scholarly journals A Value and Ambiguity-Based Ranking Method of Trapezoidal Intuitionistic Fuzzy Numbers and Application to Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xiang-tian Zeng ◽  
Deng-feng Li ◽  
Gao-feng Yu
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Implementation Process ◽  
Ranking Method ◽  
Comparison Analysis ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
A Value ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

The aim of this paper is to develop a method for ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) in the process of decision making in the intuitionistic fuzzy environment. Firstly, the concept of TrIFNs is introduced. Arithmetic operations and cut sets over TrIFNs are investigated. Then, the values and ambiguities of the membership degree and the nonmembership degree for TrIFNs are defined as well as the value-index and ambiguity-index. Finally, a value and ambiguity-based ranking method is developed and applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed using TrIFNs. A numerical example is examined to demonstrate the implementation process and applicability of the method proposed in this paper. Furthermore, comparison analysis of the proposed method is conducted to show its advantages over other similar methods.

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 Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 218 ◽  
Author(s):  
Jinming Zhou ◽  
Tomas Baležentis ◽  
Dalia Streimikiene
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Real Life ◽  
Aggregation Operators ◽  
Harmonic Mean ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Selection Of

In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.

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.

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