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.

scholarly journals Decision-Making Analysis Based on Fermatean Fuzzy Yager Aggregation Operators with Application in COVID-19 Testing Facility

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Harish Garg ◽  
Gulfam Shahzadi ◽  
Muhammad Akram
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Weighted Average ◽  
Fuzzy Topsis ◽  
Aggregation Operators ◽  
Topsis Method ◽  
Research Article ◽  
Testing Facility ◽  
Ordered Weighted Average ◽  
Excellent Tool

This research article is devoted to establish some general aggregation operators, based on Yager’s t-norm and t-conorm, to cumulate the Fermatean fuzzy data in decision-making environments. The Fermatean fuzzy sets (FFSs), an extension of the orthopair fuzzy sets, are characterized by both membership degree (MD) and nonmembership degree (NMD) that enable them to serve as an excellent tool to represent inexact human opinions in the decision-making process. In this article, the valuable properties of the FFS are merged with the Yager operator to propose six new operators, namely, Fermatean fuzzy Yager weighted average (FFYWA), Fermatean fuzzy Yager ordered weighted average (FFYOWA), Fermatean fuzzy Yager hybrid weighted average (FFYHWA), Fermatean fuzzy Yager weighted geometric (FFYWG), Fermatean fuzzy Yager ordered weighted geometric (FFYOWG), and Fermatean fuzzy Yager hybrid weighted geometric (FFYHWG) operators. A comprehensive discussion is made to elaborate the dominant properties of the proposed operators. To verify the importance of the proposed operators, an MADM strategy is presented along with an application for selecting an authentic lab for the COVID-19 test. The superiorities of the proposed operators and limitations of the existing operators are discussed with the help of a comparative study. Moreover, we have explained comparison between the proposed theory and the Fermatean fuzzy TOPSIS method to check the accuracy and validity of the proposed operators. The influence of various values of the parameter in the Yager operator on decision-making results is also examined.

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.

scholarly journals METHODS FOR PROBABILISTIC DECISION MAKING WITH LINGUISTIC INFORMATION

2014 ◽  
Vol 20 (2) ◽  
pp. 193-209 ◽  
Author(s):  
Guiwu Wei ◽  
Xiaofei Zhao
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Owa Operator ◽  
Linguistic Information ◽  
Probabilistic Information ◽  
Ordered Weighted Average ◽  
Linguistic Labels ◽  
Selection Of

With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with linguistic labels, some new decision analysis are proposed. Firstly, we shall develop three new aggregation operators: generalized probabilistic 2-tuple weighted average (GP-2TWA) operator, generalized probabilistic 2-tuple ordered weighted average (GP-2TOWA) operator and generalized immediate probabilistic 2-tuple ordered weighted average (GIP-2TOWA) operator. These operators use the weighted average (WA) operator, the ordered weighted average (OWA) operator, linguistic information, probabilistic information and immediate probabilistic information. They are quite useful because they can assess the uncertain information within the problem by using both linguistic labels and the probabilistic information that considers the attitudinal character of the decision maker. In these approaches, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.

New Einstein Hybrid Aggregation Operators for Intuitionistic Fuzzy Sets and Applications in Multi-Criteria Decision-Making

2019 ◽  
pp. 252-283
Author(s):  
Bhagawati Prasad Joshi ◽  
Abhay Kumar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Decision Maker ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Processes

The fusion of multidimensional intuitionistic fuzzy information plays an important part in decision making processes under an intuitionistic fuzzy environment. In this chapter, it is observed that existing intuitionistic fuzzy Einstein hybrid aggregation operators do not follow the idempotency and boundedness. This leads to sometimes illogical and even absurd results to the decision maker. Hence, some new intuitionistic fuzzy Einstein hybrid aggregation operators such as the new intuitionistic fuzzy Einstein hybrid weighted averaging (IFEHWA) and the new intuitionistic fuzzy Einstein hybrid weighted geometric (IFEHWG) were developed. The new IFEHWA and IFEHWG operators can weigh the arguments as well as their ordered positions the same as the intuitionistic fuzzy Einstein hybrid aggregation operators do. Further, it is validated that the defined operators are idempotent, bounded, monotonic and commutative. Then, based on the developed approach, a multi-criteria decision-making (MCDM) procedure is given. Finally, a numerical example is conducted to demonstrate the proposed method effectively.

