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.

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 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.

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.

scholarly journals Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 608 ◽  
Author(s):  
Saifullah Khan ◽  
Saleem Abdullah ◽  
Lazim Abdullah ◽  
Shahzaib Ashraf
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Vital Role ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making

The objective of this study was to create a logarithmic decision-making approach to deal with uncertainty in the form of a picture fuzzy set. Firstly, we define the logarithmic picture fuzzy number and define the basic operations. As a generalization of the sets, the picture fuzzy set provides a more profitable method to express the uncertainties in the data to deal with decision making problems. Picture fuzzy aggregation operators have a vital role in fuzzy decision-making problems. In this study, we propose a series of logarithmic aggregation operators: logarithmic picture fuzzy weighted averaging/geometric and logarithmic picture fuzzy ordered weighted averaging/geometric aggregation operators and characterized their desirable properties. Finally, a novel algorithm technique was developed to solve multi-attribute decision making (MADM) problems with picture fuzzy information. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable.

Generalized Archimedean Intuitionistic Fuzzy Averaging Aggregation Operators and their Application to Multicriteria Decision-Making

2016 ◽  
Vol 15 (02) ◽  
pp. 311-352 ◽  
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Multiple Criteria Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Triangular Norm ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Averaging Operator ◽  
Fuzzy Aggregation

Aggregation operators play a key role in multiple criteria decision-making (MCDM). Extensions of aggregation operators to intuitionistic fuzzy sets (IFSs) usually involve replacing the standard arithmetic operations with those defined over the membership and nonmembership of IFS, which is essentially a pair of special Archimedean triangular norm (t-norm) and triangular conorm (t-conorm), called probabilistic sum t-conorm and product t-norm, on the membership and nonmembership of IFS, respectively. In this paper, we first introduce some operations on IFSs by means of Archimedean t-norm and t-conorm. Then some generalized Archimedean intuitionistic fuzzy aggregation operators are proposed, such as generalized Archimedean intuitionistic fuzzy weighted averaging operator, generalized Archimedean intuitionistic fuzzy ordered weighted averaging (GAIFOWA) operator, and generalized Archimedean intuitionistic fuzzy hybird averaging operator. Some desirable properties of these operators are investigated. The relations between these operators and the existing intuitionistic fuzzy aggregation operators are discussed. Finally, applying these proposed operators, we develop an approach for multi-criteria decision-making with intuitionistic fuzzy information, an illustrative example is used to verify the developed approach and to demonstrate its practicality and effectiveness.

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.

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.

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