Modified difference-index based ranking bilinear programming approach to solving bimatrix games with payoffs of trapezoidal intuitionistic fuzzy numbers

2015 ◽  
Vol 29 (4) ◽  
pp. 1607-1618 ◽  
Author(s):  
Tina Verma ◽  
Amit Kumar ◽  
SS Appadoo
Keyword(s):  
Fuzzy Numbers ◽  
Bilinear Programming ◽  
Programming Approach ◽  
Bimatrix Games ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

scholarly journals A Difference-Index Based Ranking Bilinear Programming Approach to Solving Bimatrix Games with Payoffs of Trapezoidal Intuitionistic Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Deng-Feng Li ◽  
Jie Yang
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Solution ◽  
Fuzzy Numbers ◽  
Order Relation ◽  
Bilinear Programming ◽  
Bimatrix Games ◽  
Bimatrix Game ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

The aim of this paper is to develop a bilinear programming method for solving bimatrix games in which the payoffs are expressed with trapezoidal intuitionistic fuzzy numbers (TrIFNs), which are called TrIFN bimatrix games for short. In this method, we define the value index and ambiguity index for a TrIFN and propose a new order relation of TrIFNs based on the difference index of value index to ambiguity index, which is proven to be a total order relation. Hereby, we introduce the concepts of solutions of TrIFN bimatrix games and parametric bimatrix games. It is proven that any TrIFN bimatrix game has at least one satisfying Nash equilibrium solution, which is equivalent to the Nash equilibrium solution of corresponding parametric bimatrix game. The latter can be obtained through solving the auxiliary parametric bilinear programming model. The method proposed in this paper is demonstrated with a real example of the commerce retailers’ strategy choice problem.

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.

scholarly journals Value- and Ambiguity-Based Approach for Solving Intuitionistic Fuzzy Transportation Problem with Total Quantity Discounts and Incremental Quantity Discounts

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
C. Veeramani ◽  
M. Joseph Robinson ◽  
S. Vasanthi
Keyword(s):  
Linear Programming ◽  
Transportation Problem ◽  
Fuzzy Numbers ◽  
Quantity Discounts ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Transportation Problem ◽  
The Cost ◽  
Incremental Quantity Discounts ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

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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