scholarly journals Some Novel Picture 2-Tuple Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple Attribute Decision Making

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 943
Author(s):  
Min Feng ◽  
Yushui Geng
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Linguistic Variable ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Picture Fuzzy Set ◽  
Input Parameters ◽  
Cognitive Information

When solving multiple attribute decision making (MADM) problems, the 2-tuple linguistic variable is an effective tool that can not only express complex cognitive information but also prevent loss of information in calculation. The picture fuzzy set (PFS) has three degrees and has more freedom to express cognitive information. In addition, Archimedean t-conorm and t-norm (ATT) can generalize most existing t-conorms and t-norms and Maclaurin symmetric mean (MSM) operators can catch the relationships among the multi-input parameters. Therefore, we investigate several novel aggregation operators, such as the picture 2-tuple linguistic MSM (2TLMSM) operator based on the ATT (ATT-P2TLMSM) and the picture 2-tuple linguistic generalized MSM (2TLGMSM) operator based on ATT (ATT-P2TLGMSM). Considering that the input parameters have different importance, we proposed picture 2-tuple linguistic weighted MSM (2TLWMSM) operators based on ATT (ATT-P2TLWMSM) and picture 2-tuple linguistic weighted generalized MSM (2TLWGMSM) operators based on ATT (ATT-P2TLWGMSM). Finally, a MADM method is introduced, and an expositive example is presented to explain the availability and applicability of the developed operators and methods.

Multiple Attribute Decision-Making Methods with Unbalanced Linguistic Variables Based on Maclaurin Symmetric Mean Operators

2019 ◽  
Vol 18 (01) ◽  
pp. 105-146 ◽  
Author(s):  
Fei Teng ◽  
Peide Liu ◽  
Li Zhang ◽  
Juan Zhao
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Linguistic Variables ◽  
Numerical Example ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Linguistic Term

In this paper, we firstly introduced the unbalanced linguistic term sets, the linguistic transforming methodology, the Maclaurin symmetric mean (MSM) operator and dual MSM (DMSM) operator. Then, we proposed the closed operational rules of unbalanced linguistic variables, and several new MSM aggregation operators, including unbalanced linguistic MSM (ULMSM) operator, weighted unbalanced linguistic MSM (WULMSM) operator, unbalanced linguistic DMSM (ULDMSM) operator and weighted unbalanced linguistic DMSM (WULDMSM) operator. Further, we proposed two multiple attribute decision-making (MADM) methods under unbalanced linguistic environments based on the WULMSM operator and WULDMSM operator, respectively. Finally, a numerical example is used to show the applicability and effectiveness of the proposed MADM methods and to reveal their advantages by comparing with the existing methods.

An approach to multiple attribute decision making based on linguistic value soft rough set and VIKOR method

2021 ◽  
pp. 1-18
Author(s):  
Xiangtang Chen ◽  
Bingzhen Sun ◽  
Xinrui Zhang ◽  
Chang Qi ◽  
Xiaoli Chu ◽  
...  
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Soft Set ◽  
Linguistic Variable ◽  
Vikor Method ◽  
Multiple Attribute ◽  
Rough Approximation ◽  
Soft Rough Set

Linguistic variable is an effective method of representation the preferences of a decision-maker for inaccuracy available information in decision making under uncertainty. This article investigates a multiple attribute ranking decision making problem with linguistic preference by using linguistic value soft rough set. Firstly, we present the definition of linguistic value fuzzy set by introduce the concept of linguistic variable into the original Zadeh’s fuzzy set. We then define the concept of linguistic value soft set and the pseudo linguistic value soft set over the alternative set and parameter set of discourse. Moreover, we investigate the basic operators and the mathematical properties of the linguistic value soft set. Subsequently, we establish the rough approximation of an uncertainty concept with linguistic value over the object set and parameter set, i.e., the linguistic value soft rough set model. Meanwhile, we discuss several deformations of the linguistic value soft rough lower and upper approximations as well as some fundamental properties of the linguistic value soft approximation operators. With reference on the exploring of the fundamental of linguistic value soft rough set, we construct a new method for handling with the multiple attribute ranking decision making problems with linguistic information by combining the proposed soft rough set and the VIKOR method. Then, we give the detailed decision procedure and steps for the established decision approach. At last, an extensive numerical example is further conducted to illustrate the process of the decision making principle and the results are satisfactory. The main contribution of this paper is twofold. One is to provide a new model of granular computing by infusion the soft set and rough set theory with linguistic valued information. Another is to try making a new way to handle multiple attribute decision making problems based on linguistic value soft rough set and the VIKOR method.

scholarly journals Some Trapezoid Intuitionistic Fuzzy Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple-Attribute Decision Making

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1778
Author(s):  
Zheng Dong ◽  
Yushui Geng
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Intuitionistic Fuzzy ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Multiple Input ◽  
Fuzzy Linguistic ◽  
Magdm Problems

In order to solve multiple-attribute group decision-making (MAGDM) problems under a trapezoid intuitionistic fuzzy linguistic (TIFL) environment and the relationships between multiple input parameters needed, in this paper, we extend the Maclaurin symmetric mean (MSM) operators to TIFL numbers (TIFLNs). Some new aggregation operators are proposed, including the trapezoid intuitionistic fuzzy linguistic Maclaurin symmetric mean (TIFLMSM) operator, trapezoid intuitionistic fuzzy linguistic generalized Maclaurin symmetric mean (TIFLGMSM) operator, trapezoid intuitionistic fuzzy linguistic weighted Maclaurin symmetric mean (TIFLWMSM) operator and trapezoid intuitionistic fuzzy linguistic weighted generalized Maclaurin symmetric mean (TIFLWGMSM) operator. Next, based on the TIFLWMSM and TIFLWGMSM operators, two methods are presented to deal with MAGDM problems. Finally, there is a numerical example to verify the effectiveness and feasibility of the proposed approaches.

