scholarly journals Triangular Fuzzy Number-Typed Fuzzy Cooperative Games and Their Application to Rural E-Commerce Regional Cooperation and Profit Sharing

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 699 ◽  
Author(s):  
Wen-Jian Zhao ◽  
Jia-Cai Liu
Keyword(s):  
Quadratic Programming ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Regional Cooperation ◽  
Profit Sharing ◽  
Triangular Fuzzy Number ◽  
Programming Models ◽  
Confidence Levels ◽  
Upper Limits ◽  
Cut Set

The primary aim of this paper is to develop one kind of easy and effective method to solve fuzzy cooperative games with coalition values expressed by triangular fuzzy numbers (TFNs). This method ensures that each player should receive a TFN-typed fuzzy pay-off from the grand coalition because each coalition value is expressed by a TFN. Using the concept of Alpha-cut sets, an arbitrary TFN’s Alpha-cut set can be shown as an interval. If the 1-cut sets and 0-cut sets of the TFN-typed coalition values are known, we can easily gain some important values, such as the means, the lower limits, and the upper limits of the TFN-typed payoffs via the proposed quadratic programming models and method. Furthermore, it is also easy for us to compute the lower and upper limits of Alpha-cut sets at any confidence levels of the TFN-typed payoffs for any TFN-typed cooperative game through solving the constructed quadratic programming models. Hereby the players’ TFN-typed payoffs for the TFN-typed cooperative game can be explicitly solved via the representation theorem for fuzzy sets. It is easy to prove that the proposed solutions of the fuzzy cooperative games with coalition values expressed by TFNs satisfy some useful and important properties, such as symmetry, additivity, and anonymity. Finally, the validity, applicability and advantages of the proposed method is proved and discussed through a numerical example.

scholarly journals Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Jia-Cai Liu ◽  
Yuan-Fei Zhu ◽  
Wen-Jian Zhao
Keyword(s):  
Quadratic Programming ◽  
Fuzzy Set ◽  
Cooperative Games ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Least Square ◽  
Triangular Fuzzy Numbers ◽  
Profit Distribution ◽  
Cut Set ◽  
Quadratic Programming Method

A quadratic programming model is constructed for solving the fuzzy cooperative games with coalition values expressed by triangular fuzzy numbers, which will be abbreviated to TFN-typed cooperative games from now on. Based on the concept of α-cut set and the representation theorem for the fuzzy set, the least square distance solution for solving TFN-typed cooperative games is proposed. The least square distance solution successfully avoids the subtraction operation of TFNs, which may inevitably lead to the amplification of uncertainty and the distortion of decision information. A calculating example related to the profit distribution of logistics coalition is illustrated to show the advantages, validity, and applicability of the proposed method. Besides, the least square distance solution for solving TFN-typed cooperative games satisfies many important properties of cooperative games, such as uniqueness, additivity, symmetry, and uniqueness.

scholarly journals PROFIT DISTRIBUTION IN IPD PROJECTS BASED ON WEIGHT FUZZY COOPERATIVE GAMES

2021 ◽  
Vol 0 (0) ◽  
pp. 1-13
Author(s):  
Shuwen Guo ◽  
Junwu Wang
Keyword(s):  
Quadratic Programming ◽  
Cooperative Games ◽  
Rapid Development ◽  
Payoff Function ◽  
Programming Models ◽  
Project Delivery ◽  
Integrated Project Delivery ◽  
Profit Distribution ◽  
Interval Valued

Integrated Project Delivery (IPD) is regarded as an effective project delivery method that can deal with the challenge of the rapid development of the architecture, engineering, and construction (AEC) industry. In the IPD team, the alliance profit is not distributed fairly and effectively due to uncertainty, preventing the achievement of the IPD project goals. This study focuses on optimizing the profit distribution among stakeholders in IPD projects and uses quadratic programming models to solve fuzzy cooperative games in the IPD. A payoff function is used in the fuzzy alliance to determine the characteristics of the interval-valued fuzzy numbers, and different weights of the alliance and the efficiency of the player’s participation in the IPD are considered in the profit distribution. A case study is conducted, and the results of the proposed method are compared with those of crisp cooperative games. The results show that the fuzzy cooperative game increases the profit of participants in IPD projects. It is more practical to use weight fuzzy cooperative games than crisp games to express imputation. Moreover, the quadratic programming models and methods result in a fair and efficient profit distribution scheme in IPD projects.

scholarly journals Solution of Quadratic Programming with Interval Variables Using a Two-Level Programming Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Syaripuddin ◽  
Herry Suprajitno ◽  
Fatmawati
Keyword(s):  
Quadratic Programming ◽  
Programming Model ◽  
Programming Models ◽  
Programming Approach ◽  
Optimum Point ◽  
Interval Variables ◽  
Interval Coefficients ◽  
Optimum Solution

Quadratic programming with interval variables is developed from quadratic programming with interval coefficients to obtain optimum solution in interval form, both the optimum point and optimum value. In this paper, a two-level programming approach is used to solve quadratic programming with interval variables. Procedure of two-level programming is transforming the quadratic programming model with interval variables into a pair of classical quadratic programming models, namely, the best optimum and worst optimum problems. The procedure to solve the best and worst optimum problems is also constructed to obtain optimum solution in interval form.

LINEAR AND INTEGER PROGRAMMING TECHNIQUES FOR COOPERATIVE GAMES

2002 ◽  
Vol 13 (05) ◽  
pp. 653-666 ◽  
Author(s):  
Qizhi Fang ◽  
Shanfeng Zhu
Keyword(s):  
Integer Programming ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Value Function ◽  
Linear Program ◽  
Grand Coalition ◽  
The Core ◽  
Programming Techniques ◽  
Theoretical Results

Let Γ = (N, v) be a cooperative game with the player set N and value function v : 2N → R. A solution of the game is in the core if no subset of players could gain advantage by breaking away from the grand coalition of all players. This paper surveys theoretical results on the cores for some cooperative game models. These results proved that the linear program duality characterization of the core is a very powerful tool. We will focus on linear and integer programming techniques applied in this area.

scholarly journals INFORMATION SHARING GAMES

2003 ◽  
Vol 05 (01) ◽  
pp. 1-12 ◽  
Author(s):  
MARCO SLIKKER ◽  
HENK NORDE ◽  
STEF TIJS
Keyword(s):  
Information Sharing ◽  
Cooperative Game ◽  
Cooperative Games ◽  
Allocation Scheme ◽  
Population Monotonic Allocation Scheme ◽  
Monotonic Allocation Scheme

In this paper we study information sharing situations. For every information sharing situation we construct an associated cooperative game, which we call an information sharing game. We show that the class of information sharing games coincides with the class of cooperative games with a population monotonic allocation scheme.

scholarly journals Extension of Wolfe Method for Solving Quadratic Programming with Interval Coefficients

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Syaripuddin ◽  
Herry Suprajitno ◽  
Fatmawati
Keyword(s):  
Linear Programming ◽  
Quadratic Programming ◽  
Programming Models ◽  
Interval Coefficients ◽  
Extension Process

Quadratic programming with interval coefficients developed to overcome cases in classic quadratic programming where the coefficient value is unknown and must be estimated. This paper discusses the extension of Wolfe method. The extended Wolfe method can be used to solve quadratic programming with interval coefficients. The extension process of Wolfe method involves the transformation of the quadratic programming with interval coefficients model into linear programming with interval coefficients model. The next step is transforming linear programming with interval coefficients model into two classic linear programming models with special characteristics, namely, the optimum best and the worst optimum problem.

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