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

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

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,...

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Main Authors: Jia-Cai Liu, Yuan-Fei Zhu, Wen-Jian Zhao
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2019/5843751
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spelling doaj-d018cac1404347a5ae6ad555bb2abee12020-11-24T21:47:06ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472019-01-01201910.1155/2019/58437515843751Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics CoalitionJia-Cai Liu0Yuan-Fei Zhu1Wen-Jian Zhao2College of Management & College of Tourism, Fujian Agriculture and Forestry University, Fuzhou 350002, ChinaCollege of Transportation and Civil Engineering, Fujian Agriculture and Forestry University, Fuzhou 350002, ChinaJinshan College, Fujian Agriculture and Forestry University, Fuzhou 350002, ChinaA 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.http://dx.doi.org/10.1155/2019/5843751
collection DOAJ
language English
format Article
sources DOAJ
author Jia-Cai Liu
Yuan-Fei Zhu
Wen-Jian Zhao
spellingShingle Jia-Cai Liu
Yuan-Fei Zhu
Wen-Jian Zhao
Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition
Mathematical Problems in Engineering
author_facet Jia-Cai Liu
Yuan-Fei Zhu
Wen-Jian Zhao
author_sort Jia-Cai Liu
title Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition
title_short Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition
title_full Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition
title_fullStr Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition
title_full_unstemmed Quadratic Programming Method for Cooperative Games with Coalition Values Expressed by Triangular Fuzzy Numbers and Its Application in the Profit Distribution of Logistics Coalition
title_sort quadratic programming method for cooperative games with coalition values expressed by triangular fuzzy numbers and its application in the profit distribution of logistics coalition
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2019-01-01
description 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.
url http://dx.doi.org/10.1155/2019/5843751
work_keys_str_mv AT jiacailiu quadraticprogrammingmethodforcooperativegameswithcoalitionvaluesexpressedbytriangularfuzzynumbersanditsapplicationintheprofitdistributionoflogisticscoalition
AT yuanfeizhu quadraticprogrammingmethodforcooperativegameswithcoalitionvaluesexpressedbytriangularfuzzynumbersanditsapplicationintheprofitdistributionoflogisticscoalition
AT wenjianzhao quadraticprogrammingmethodforcooperativegameswithcoalitionvaluesexpressedbytriangularfuzzynumbersanditsapplicationintheprofitdistributionoflogisticscoalition
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