The Experts below are selected from a list of 9492 Experts worldwide ranked by ideXlab platform
Mao Lu - One of the best experts on this subject based on the ideXlab platform.
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models for multiple attribute decision making with some 2 tuple linguistic Pythagorean fuzzy hamy mean operators
Mathematics, 2018Co-Authors: Xiumei Deng, Jie Wang, Mao LuAbstract:The Hamy mean (HM) operator, as a useful aggregation tool, can capture the correlation between multiple integration parameters, and the 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are a special kind of Pythagorean fuzzy numbers (PFNs), which can easily describe the fuzziness in actual decision making by 2-tuple linguistic terms (2TLTs). In this paper, to consider both Hamy mean (HM) operator and 2TLPFNs, we combine the HM operator, weighted HM (WHM) operator, dual HM (DHM) operator, and dual WHM (DWHM) operator with 2TLPFNs to propose the 2-tuple linguistic Pythagorean fuzzy HM (2TLPFHM) operator, 2-tuple linguistic Pythagorean fuzzy WHM (2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy DHM (2TLPFDHM) operator and 2-tuple linguistic Pythagorean fuzzy DWHM (2TLPFDWHM) operator. Then some multiple attribute decision making (MADM) procedures are developed based on these operators. At last, an applicable example for green supplier selection is given.
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Pythagorean fuzzy maclaurin symmetric mean operators in multiple attribute decision making
International Journal of Intelligent Systems, 2018Co-Authors: Mao LuAbstract:The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multiinput arguments. In this paper, we extend MSM to Pythagorean fuzzy environment to propose the Pythagorean fuzzy Maclaurin symmetric mean and Pythagorean fuzzy weighted Maclaurin symmetric mean operators. Then, some desirable properties and special cases of these operators are discussed in detail. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver a comparative analysis.
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Pythagorean fuzzy power aggregation operators in multiple attribute decision making
International Journal of Intelligent Systems, 2018Co-Authors: Mao LuAbstract:In this paper, we utilize power aggregation operators to develop some Pythagorean fuzzy power aggregation operators: Pythagorean fuzzy power average operator, Pythagorean fuzzy power geometric operator, Pythagorean fuzzy power weighted average operator, Pythagorean fuzzy power weighted geometric operator, Pythagorean fuzzy power ordered weighted average operator, Pythagorean fuzzy power ordered weighted geometric operator, Pythagorean fuzzy power hybrid average operator, and Pythagorean fuzzy power hybrid geometric operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
Jie Wang - One of the best experts on this subject based on the ideXlab platform.
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Dual Hesitant Pythagorean Fuzzy Hamy Mean Operators in Multiple Attribute Decision Making
IEEE Access, 2019Co-Authors: Jie Wang, Yi ZhangAbstract:To fuse the information in dual-hesitant Pythagorean fuzzy sets (DHPFSs) more effectively, in this paper, some dual hesitant Pythagorean fuzzy Hamy mean (DHPFHM) operators, which can consider the relationships between being fused arguments, are defined and studied. Afterward, the defined aggregation operators are used to multiple attribute decision-making (MADM) with dual-hesitant Pythagorean fuzzy elements (DHPFEs), and the MADM decision-making model is developed. In accordance with the defined operators and the built model, the dual-hesitant Pythagorean fuzzy weighted Hamy mean (DHPFWHM) operator and the dual-hesitant Pythagorean fuzzy weighted dual Hamy mean (DHPFWDHM) operator are applied to deal with green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing with some existing approaches. The method presented in this paper can effectually solve the MADM problems, which the decision-making information is expressed by DHPFEs and the attributes are interactive.
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models for multiple attribute decision making with some 2 tuple linguistic Pythagorean fuzzy hamy mean operators
Mathematics, 2018Co-Authors: Xiumei Deng, Jie Wang, Mao LuAbstract:The Hamy mean (HM) operator, as a useful aggregation tool, can capture the correlation between multiple integration parameters, and the 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are a special kind of Pythagorean fuzzy numbers (PFNs), which can easily describe the fuzziness in actual decision making by 2-tuple linguistic terms (2TLTs). In this paper, to consider both Hamy mean (HM) operator and 2TLPFNs, we combine the HM operator, weighted HM (WHM) operator, dual HM (DHM) operator, and dual WHM (DWHM) operator with 2TLPFNs to propose the 2-tuple linguistic Pythagorean fuzzy HM (2TLPFHM) operator, 2-tuple linguistic Pythagorean fuzzy WHM (2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy DHM (2TLPFDHM) operator and 2-tuple linguistic Pythagorean fuzzy DWHM (2TLPFDWHM) operator. Then some multiple attribute decision making (MADM) procedures are developed based on these operators. At last, an applicable example for green supplier selection is given.
