidal valued hesitant fuzzy sets. An example is constructed to show usefulness of this extension for multicriteria group decision making, where the opinions about the criteria values are expressed as trapezoidal valued hesitant fuzzy set.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

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.

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