Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making

Kybernetes ◽  
2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Bushra Batool ◽  
Saleem Abdullah ◽  
Shahzaib Ashraf ◽  
Mumtaz Ahmad
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Content Type ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Emergency Decision Making ◽  
Emergency Decision ◽  
Established Technique

PurposeThis is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.Design/methodology/approachPyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.FindingsIn addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.Originality/valuePaper is original and not submitted elsewhere.

Hesitant Trapezoid Fuzzy Hamacher Aggregation Operators and Their Application to Multiple Attribute Decision Making

2020 ◽  
Vol 8 (6) ◽  
pp. 524-548
Author(s):  
Qian Yu ◽  
Jun Cao ◽  
Ling Tan ◽  
Yubing Zhai ◽  
Jiongyan Liu
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Definition Of

Abstract In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant trapezoid fuzzy information. Firstly, inspired by the idea of hesitant fuzzy sets and trapezoid fuzzy numbers, the definition of hesitant trapezoid fuzzy set and some operational laws of hesitant trapezoid fuzzy elements are proposed. Then some hesitant trapezoid fuzzy aggregation operators based on Hamacher operation are developed, such as the hesitant trapezoid fuzzy Hamacher weighted average (HTrFHWA) operator, the hesitant trapezoid fuzzy Hamacher weighted geometric (HTrFHWG) operator, the hesitant trapezoid fuzzy Hamacher Choquet average (HTrFHCA), the hesitant trapezoid fuzzy Hamacher Choquet geometric (HTrFHCG), etc. Furthermore, an approach based on the hesitant trapezoid fuzzy Hamacher weighted average (HTrFHWA) operator and the hesitant trapezoid fuzzy Hamacher weighted geometric (HTrFHWG) operator is proposed for MADM problems under hesitant trapezoid fuzzy environment. Finally, a numerical example for supplier selection is given to illustrate the application of the proposed approach.

scholarly journals A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1489
Author(s):  
Shahzad Faizi ◽  
Wojciech Sałabun ◽  
Nisbha Shaheen ◽  
Atiq ur Rehman ◽  
Jarosław Wątróbski
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Geometric Bonferroni Mean ◽  
The Individual ◽  
Heronian Mean

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

An approach to hesitant fuzzy multi-stage multi-criterion decision making

Kybernetes ◽  
2014 ◽  
Vol 43 (9/10) ◽  
pp. 1447-1468 ◽  
Author(s):  
Huchang Liao ◽  
Zeshui Xu ◽  
Jiuping Xu
Keyword(s):  
Decision Making ◽  
Fuzzy Variable ◽  
Entropy Method ◽  
Aggregation Operators ◽  
Average Deviation ◽  
Content Type ◽  
Preference Information ◽  
Multi Stage ◽  
Fuzzy Aggregation ◽  
Decision Making Problem

Purpose – The purpose of this paper is to develop some weight determining methods for hesitant fuzzy multi-criterion decision making (MCDM) in which the preference information on attributes is collected over different periods. Design/methodology/approach – Based on the proposed weight determining methods and dynamic hesitant fuzzy aggregation operators, an approach is developed to solve the hesitant fuzzy multi-stage multi-attribute decision-making problem where all the preference information of attributes over different periods is represented in hesitant fuzzy values. Findings – In order to determine the weights associated with dynamic hesitant fuzzy operators, the authors propose the improved maximum entropy method and the minimum average deviation method. Research limitations/implications – This paper does not consider the multi-stage multi-criteria group decision-making problem. Practical implications – An example concerning the evaluation of rangelands is given to illustrate the validation and efficiency of the proposed approach. It should be stated that the proposed approach can also be implemented into other multi-stage MCDM problems. Originality/value – The concept of hesitant fuzzy variable (HFV) is defined. Some operational laws and properties of the HFVs are given. Moreover, to fuse the multi-stage hesitant fuzzy information, the aggregation operators of hesitant fuzzy sets are extended to that of the HFVs.