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approaches to multiple attribute decision making with interval valued 2 tuple linguistic Pythagorean fuzzy information
Mathematics, 2018Co-Authors: Jie WangAbstract:The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among multi-input arguments. Motivated by the ideal characteristic of the MSM operator, in this paper, we expand the MSM operator, generalized MSM (GMSM), and dual MSM (DMSM) operator with interval-valued 2-tuple linguistic Pythagorean fuzzy numbers (IV2TLPFNs) to propose the interval-valued 2-tuple linguistic Pythagorean fuzzy MSM (IV2TLPFMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted MSM (IV2TLPFWMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy GMSM (IN2TLPFGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted GMSM (IV2TLPFWGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy DMSM (IN2TLPFDMSM) operator, Interval-valued 2-tuple linguistic Pythagorean fuzzy weighted DMSM (IV2TLPFWDMSM) operator. Then the multiple attribute decision making (MADM) methods are developed with these three operators. Finally, an example of green supplier selection is used to show the proposed methods.
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CODAS method for Pythagorean 2-tuple linguistic multiple attribute group decision making
IEEE Access, 1Co-Authors: Tingting He, Jie WangAbstract:The evaluation of the financial performance of universities is conducive to the sustainable development of universities. Based on this, we extend the traditional CODAS (COmbinative Distance-based ASsessment) method to the Pythagorean 2-tuple linguistic fuzzy environment and propose a P2TL-CODAS model to evaluate the financial management performance of universities. Firstly, we briefly describe the definition, the score function, accuracy function, operational laws and the distance calculating method of P2TLSs. Next, two aggregation operators of P2TL including Pythagorean 2-tuple linguistic weighted averaging (P2TLWA) operator and Pythagorean 2-tuple linguistic weighted geometric (P2TLWG) operator are also introduced to fuse overall Pythagorean 2-tuple linguistic evaluation information. Then the steps of CODAS method are depicted briefly. Moreover, we use linguistic Pythagorean 2-tuple linguistic fuzzy numbers to extend the CODAS method. The P2TL-CODAS model is established and all computing steps are simply presented. Furthermore, we apply the proposed method to evaluate the financial management performance about five universities. Finally, a comparison between P2TL-CODAS method and P2TL-TODIM method is made to demonstrate the stability of the new method. The results show that the proposed method has unique advantages.
Muhammad Akram - One of the best experts on this subject based on the ideXlab platform.
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Decision-making approach based on Pythagorean Dombi fuzzy soft graphs
Granular Computing, 2020Co-Authors: Muhammad Akram, Gulfam ShahzadiAbstract:A Pythagorean fuzzy set model is more useful than intuitionistic fuzzy set model to handle the imprecise information involving both membership and nonmembership degrees, and a soft set is an other parameterized point of view for handling the vagueness. A Pythagorean fuzzy soft graph is considered more capable than intuitionistic fuzzy soft graph for representing the parametric relationships between objects, and the Dombi operators with operational parameters have creditable extensibility. Based on these two notions, we propose the concept of Pythagorean Dombi fuzzy soft graph (PDFSG). We describe certain concepts of graph theory under Pythagorean Dombi fuzzy soft environment. Further, we define the degree sequence and degree set in PDFSG, and the concept of edge regular PDFSG with consequential properties. Moreover, we illustrate the examples in decision making including selection of suitable ETL software for a business intelligence project and evaluation of electronics companies. Finally, we present the comparison analysis of our proposed model to show the superiority than existing model.