scholarly journals Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

2019 ◽  
Vol 10 (1) ◽  
pp. 276
Author(s):  
Saleem Abdullah ◽  
Omar Barukab ◽  
Muhammad Qiyas ◽  
Muhammad Arif ◽  
Sher Afzal Khan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Comparison Analysis ◽  
Practical Application ◽  
Multiple Attribute ◽  
Ordered Weighted Average ◽  
Selection For ◽  
Fuzzy Linguistic

The aim of this paper is to propose the 2-tuple spherical fuzzy linguistic aggregation operators and a decision-making approach to deal with uncertainties in the form of 2-tuple spherical fuzzy linguistic sets. 2-tuple spherical fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a numbers of aggregation operators, namely 2-tuple spherical fuzzy linguistic weighted average, 2-tuple spherical fuzzy linguistic ordered weighted average, 2-tuple spherical fuzzy linguistic hybrid average, 2-tuple spherical fuzzy linguistic weighted geometric, 2-tuple spherical fuzzy linguistic ordered geometric, and 2-tuple spherical fuzzy linguistic hybrid geometric operators. The distinguishing feature of these proposed operators is studied. At that point, we have used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple spherical fuzzy linguistic information. Then, a practical application for best company selection for feeds is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantage of our method. Results indicate that the proposed method is suitable and effective for decision making problems.

On Extending Power-Geometric Operators to Interval-Valued Hesitant Fuzzy Sets and Their Applications to Group Decision Making

2016 ◽  
Vol 15 (05) ◽  
pp. 1055-1114 ◽  
Author(s):  
Sheng-Hua Xiong ◽  
Zhen-Song Chen ◽  
Yan-Lai Li ◽  
Kwai-Sang Chin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Individual Decision ◽  
Hesitant Fuzzy Sets ◽  
Variable Power ◽  
Interval Valued

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some “false” or “biased” arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques.

Novel Multi-criteria Decision-making Approaches Based on Hesitant Fuzzy Sets and Prospect Theory

2016 ◽  
Vol 15 (03) ◽  
pp. 621-643 ◽  
Author(s):  
Juan-Juan Peng ◽  
Jian-Qiang Wang ◽  
Xiao-Hui Wu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Prospect Theory ◽  
Hausdorff Distance ◽  
Comparison Method ◽  
Distance Measures ◽  
Preference Ranking ◽  
Multi Criteria Decision Making ◽  
The Novel ◽  
Hesitant Fuzzy Sets

Hesitant fuzzy sets (HFSs), an extension of fuzzy sets, are considered to be useful in solving decision making problems where decision makers are unable to choose between several values when expressing their preferences. The purpose of this paper is to develop two hesitant fuzzy multi-criteria decision making (MCDM) methods based on prospect theory (PT). First, the novel component-wise ordering method for two hesitant fuzzy numbers (HFNs) is defined; however, this method does not consider the length of the two HFNs. Second, by utilizing the directed Hausdorff distance between two imprecise point sets, the generalized hesitant Hausdorff distance is developed, which overcomes the shortcomings of the existing distance measures. Third, based on the proposed comparison method and distance, as well as PT, the extended TODIM and Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE) approaches are developed in order to solve MCDM problems with hesitant fuzzy information. Finally, a practical example is provided to illustrate the pragmatism and effectiveness of the proposed approaches. Sensitivity and comparison analyses are also conducted using the same example. The findings indicate that the proposed methods do not require complicated computation procedures, yet still yield a reasonable and credible solution.

scholarly journals Induced Unbalanced Linguistic Ordered Weighted Average and Its Application in Multiperson Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Lucas Marin ◽  
Aida Valls ◽  
David Isern ◽  
Antonio Moreno ◽  
José M. Merigó
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
New Order ◽  
Linguistic Variables ◽  
Linguistic Terms ◽  
Ordered Weighted Average ◽  
Decision Making Model

Linguistic variables are very useful to evaluate alternatives in decision making problems because they provide a vocabulary in natural language rather than numbers. Some aggregation operators for linguistic variables force the use of a symmetric and uniformly distributed set of terms. The need to relax these conditions has recently been posited. This paper presents the induced unbalanced linguistic ordered weighted average (IULOWA) operator. This operator can deal with a set of unbalanced linguistic terms that are represented using fuzzy sets. We propose a new order-inducing criterion based on the specificity and fuzziness of the linguistic terms. Different relevancies are given to the fuzzy values according to their uncertainty degree. To illustrate the behaviour of the precision-based IULOWA operator, we present an environmental assessment case study in which a multiperson multicriteria decision making model is applied.

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