Concept of Yager operators with the picture fuzzy set environment and its application to emergency program selection

2020 ◽  
Vol 13 (4) ◽  
pp. 455-483
Author(s):  
Muhammad Qiyas ◽  
Muhammad Ali Khan ◽  
Saifullah Khan ◽  
Saleem Abdullah
Keyword(s):  
Fuzzy Set ◽  
Design Methodology ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Accuracy Function ◽  
Content Type ◽  
Program Selection ◽  
Operational Laws ◽  
Picture Fuzzy Set ◽  
Ordered Weighted Average

PurposeThe aim of this study as to find out an approach for emergency program selection.Design/methodology/approachThe authors have generated six aggregation operators (AOs), namely picture fuzzy Yager weighted average (PFYWA), picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, picture fuzzy Yager weighted geometric (PFYWG), picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators.FindingsFirst of all, the authors defined the score and accuracy function for picture fuzzy set (FS), and some fundamental operational laws for picture FS using the Yager aggregation operation. After that, using the developed operational laws, developed some AOs, namely PFYWA, picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, PFYWG, picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators, have been proposed along with their desirable properties. A decision-making (DM) approach based on these operators has also been presented. An illustrative example has been given for demonstrating the approach. Finally, discussed the comparison of the proposed method with the other existing methods and write the conclusion of the article.Originality/valueTo find the best alternative for emergency program selection.

scholarly journals Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chunyong Wang ◽  
Qingguo Li ◽  
Xiaoqiang Zhou ◽  
Tian Yang
Keyword(s):  
Decision Making ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Special Cases ◽  
Fuzzy Aggregation

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness.

Pythagorean Hesitant Fuzzy Hamacher Aggregation Operators in Multiple-Attribute Decision Making

2017 ◽  
Vol 28 (5) ◽  
pp. 759-776 ◽  
Author(s):  
Guiwu Wei ◽  
Mao Lu
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Average Operator ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Ordered Weighted Average ◽  
Algebraic Operations ◽  
Geometric Operator

Abstract The Hamacher product is a t-norm and the Hamacher sum is a t-conorm. They are good alternatives to the algebraic product and the algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on algebraic operations. In this paper, we utilize Hamacher operations to develop some Pythagorean hesitant fuzzy aggregation operators: Pythagorean hesitant fuzzy Hamacher weighted average operator, Pythagorean hesitant fuzzy Hamacher weighted geometric operator, Pythagorean hesitant fuzzy Hamacher ordered weighted average operator, Pythagorean hesitant fuzzy Hamacher ordered weighted geometric operator, Pythagorean hesitant fuzzy Hamacher hybrid average operator, and Pythagorean hesitant fuzzy Hamacher hybrid geometric operator. The prominent characteristics of these proposed operators are studied. Then, we utilize these operators to develop some approaches for solving the Pythagorean hesitant fuzzy multiple-attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals Multiple Attribute Decision Making Based on Hesitant Fuzzy Einstein Geometric Aggregation Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoqiang Zhou ◽  
Qingguo Li
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Fuzzy Information ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Fuzzy Aggregation ◽  
Geometric Operator

We first define an accuracy function of hesitant fuzzy elements (HFEs) and develop a new method to compare two HFEs. Then, based on Einstein operators, we give some new operational laws on HFEs and some desirable properties of these operations. We also develop several new hesitant fuzzy aggregation operators, including the hesitant fuzzy Einstein weighted geometric (HFEWGε) operator and the hesitant fuzzy Einstein ordered weighted geometric (HFEWGε) operator, which are the extensions of the weighted geometric operator and the ordered weighted geometric (OWG) operator with hesitant fuzzy information, respectively. Furthermore, we establish the connections between the proposed and the existing hesitant fuzzy aggregation operators and discuss various properties of the proposed operators. Finally, we apply the HFEWGεoperator to solve the hesitant fuzzy decision making problems.

Probabilistic hesitant fuzzy TOPSIS emergency decision-making method based on the cumulative prospect theory

2021 ◽  
pp. 1-17
Author(s):  
Xiuyan Sha ◽  
Chuancun Yina ◽  
Zeshui Xu ◽  
Shen Zhang
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Weighted Average ◽  
Original Data ◽  
Fuzzy Topsis ◽  
Cumulative Prospect Theory ◽  
New Method ◽  
Attribute Weights ◽  
Emergency Decision Making ◽  
Emergency Decision

