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 A fuzzy multi-objective linear programming with interval-typed triangular fuzzy numbers

2019 ◽  
Vol 17 (1) ◽  
pp. 607-626 ◽  
Author(s):  
Chunquan Li
Keyword(s):  
Linear Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Objective Functions ◽  
Triangular Fuzzy Numbers ◽  
Matlab Toolbox ◽  
Multi Objective ◽  
Cut Set ◽  
The Stability

Abstract A multi-objective linear programming problem (ITF-MOLP) is presented in this paper, in which coefficients of both the objective functions and constraints are interval-typed triangular fuzzy numbers. An algorithm of the ITF-MOLP is provided by introducing the cut set of interval-typed triangular fuzzy numbers and the dominance possibility criterion. In particular, for a given level, the ITF-MOLP is converted to the maximization of the sum of membership degrees of each objective in ITF-MOLP, whose membership degrees are established based on the deviation from optimal solutions of individual objectives, and the constraints are transformed to normal inequalities by utilizing the dominance possibility criterion when compared with two interval-typed triangular fuzzy numbers. Then the equivalent linear programming model is obtained which could be solved by Matlab toolbox. Finally several examples are provided to illuminate the proposed method by comparing with the existing methods and sensitive analysis demonstrates the stability of the optimal solution.

The least square pre-nucleolus for interval cooperative games based on anti-symmetric interval excess values

2020 ◽  
Vol 39 (3) ◽  
pp. 3561-3575
Author(s):  
Jian Lin ◽  
Meiling Li ◽  
Chunsheng Cui ◽  
Zhiyong Tian
Keyword(s):  
Quadratic Programming ◽  
Lagrange Multiplier ◽  
Pollution Control ◽  
Cooperative Games ◽  
Programming Model ◽  
Least Square ◽  
Cardinal Characteristics ◽  
Excess Value ◽  
Analytic Expression ◽  
Single Objective

Considering both cardinal characteristics and double powers, the anti-symmetric interval excess value is defined. The least square pre-nucleolus for interval cooperative games is presented by making a single-objective programming model. We obtain the analytic expression of least square pre-nucleolus using Lagrange multiplier method, and construct an effective quadratic programming model to derive the least square pre-nucleolus of incomplete interval cooperative games. In addition, the application of least square pre-nucleolus in land pollution control is provided to show the validity of the proposed solution concepts.

Method for Fuzzy Multi-Attribute Decision-Making with Fuzzy Reciprocal Preference Relation on Alternatives under Partical Weight Information

2011 ◽  
Vol 58-60 ◽  
pp. 869-874
Author(s):  
Hong An Zhou
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Preference Relation ◽  
Triangular Fuzzy Numbers ◽  
Attribute Weights ◽  
Translation Function ◽  
Goal Programming Model ◽  
Subjective Preference ◽  
Multi Attribute Decision Making

The fuzzy multi-attribute decision-making (FMADM) problems, in which the information about attribute weights is partly known, the attribute values take the form of triangular fuzzy numbers, and the decision maker (DM) has fuzzy reciprocal preference relation on alternatives, are investigated. Firstly, some concepts, such as the multiply between two triangular fuzzy numbers, the projection of triangular fuzzy numbers vectors, etc, are given. Secondly, in order to reflect to the DM’s subjective preference information on alternatives, we make the objective decision information uniform by using a translation function and establish a goal programming model, and then the attribute weights is obtained by solving the model, thus the weighted attribute values of all alternatives are gained. The concept of fuzzy positive ideal solution (FPIS) of alternatives is introduced, and the alternatives are ranked by using the projection of the weighted attribute values of every alternative on FPIS. The method not only can sufficiently utilize the objective information and meet the DM’s subjective preferences on alternatives as much as possible, but also it is characterized by simple operation and easy to implement on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

scholarly journals Reliability Analysis in Planning of Traction Substation Reconstruction Based on Fuzzy Set Theory

2020 ◽  
pp. 52-62
Author(s):  
Vladislav G. Belov ◽  
Vladimir A. Tremyasov
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Probabilistic Method ◽  
Reliability Assessment ◽  
Electrical Equipment ◽  
Triangular Fuzzy Numbers ◽  
Traction Substation ◽  
Reliability Indicators

The study proposes a probabilistic method using triangular fuzzy numbers to analyze the reliability of the traction substation. With this approach, the reliability assessment of the traction substation can be performed considering changes in the values of reliability indicators of electrical equipment, determined on the basis of the fuzzy set theory

scholarly journals A Quadratic Programming with Triangular Fuzzy Numbers

2017 ◽  
Vol 05 (11) ◽  
pp. 2218-2227 ◽  
Author(s):  
Seyedeh Maedeh Mirmohseni ◽  
Seyed Hadi Nasseri
Keyword(s):  
Quadratic Programming ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers

scholarly journals A Systematic Approach to OptimizinghValue for Fuzzy Linear Regression with Symmetric Triangular Fuzzy Numbers

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xilong Liu ◽  
Yizeng Chen
Keyword(s):  
Linear Regression ◽  
Systematic Approach ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Numerical Study ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Linear Regression ◽  
The Real ◽  
Optimal Value ◽  
Sample Data

A systematic approach is proposed to optimizehvalue for fuzzy linear regression (FLR) analysis using minimum fuzziness criteria with symmetric triangular fuzzy numbers (TFNs). Firstly, a new concept of credibility is defined to evaluate the performance of FLR models with differenthvalues when a set of sample data pairs is given. Secondly, based on the defined concept of credibility, a programming model is formulated to optimize the value ofh. Finally, both the numerical study and the real application show that the approach proposed in this paper is effective and efficient; that is, optimal value forhcan be determined definitely with respect to a set of given sample data pairs.

Ranking Triangular Fuzzy Numbers Using Fuzzy Set Inclusion Index

2013 ◽  
pp. 100-108 ◽  
Author(s):  
Azedine Boulmakoul ◽  
Mohamed Haitam Laarabi ◽  
Roberto Sacile ◽  
Emmanuel Garbolino
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Set Inclusion

scholarly journals Interval-Valued Fuzzy Cooperative Games Based on the Least Square Excess and Its Application to the Profit Allocation of the Road Freight Coalition

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 709 ◽  
Author(s):  
Wen-Jian Zhao ◽  
Jia-Cai Liu
Keyword(s):  
Analytical Solution ◽  
Cooperative Games ◽  
Programming Model ◽  
Solution Concept ◽  
Least Square ◽  
Real Situation ◽  
The Road ◽  
Profit Allocation ◽  
Road Freight ◽  
Interval Valued

This paper is mainly committed to constructing a new model for solving interval-valued fuzzy cooperative games based on the least square excess. We propose the interval-valued least square excess solution according to the solution concept of the least square prenucleolus and the least square nucleolus for solving crisp cooperative games. In order to obtain the corresponding optimal analytical solution, one mathematic programming model is constructed. The least square excess solution can be used to determine plays’ payoffs directly. Considering the fuzziness and uncertainty existing in the process of the road freight coalition, we establish the interval-valued fuzzy utility function of the road freight coalition that can properly reflect the real situation in view of the green logistics. The illustratively calculated results show that the least square excess solution proposed in this paper is effectual and ascendant, and satisfied many important and useful properties of cooperative games, such as symmetry and uniqueness. As for the problems of interval-valued cooperative games, the model proposed in this paper can be applied appropriately to obtain the players’ interval-valued payoffs.

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.

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