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Complex Pythagorean Dombi fuzzy graphs for decision making
Granular Computing, 2020Co-Authors: Muhammad Akram, Ayesha KhanAbstract:A complex Pythagorean fuzzy set (CPFS) is the generalization of Pythagorean fuzzy set (PFS) in which the range of degrees is extended from [0, 1] to complex plane with unit disk. The averaging operators play a significant role to transform the information into a single value. The flexibility of Dombi operators with operational parameters is outstanding, and the Dombi operators are very efficient in decision-making problems. In this research article, we present a new graph called, complex Pythagorean Dombi fuzzy graph (CPDFG) as the Dombi operators are not yet applied on CPFSs. We employ graph terminology on CPFSs using Dombi operators. We define regular, totally regular, strongly regular and biregular graphs with appropriate elaboration, and their pivotal properties are discussed. Moreover, edge regularity of CPDFG is also explained with significant characteristics. We introduce two operators, namely complex Pythagorean Dombi fuzzy arithmetic averaging (CPDFAA) and complex Pythagorean Dombi fuzzy geometric averaging (CPDFGA) operators, which are capable to aggregate the complex Pythagorean fuzzy information. We utilize CPDFAA and CPDFGA operators in solving a decision-making numerical example, which is related to the selection of suitable place to build a bus terminal in a city. In order to examine the superiority of our propose operators, we provide a comparative analysis with the existing operators.
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Pythagorean Fuzzy Matroids with Application
Symmetry, 2020Co-Authors: Muhammad Asif, Muhammad AkramAbstract:The Pythagorean fuzzy models deal with graphical and algebraic structures in case of vague information related to membership and non-membership grades. Here, we use Pythagorean fuzzy sets to generalize the concept of vector spaces and discuss their basis and dimensions. We also highlight the concept of Pythagorean fuzzy matroids and examine some of their fundamental characteristics like circuits, basis, dimensions, and rank functions. Additionally, we explore the concept of Pythagorean fuzzy matroids in linear algebra, graph theory, and combinatorics. Finally, we demonstrate the use of Pythagorean fuzzy matroids for minimizing the time taken by a salesman in delivering given products.
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Competition graphs under complex Pythagorean fuzzy information
Journal of Applied Mathematics and Computing, 2020Co-Authors: Muhammad Akram, Aqsa SattarAbstract:A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is useful model to deal the vagueness with the degrees whose ranges are extended from real to complex subset with unit circle. This set deals with vagueness and periodicity more precisely as compared to complex fuzzy set and complex intuitionistic fuzzy set. In this paper, we propose a new graph, complex Pythagorean fuzzy competition graph by combining the complex Pythagorean fuzzy information with competition graph. We also investigate the two extensions of complex Pythagorean fuzzy competition graphs, namely, complex Pythagorean fuzzy k -competition and complex Pythagorean fuzzy p -competition graphs. Moreover, we present complex Pythagorean fuzzy neighborhood graphs and m -step complex Pythagorean fuzzy competition graphs. In addition, we illustrate an application of complex Pythagorean fuzzy competition graphs with algorithm to highlight the importance of these graphs in real life.
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Pythagorean Dombi fuzzy graphs
Complex & Intelligent Systems, 2019Co-Authors: Muhammad AkramAbstract:Pythagorean fuzzy graph, a broadly used extension of fuzzy and intuitionistic fuzzy graph, is helpful in representing structural relationships between several objects where the relation between these objects is vague, while the Dombi operators with operational parameters have excellent flexibility. Utilizing these two concepts, this research paper proposes the novel concept of Pythagorean Dombi fuzzy graphs (PDFGs). Basically, graph terminology is employed for introducing Pythagorean fuzzy analogs of various fundamental graphical ideas using Dombi operator. Further, under Pythagorean Dombi fuzzy environment, regular, totally regular, strongly regular and biregular graphs are defined with appropriate illustration and some of their crucial properties are examined. Meanwhile, the notion of edge regularity of PDFG is also initiated with substantial characteristics. Finally, a numerical example related to evaluation of appropriate ETL software for a business intelligence project is presented to better understand PDFGs.
Ronald R. Yager - One of the best experts on this subject based on the ideXlab platform.
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properties and applications of Pythagorean fuzzy sets
Imprecision and Uncertainty in Information Representation and Processing, 2016Co-Authors: Ronald R. YagerAbstract:We introduce the concept of Pythagorean fuzzy subsets and discuss its relationship with intuitionistic fuzzy subsets. We focus on the negation and its relationship to the Pythagorean theorem. We describe some of the basic set operations on Pythagorean fuzzy subsets. We look at the relationship between Pythagorean membership grades and complex numbers. We consider the problem of multi-criteria decision making with satisfactions expressed as Pythagorean membership grades. We look at the use of the geometric mean and ordered weighted geometric (OWG) operator for aggregating criteria satisfaction. We provide a method for comparing alternatives whose degrees of satisfaction to the decision criteria are expressed as Pythagorean membership grades.
