An Approach to Interval-Valued Intuitionistic Fuzzy Multiple Attribute Decision Making Based on the MSM Operator and Their Applications to Online Advertising Publisher Evaluation

2016 ◽  
Vol 13 (10) ◽  
pp. 7280-7284 ◽  
Author(s):  
Xiaoli Liang
Keyword(s):  
Decision Making ◽  
Online Advertising ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Special Cases ◽  
Interval Valued

The Maclaurin symmetric mean (MSM) was originally introduced by Maclaurin. The prominent characteristic of the MSM is that it can capture the interrelationship among the multi-input arguments. However, the researches on MSM are very rare, especially in fuzzy decision making. In this paper, we investigate the MSM operator and extend the MSM operator to interval-valued intuitionistic fuzzy environment and develop the interval-valued intuitionistic fuzzy Maclaurin symmetric mean (IVIFMSM) operator. Some desirable properties and special cases of IVIFMSM operator are discussed in detail. Based on IVIFMSM operator, an approach to multiple attribute decision making problems with interval-valued intuitionistic fuzzy information is developed. Finally, an illustrative example for online advertising publisher evaluation is given to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals INTUITIONISTIC FUZZY INTERACTION MACLAURIN SYMMETRIC MEANS AND THEIR APPLICATION TO MULTIPLE-ATTRIBUTE DECISION-MAKING

2018 ◽  
Vol 24 (4) ◽  
pp. 1533-1559 ◽  
Author(s):  
Peide Liu ◽  
Weiqiao Liu
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Group Decision ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute ◽  
Special Cases ◽  
Magdm Problems

The Maclaurin symmetric mean (MSM) can capture the interrelationship among the multi-input arguments and it also can generalize most of the existing operators. Now MSM has been extended to intuitionistic fuzzy sets (IFSs) which can easily express the vague information. However, the operational rules of IFSs used in the extended MSM operator didn’t consider the interaction between the membership function and non-membership function, so there are some weaknesses. In this paper, in order to combine the advantages of the MSM and interaction operational rules of IFSs, we propose the intuitionistic fuzzy interaction Maclaurin symmetric mean (IFIMSM) operator, the intuitionistic fuzzy weighted interaction Maclaurin symmetric mean (IFWIMSM) operator, respectively. Furthermore, we research some desirable properties and some special cases of them. Further, we develop a new method to deal with some multi-attribute group decision-making (MAGDM) problems under intuitionistic fuzzy environment based on these operators. Finally, an illustrative example is given to testify the availability of the developed method by comparing with the other existing methods.

scholarly journals Multiple Attribute Decision-Making Method Based upon Intuitionistic Fuzzy Partitioned Dual Maclaurin Symmetric Mean Operators

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
HongJuan Wang ◽  
Yi Liu ◽  
Fang Liu ◽  
Jun Lin
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Maclaurin Symmetric Mean ◽  
Multiple Attribute

AbstractWe propound the idea of the partitioned dual Maclaurin symmetric mean (PDMSM) operator stimulated by the partitioned Maclaurin symmetric mean, suppose that we can partition overall attributes into some portions and the attributes are interrelated in the same portion, but the attributes are not interrelated in different portions. We can deal with decision-making issues using PDMSM operator in the intuitionistic fuzzy environment. We also analysis features and peculiar instance of the PDMSM operator. And, we extend the PDMSM operator to introduce the intuitionistic fuzzy partitioned dual Maclaurin symmetric mean operator and the weighted intuitionistic fuzzy partitioned dual Maclaurin symmetric mean operator. Then, we analysis several characteristics and peculiar instances of the developed operators. A new multiple attribute decision-making (MADM) approach grounded on the established weighted intuitionistic fuzzy partitioned dual Maclaurin symmetric mean operator is propounded; the MADM method is to choose the optimal alternative from several alternatives. Finally, we demonstrate the designed method is more general and effective than existing methods through comparative analysis.

