Fuzzy Risk Analysis Method Based on Trapezoidal Intuitionistic Fuzzy Numbers

Author(s):  
Xiaojie Zhou ◽  
Shuai Wang ◽  
Cheng Zhang
2011 ◽  
Vol 6 (9) ◽  
Author(s):  
Xiaoyan Su ◽  
Wen Jiang ◽  
Jianling Xu ◽  
Peida Xu ◽  
Yong Deng

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xiang-tian Zeng ◽  
Deng-feng Li ◽  
Gao-feng Yu

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.


2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
C. Veeramani ◽  
M. Joseph Robinson ◽  
S. Vasanthi

The cost of goods per unit transported from the source to the destination is considered to be fixed regardless of the number of units transported. But, in reality, the cost is often not fixed. Quantity discount is often allowed for large shipments. Furthermore, the transportation cost and the price break quantities are not deterministic. In this study, we introduce the concept of Value- and Ambiguity-based approach for solving the intuitionistic fuzzy transportation problem with total quantity discounts and incremental quantity discounts. Here, the cost and quantity price breakpoints are represented by trapezoidal intuitionistic fuzzy numbers. The Values and Ambiguities are defined as the degree of acceptance and rejection for trapezoidal intuitionistic fuzzy numbers. The trapezoidal intuitionistic fuzzy transportation problem is converted to a parametric transportation problem based on their Value indices and Ambiguity indices. Then, for different Values of the parameter, the transformed problem is reduced to the linear programming problem. Then, the linear programming problem is solved by using the classical methods. The proposed method is demonstrated with a numerical example. In conclusion, the intuitionistic fuzzy transportation problem with total quantity discounts is compared with the intuitionistic fuzzy transportation problem with incremental quantity discounts.


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