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Pythagorean membership grades in multicriteria decision making
IEEE Transactions on Fuzzy Systems, 2014Co-Authors: Ronald R. YagerAbstract:We first look at some nonstandard fuzzy sets, intuitionistic, and interval-valued fuzzy sets. We note both these allow a degree of commitment of less then one in assigning membership. We look at the formulation of the negation for these sets and show its expression in terms of the standard complement with respect to the degree of commitment. We then consider the complement operation. We describe its properties and look at alternative definitions of complement operations. We then focus on the Pythagorean complement. Using this complement, we introduce a class of nonstandard Pythagorean fuzzy subsets whose membership grades are pairs, (a, b) satisfying the requirement a 2 + b 2 ≤ 1. We introduce a variety of aggregation operations for these Pythagorean fuzzy subsets. We then look at multicriteria decision making in the case where the criteria satisfaction are expressed using Pythagorean membership grades. The issue of having to choose a best alternative in multicriteria decision making leads us to consider the problem of comparing Pythagorean membership grades.
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Pythagorean fuzzy subsets
2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA NAFIPS), 2013Co-Authors: Ronald R. YagerAbstract:We introduce a new class of non-standard fuzzy subsets called Pythagorean fuzzy subsets and the related idea of Pythagorean membership grades. We focus on the negation operation and its relationship to the Pythagorean theorem. We compare Pythagorean fuzzy subsets with intuitionistic fuzzy subsets. We look at the basic set operations for the Pythagorean fuzzy subsets.
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IFSA/NAFIPS - Pythagorean fuzzy subsets
2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA NAFIPS), 2013Co-Authors: Ronald R. YagerAbstract:We introduce a new class of non-standard fuzzy subsets called Pythagorean fuzzy subsets and the related idea of Pythagorean membership grades. We focus on the negation operation and its relationship to the Pythagorean theorem. We compare Pythagorean fuzzy subsets with intuitionistic fuzzy subsets. We look at the basic set operations for the Pythagorean fuzzy subsets.
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Pythagorean membership grades complex numbers and decision making
International Journal of Intelligent Systems, 2013Co-Authors: Ronald R. Yager, Ali M AbbasovAbstract:We describe the idea of Pythagorean membership grades and the related idea of Pythagorean fuzzy subsets. We focus on the negation and its relationship to the Pythagorean theorem. We look at the basic set operations for the case of Pythagorean fuzzy subsets. A relationship is shown between Pythagorean membership grades and complex numbers. We specifically show that Pythagorean membership grades are a subclass of complex numbers called Π-i numbers. We investigate operations that are closed under Π-i numbers. We consider the problem of multicriteria decision making with satisfactions expressed as Pythagorean membership grades, Π-i numbers. We look at the use of the geometric mean and ordered weighted geometric operator for aggregating criteria satisfaction.
Harish Garg - One of the best experts on this subject based on the ideXlab platform.
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generalized Pythagorean fuzzy geometric aggregation operators using einstein t norm and t conorm for multicriteria decision making process
International Journal of Intelligent Systems, 2017Co-Authors: Harish GargAbstract:The objective of this paper is to present some series of geometric-aggregated operators under Pythagorean fuzzy environment by relaxing the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted geometric, Pythagorean fuzzy Einstein ordered weighted geometric, generalized Pythagorean fuzzy Einstein weighted geometric, and generalized Pythagorean fuzzy Einstein ordered weighted geometric operators, are proposed in this paper. Some of its properties have also been investigated in details. Finally, an illustrative example for multicriteria decision-making problems of alternatives is taken to demonstrate the effectiveness of the approach.
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a new generalized Pythagorean fuzzy information aggregation using einstein operations and its application to decision making
Journal of intelligent systems, 2016Co-Authors: Harish GargAbstract:The objective of this article is to extend and present an idea related to weighted aggregated operators from fuzzy to Pythagorean fuzzy sets PFSs. The main feature of the PFS is to relax the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted averaging PFEWA, Pythagorean fuzzy Einstein ordered weighted averaging PFEOWA, generalized Pythagorean fuzzy Einstein weighted averaging GPFEWA, and generalized Pythagorean fuzzy Einstein ordered weighted averaging GPFEOWA, are proposed in this article. Some desirable properties corresponding to it have also been investigated. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.
