scholarly journals Some Normal Intuitionistic Fuzzy Heronian Mean Operators Using Hamacher Operation and Their Application

2018 ◽  
Author(s):  
Guofang Zhang ◽  
Zhiming Zhang ◽  
Hang Kong
Keyword(s):  
Decision Making ◽  
Normal Distribution ◽  
Fuzzy Numbers ◽  
New Method ◽  
Arithmetical Operation ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Einstein Operation ◽  
Heronian Mean

Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2011 ◽  
Vol 2 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

scholarly journals Some New Logarithmic Aggregation Operators and their Application to Group Decision Making Problem Based on t-Norm and t-Conorm

2021 ◽  
Author(s):  
khaista Rahman
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Averaging ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Decision Making Problem ◽  
Algebraic Operators

Abstract In this paper, a logarithmic operational law for intuitionistic fuzzy numbers is defined, in which the based1 is a real number such that1 ∈(0,1) with condition1 ≠ 1. Some properties of logarithmic operational laws have been studied and based on these, several Einstein averaging and Einstein geometric operators namely, logarithmic intuitionistic fuzzy Einstein weighted averaging (LIFEWA) operator, logarithmic intuitionistic fuzzy Einstein ordered weighted averaging (LIFEOWA) operator, logarithmic intuitionistic fuzzy Einstein hybrid averaging (LIFEHA) operator, logarithmic intuitionistic fuzzy Einstein weighted geometric (LIFEWG) operator, logarithmic intuitionistic fuzzy Einstein ordered weighted geometric (LIFEOWG) operator, and logarithmic intuitionistic fuzzy Einstein hybrid geometric (LIFEHG) operator have been introduced, which can overcome the weaknesses of algebraic operators. Furthermore, based on the proposed operators a multi-attribute group decision-making problem is established under logarithmic operational laws. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2013 ◽  
pp. 45-51
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

Generalized Choquet Integral Operator of Triangular Atanassov’s Intuitionistic Fuzzy Numbers and Application to Multi-Attribute Group Decision Making

2016 ◽  
Vol 24 (05) ◽  
pp. 647-683 ◽  
Author(s):  
Jiu-Ying Dong ◽  
Li-Lian Lin ◽  
Feng Wang ◽  
Shu-Ping Wan
Keyword(s):  
Decision Making ◽  
Integral Operator ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Average ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Goal Programming Model ◽  
Ordered Weighted Average

The purpose of this paper is to propose a new approach to interactive multi-attribute group decision making with triangular Atanassov's intuitionistic fuzzy numbers (TAIFNs). The contribution of this study is fivefold: (1) Minkowski distance between TAIFNs is firstly defined; (2) We define the possibility attitudinal expected values of TAIFNs and thereby present a novel risk attitudinal ranking method of TAIFNs which can sufficiently consider the risk attitude of decision maker; (3) The weighted average operator (TAIFWA) and generalized ordered weighted average (TAIFGWA) operator of TAIFNs are defined as well as the hybrid ordered weighted average (TAIFHOWA) operator; (4) To study the interaction between attributes, we further develop the generalized Choquet (TAIF-GC) integral operator and generalized hybrid Choquet (TAIF-GHC) integral operator of TAIFNs. Their desirable properties are also discussed; (5) The individual overall value of alternative is obtained by TAIF-GC operator and the collective one is derived through TAIFWA operator. Fuzzy measures of attribute subsets and expert weights are objectively derived through constructing multi-objective optimization model which is transformed into the goal programming model to solve. The system analyst selection example verifies effectiveness of the proposed approach.

scholarly journals Methods for Multiple Attribute Group Decision Making Based on Intuitionistic Fuzzy Dombi Hamy Mean Operators

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 574 ◽  
Author(s):  
Zengxian Li ◽  
Hui Gao ◽  
Guiwu Wei
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Selection Of

In this paper, we extended the Hamy mean (HM) operator, the Dombi Hamy mean (DHM) operator, the Dombi dual Hamy mean (DDHM), with the intuitionistic fuzzy numbers (IFNs) to propose the intuitionistic fuzzy Dombi Hamy mean (IFDHM) operator, intuitionistic fuzzy weighted Dombi Hamy mean (IFWDHM) operator, intuitionistic fuzzy Dombi dual Hamy mean (IFDDHM) operator, and intuitionistic fuzzy weighted Dombi dual Hamy mean (IFWDDHM) operator. Following this, the multiple attribute group decision-making (MAGDM) methods are proposed with these operators. To conclude, we utilized an applicable example for the selection of a car supplier to prove the proposed methods.

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