scholarly journals Analysis of Robot Selection Based on 2-Tuple Picture Fuzzy Linguistic Aggregation Operators

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 1000
Author(s):  
Arshad Ahmad Khan ◽  
Muhammad Qiyas ◽  
Saleem Abdullah ◽  
Jianchao Luo ◽  
Mahwish Bano
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Comparison Analysis ◽  
Practical Application ◽  
Multiple Attribute ◽  
Decision Making Model ◽  
Fuzzy Linguistic ◽  
Robot Selection

The aim of this article is to propose the 2-tuple picture fuzzy linguistic aggregation operators and a decision-making model to deal with uncertainties in the form of 2-tuple picture fuzzy linguistic sets; 2-tuple picture fuzzy linguistic operators have more flexibility than general fuzzy set. We proposed a number of aggregation operators, namely, 2-TPFLWA, 2-TPFLOWA, 2-TPFLHA, 2-TPFLWG, 2-TPFLOWG, and 2-TPFLHG operators. The distinguished feature of the developed operators are studied. At that point, we used these operators to design a model to deal with multiple attribute decision-making issues under the 2-tuple picture fuzzy linguistic information. Then, a practical application of robot selection by manufacturing unit is given to prove the introduced technique and to show its practicability and effectiveness. Besides this, a systematic comparison analysis with other existent approaches is conducted to reveal the advantage of our developed method. Results indicate that the proposed method is suitable and effective for decision-making problems.

scholarly journals Pythagorean Fuzzy Interaction Partitioned Bonferroni Mean Operators and Their Application in Multiple-Attribute Decision-Making

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-25 ◽  
Author(s):  
Wei Yang ◽  
Jiarong Shi ◽  
Yong Liu ◽  
Yongfeng Pang ◽  
Ruiyue Lin
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Investment Company ◽  
Pythagorean Fuzzy Set ◽  
Bonferroni Mean ◽  
Multiple Attribute ◽  
Special Cases ◽  
Geometric Bonferroni Mean

The aim of this paper is to develop partitioned Pythagorean fuzzy interaction Bonferroni mean operators based on the Pythagorean fuzzy set, Bonferroni mean, and interaction between membership and nonmembership. Several new aggregation operators are developed including the Pythagorean fuzzy interaction partitioned Bonferroni mean (PFIPBM) operator, the Pythagorean fuzzy weighted interaction partitioned Bonferroni mean (PFWIPBM) operator, the Pythagorean fuzzy interaction partitioned geometric Bonferroni mean (PFIPGBM) operator, and the Pythagorean fuzzy weighted interaction partitioned geometric Bonferroni mean (PFWIPGBM) operator. Some main properties and some special particular cases of the new operators are studied. Many existing operators are the special cases of new aggregation operators. Moreover, a multiple-attribute decision-making method based on the proposed operator has been developed and the investment company selection problem is presented to illustrate feasibility and practical advantages of the new method.

Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making

2019 ◽  
Vol 7 (3) ◽  
pp. 227-256
Author(s):  
Chao Jiang ◽  
Shenqing Jiang ◽  
Jianlan Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Hesitant Fuzzy Set ◽  
Dual Hesitant Fuzzy Set ◽  
Operation Rules ◽  
Multiple Attribute ◽  
Special Cases ◽  
Interval Valued

AbstractAs an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given, and an numerical example is provided to demonstrate that the developed approach is both valid and practical.

scholarly journals Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 594 ◽  
Author(s):  
Mi Jung Son ◽  
Jin Han Park ◽  
Ka Hyun Ko
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Multiple Attribute

As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

Some improved pythagorean fuzzy Dombi power aggregation operators with application in multiple-attribute decision making

2021 ◽  
pp. 1-21
Author(s):  
Peide Liu ◽  
Qaisar Khan ◽  
Tahir Mahmood ◽  
Rashid Ali Khan ◽  
Hidayat Ullah Khan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Pythagorean Fuzzy Set ◽  
Operational Laws ◽  
Multiple Attribute ◽  
General Parameter ◽  
Pythagorean Fuzzy Numbers

Pythagorean fuzzy set (PyFS) is an extension of various fuzzy concepts, such as fuzzy set (FS), intuitionistic FS, and it is enhanced mathematical gizmo to pact with uncertain and vague information. In this article, some drawbacks in the Dombi operational rules for Pythagorean fuzzy numbers (PyFNs) are examined and some improved Dombi operational laws for PyFNs are developed. We also find out that the value aggregated using the existing Dombi aggregation operators (DAOs) is not a PyFN. Furthermore, we developed two new aggregations, improved existing aggregation operators (AOs) for aggregating Pythagorean fuzzy information (PyFI) and are applied to multiple-attribute decision making (MADM). To acquire full advantage of power average (PA) operators proposed by Yager, the Pythagorean fuzzy Dombi power average (PyFDPA) operator, the Pythagorean fuzzy Dombi weighted power average (PyFDWPA) operator, Pythagorean fuzzy Dombi power geometric (PyFDPG) operator, Pythagorean fuzzy Dombi weighted geometric (PyFDPWG) operator, improved the existing AOs and their desirable properties are discussed. The foremost qualities of these developed Dombi power aggregation operators is that they purge the cause of discomfited data and are more supple due to general parameter. Additionally, based on these Dombi power AOs, a novel MADM approach is instituted. Finally, a numerical example is given to show the realism and efficacy of the proposed approach and judgment with the existing approaches is also specified.

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