In order to fully consider the decision-maker’s limited rationality and attitude to risk, this paper constructs the probabilistic hesitant fuzzy TOPSIS emergency decision-making model based on the cumulative prospect theory under the probabilistic hesitant fuzzy environment. Aiming at the problem of missing probabilistic information in the probabilistic hesitant fuzzy element, a new complement scheme is proposed. In this scheme, the weighted average result of the original data information is used to complement, and the original data information is retained to a large extent. Then this paper proposes several probabilistic hesitant fuzzy distance measures based on Lance distance. The decision reference point is constructed by the probabilistic hesitant fuzzy Lance distance, which overcomes the influence of the extreme value on the decision-making result, and defines the value function based on the probability hesitation fuzzy Lance distance. In view of the fact that the attribute weights are completely unknown, the probabilistic hesitant fuzzy exponential entropy is constructed by using the actual data, and the attribute weights of different prospect states are obtained. Aiming at the problem that attribute weights of different prospect states have different effects on the cumulative prospect value, the expression of the cumulative prospect value is improved. The improved closeness coefficient of the TOPSIS method is used to order the emergency schemes. Finally, the new method is applied to the emergency decision-making case of a sudden outbreak of epidemic respiratory disease. The results show that the contrast of the new method is obvious, which is conducive to distinguish different schemes. The new method is more suitable for the complex and changeable emergency decision-making field.

scholarly journals Complex pythagorean fuzzy aggregation operators based on confidence levels and their applications

2021 ◽  
Vol 19 (1) ◽  
pp. 1078-1107
Author(s):  
Tahir Mahmood ◽  
◽  
Zeeshan Ali ◽  
Kifayat Ullah ◽  
Qaisar Khan ◽  
...  
Keyword(s):  
Decision Making ◽  
Sensitivity Analysis ◽  
Comparative Analysis ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Confidence Levels ◽  
Ordered Weighted Averaging ◽  
Operational Laws ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

<abstract> <p>The most important influence of this assessment is to analyze some new operational laws based on confidential levels (CLs) for complex Pythagorean fuzzy (CPF) settings. Moreover, to demonstrate the closeness between finite numbers of alternatives, the conception of confidence CPF weighted averaging (CCPFWA), confidence CPF ordered weighted averaging (CCPFOWA), confidence CPF weighted geometric (CCPFWG), and confidence CPF ordered weighted geometric (CCPFOWG) operators are invented. Several significant features of the invented works are also diagnosed. Moreover, to investigate the beneficial optimal from a large number of alternatives, a multi-attribute decision-making (MADM) analysis is analyzed based on CPF data. A lot of examples are demonstrated based on invented works to evaluate the supremacy and ability of the initiated works. For massive convenience, the sensitivity analysis and merits of the identified works are also explored with the help of comparative analysis and they're graphical shown.</p> </abstract>

scholarly journals A Hybrid Method for Complex Pythagorean Fuzzy Decision Making

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Muhammad Akram ◽  
Samirah Alsulami ◽  
Kiran Zahid
Keyword(s):  
Decision Making ◽  
Uncertain Data ◽  
Fuzzy Model ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Decision Making ◽  
Average Operator ◽  
Fuzzy Aggregation ◽  
Selection Of

This article takes advantage of advancements in two different fields in order to produce a novel decision-making framework. First, we contribute to the theory of aggregation operators, which are mappings that combine large amounts of data into more advantageous forms. They are extensively used in different settings from classical to fuzzy set theory alike. Secondly, we expand the literature on complex Pythagorean fuzzy model, which has an edge over other models due to its ability to handle uncertain data of periodic nature. We propose some aggregation operators for complex Pythagorean fuzzy numbers that depend on the Hamacher t-norm and t-conorm, namely, the complex Pythagorean fuzzy Hamacher weighted average operator, the complex Pythagorean fuzzy Hamacher ordered weighted average operator, and the complex Pythagorean fuzzy Hamacher hybrid average operator. We explore some properties of these operators inclusive of idempotency, monotonicity, and boundedness. Then, the operators are applied to multicriteria decision-making problems under the complex Pythagorean fuzzy environment. Furthermore, we present an algorithm along with a flow chart, and we demonstrate their applicability with the assistance of two numerical examples (selection of most favorable country for immigrants and selection of the best programming language). We investigate the adequacy of this algorithm by conducting a comparative study with the case of complex intuitionistic fuzzy aggregation operators.

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