IFWA and IFWGM Methods for MADM under Atanassov's Intuitionistic Fuzzy Environment

2015 ◽  
Vol 23 (02) ◽  
pp. 263-284 ◽  
Author(s):  
Yejun Xu ◽  
Huimin Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Geometric Mean ◽  
Weighted Average ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Multiple Attribute

In this paper, we first give the formula of possibility degree to rank the Atanassov's intuitionistic fuzzy numbers. Two methods called Atanassov's intuitionistic fuzzy weighted average (IFWA) and Atanassov's intuitionistic fuzzy weighted geometric mean (IFWGM) are developed to solve the multiple attribute decision making problems under Atanassov's intuitionistic fuzzy environment, in which the performance ratings of alternatives and relative importance of attributes are expressed with Atanassov's intuitionistic fuzzy sets. The IFWA and IFWGM methods, respectively, are treated as an auxiliary pair of fractional programming models and two linear programming (LP) solution procedures are proposed simultaneously by using Charnes and Cooper transformation. Furthermore, two algorithms which are based on the IFWA and IFWGM models, respectively, are developed to solve Atanassov's intuitionistic fuzzy decision making problems where attribute values and weights of attributes are all in Atanassov's intuitionistic fuzzy numbers. The order relationship between IFWA and IFWGM are investigated. Finally, a numerical example is illustrated to show the feasibility and effectiveness of the proposed methods.

scholarly journals Multiple Attribute Group Decision-Making Based on Power Heronian Aggregation Operators under Interval-Valued Dual Hesitant Fuzzy Environment

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Shenqing Jiang ◽  
Wei He ◽  
Fangfang Qin ◽  
Qingqing Cheng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Fuzzy Environment ◽  
Multiple Attribute ◽  
Special Cases ◽  
Magdm Problems ◽  
Interval Valued ◽  
Heronian Mean

In this paper, we focus on new methods to deal with multiple attribute group decision-making (MAGDM) problems and a new comparison law of interval-valued dual hesitant fuzzy elements (IVDHFEs). More explicitly, the interval-valued dual hesitant fuzzy 2nd-order central polymerization degree (IVDHFCP2) function is introduced, for the case that score values of different IVDHFEs are identical. This function can further compare different IVDHFEs. Then, we develop a series of interval-valued dual hesitant fuzzy power Heronian aggregation operators, i.e., the interval-valued dual hesitant fuzzy power Heronian mean (IVDHFPHM) operator, the interval-valued dual hesitant fuzzy power geometric Heronian mean (IVDHFPGHM) operator, and their weighted forms. Some desirable properties and their special cases are discussed. These proposed operators can simultaneously reflect the interrelationship of aggregated arguments and reduce the influence of unreasonable evaluation values. Finally, two approaches for interval-valued dual hesitant fuzzy MAGDM with known or unknown weight information are presented. An illustrative example and comparative studies are given to verify the advantages of our methods. A sensitivity analysis of the decision results is analyzed with different parameters.

scholarly journals Generalized Linguistic Hesitant Intuitionistic Fuzzy Hybrid Aggregation Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Yang ◽  
Jiarong Shi ◽  
Yongfeng Pang
Keyword(s):  
Decision Making ◽  
Geometric Mean ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
New Method ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Special Cases

Some hybrid aggregation operators have been developed based on linguistic hesitant intuitionistic fuzzy information. The generalized linguistic hesitant intuitionistic fuzzy hybrid weighted averaging (GLHIFHWA) operator and the generalized linguistic hesitant intuitionistic fuzzy hybrid geometric mean (GLHIFHGM) operator are defined. Some special cases of the new aggregation operators are studied and many existing aggregation operators are special cases of the new operators. A new multiple attribute decision making method based on the new aggregation operators is proposed and a practical numerical example is presented to illustrate the feasibility and practical advantages of the new method.

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