scholarly journals A Novel Approach for Ranking Intuitionisitc Fuzzy Numbers and its Application to Decision Making

2021 ◽  
Author(s):  
Meishe Liang ◽  
Ju-Sheng Mi ◽  
Shaopu Zhang ◽  
Chenxia Jin
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Membership Degree ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Novel Approach ◽  
Multi Attribute Decision Making ◽  
Fuzzy Order ◽  
Ideal Measure ◽  
The Ideal

Abstract Ranking intuitionistic fuzzy numbers is an important issue in practical application of intuitionistic fuzzy sets. For making a rational decision, people need to get an effective sorting over the set of intuitionistic fuzzy numbers. Many scholars rank intuitionistic fuzzy numbers by defining different measures. These measures do not comprehensively consider the fuzzy semantics expressed by membership degree, nonmembership degree and hesitancy degree of intuitionistic fuzzy numbers. As a result, the ranking results are often counterintuitive, such as the indifference problems, the non-robustness problems, etc. In this paper, according to geometrical representation, a novel measure for intuitionistic fuzzy number is defined, which is called the ideal measure. After that a new sorting approach of intuitionistic fuzzy numbers is proposed. It is proved that the intuitionistic fuzzy order obtained by the ideal measure satisfies the properties of weak admissibility, membership degree robustness, nonmembership degree robustness, and determinism. Numerical example is applied to illustrate the effectiveness and feasibility of this method. Finally, using the presented approach, the optimal alternative can be acquired in multi-attribute decision making problem. Comparison analysis shows that the intuitionistic fuzzy value ordering method obtained by the ideal measure is more effectiveness and simplicity than other existing methods.

scholarly journals Heronian Means as Aggregation Operators for Multi-Attribute Decision Making Applications

2018 ◽  
Author(s):  
Xiaopu Shang ◽  
Jun Wang ◽  
Anupam Nanda ◽  
Weizi Li
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Novel Approach ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Heronian Mean

The Pythagorean fuzzy set (PFS), which is characterized by a membership and a non-membership degree and the square sum of them is less or equal to one, can act as an effective tool to express decision makers’ fuzziness and uncertainty. Considering that the Heronian mean (HM) is a powerful aggregation operator which can take the interrelationship between any two arguments, we study the HM in Pythagorean fuzzy environment and propose new operators for aggregating interval-valued Pythagorean fuzzy information. First, we investigate the HM and geometric HM (GHM) under interval-valued intuitionistic fuzzy environment and develop a series of aggregation operators for interval-valued intuitionistic fuzzy numbers (IVIFNs) including interval-valued intuitionistic fuzzy Heronian mean (IVIFHM), interval-valued intuitionistic fuzzy geometric Heronian mean (IVIFGHM), interval-valued intuitionistic fuzzy weighted Heronian mean (IVIFWHM) and interval-valued intuitionistic fuzzy weighted geometric Heronian mean (IVIFWGHM). Second, some desirable and important properties of these aggregation operators are discussed. Third, based on these aggregation operators, a novel approach to multi-attribute decision making (MADM) is proposed. Finally, to demonstrate the validity of the approach, a numerical example is provided and discussed. Moreover, we discuss several real-world applications of these operators within policy-making contexts.

MULTI-ATTRIBUTE DECISION MAKING METHOD BASED ON POSSIBILITY VARIANCE COEFFICIENT OF TRIANGULAR INTUITIONISTIC FUZZY NUMBERS

2013 ◽  
Vol 21 (02) ◽  
pp. 223-243 ◽  
Author(s):  
SHU-PING WAN
Keyword(s):  
Decision Making ◽  
Mathematical Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Programming Models ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Ranking Order

Triangular intuitionistic fuzzy numbers (TIFNs) are a special case of intuitionistic fuzzy sets. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multi-attribute decision making (MADM) problems, in which the attribute values are in the form of TIFNs and the weight preference information is incomplete. The possibility mean, variance and standard deviation for a TIFN are introduced as well as the possibility variance coefficient. Hereby, a new method to rank TIFNs is given on the basis of the possibility variance coefficients. The bi-objective mathematical programming, which minimizes the possibility variance coefficients of membership and non-membership functions for alternative's overall attribute values, is constructed. Using the max-min method, two non-linear fractional programming models are transformed into the linear programming models through the Charnes and Cooper transformation. Thus, the Pareto optimal solution to the bi-objective mathematical programming can be derived by solving the single-objective programming model. The ranking order of alternatives is obtained according to the minimum possibility variance coefficients. A personal selection example is given to verify the developed method and to demonstrate its feasibility and effectiveness. The analysis of comparison with other method is also conducted.

scholarly journals Heavy OWA Operator of Trapezoidal Intuitionistic Fuzzy Numbers and its Application to Multi-Attribute Decision Making

2015 ◽  
Vol 3 (1) ◽  
pp. 86-96 ◽  
Author(s):  
Chunlin Luo ◽  
Xin Tian ◽  
Shuping Wan
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Set ◽  
Special Kind ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

AbstractHeavy ordered weighted averaging (OWA) operator is important for characterizing the decision maker’s attitudinal character in multi-attribute decision making (MADM) problem with part or total ignorance. This paper develops a new method based on heavy OWA operator to solve the MADM problem in which the attributes are characterized by some trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFN, as a special kind of intuitionistic fuzzy set defined on the real numbers, is useful for characterizing the ill-known quantity in reality. Firstly, the operation laws and the cut sets concept for TrIFNs are introduced. Then the authors define the membership and non-membership average indexes. A new ranking method is developed on the basis of the two indexes. In the proposed decision model, the multi-attribute TrIFN values of the candidates are aggregated by the Heavy OWA operator, and ranked by their membership and non-membership average indexes. Lastly, the authors illustrate the proposed method by a numerical example which implies the practicality and effectiveness of the method.

Method of Multi-Attribute Decision Making for Interval-Valued Intuitionistic Fuzzy Sets Based on Mentality Function

2010 ◽  
Vol 44-47 ◽  
pp. 1075-1079
Author(s):  
Liang Zhong Shen ◽  
Guang Bo Li ◽  
Wen Bin Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Sets ◽  
Decision Makers ◽  
Ranking Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Decision Making Model ◽  
Interval Valued

This paper has summarized the current ranking method for interval-valued intuitionistic fuzzy numbers, and then through the introduction of decision-makers’ mentality indicator, presented a new ranking method for interval-valued intuitionistic fuzzy numbers based on mentality function. Not only the nature of mentality function is deeply discussed but also the decision-making model based on the interval-valued intuitionistic fuzzy numbers is constructed. At last, an example is illustrated to prove the model's accuracy and effectiveness.

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