The Experts below are selected from a list of 10383 Experts worldwide ranked by ideXlab platform

Zhigeng Fang - One of the best experts on this subject based on the ideXlab platform.

  • Study on the model of grey Matrix Game based on grey mixed strategy—properties of grey mixed strategy and model of linear program
    2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 2008
    Co-Authors: Hongxing Shi, Sifeng Liu, Zhigeng Fang, Yong Zhao
    Abstract:

    Model of grey linear program is one of good methods on the process of finding the solution of grey Matrix Game. Studying interchangeabilities of grey mixed optimal strategy, we certify necessary and sufficient condition that there is grey mixed optimal strategy in the grey Matrix Game, which the grey Game value between player 1 and 2 is equality in the grey saddle point. Based on these, we prove that grey mixed optimal strategy of grey Matrix Game can be found by the way of the grey linear program model. And, we build up the solution framework system of grey linear program on the program of grey Matrix Game by using of the grey system and operation research theories.

  • FUZZ-IEEE - Study on the model of grey Matrix Game based on grey mixed strategy—properties of grey mixed strategy and model of linear program
    2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 2008
    Co-Authors: Hongxing Shi, Sifeng Liu, Zhigeng Fang, Yong Zhao
    Abstract:

    Model of grey linear program is one of good methods on the process of finding the solution of grey Matrix Game. Studying interchangeabilities of grey mixed optimal strategy, we certify necessary and sufficient condition that there is grey mixed optimal strategy in the grey Matrix Game, which the grey Game value between player 1 and 2 is equality in the grey saddle point. Based on these, we prove that grey mixed optimal strategy of grey Matrix Game can be found by the way of the grey linear program model. And, we build up the solution framework system of grey linear program on the program of grey Matrix Game by using of the grey system and operation research theories.

  • study on Matrix solution method of grey Matrix Game based on full rank grey payoff Matrix
    Systems Man and Cybernetics, 2006
    Co-Authors: Zhigeng Fang, Sifeng Liu, Haowei Zhang
    Abstract:

    Game theory based on the theory and thought of classical math has brought far-reaching affects in the field of economics, sociology, and so on. However, classical Game theory can find no way out when Game circumstance faces to uncertainty condition, such as finite logos, finite knowledge, small sample, and inadequate information, the payoff value of Game can only be described with grey number. So study on grey Matrix Game has the most important theoretic value and actualistic meaning. How to solve the grey Matrix Game with high efficiency is the key problem which must be solved in the theory research and application of this field. Matrix solution method of grey Matrix Game is simple and effective. This paper has defined grey full rank payoff value expansion square Matrix of grey Matrix Game, and has also proved that besides the value of grey element at the right and bottom edge of inverse Matrix of grey full rank expansion square Matrix, the value of grey element at its last line and right column is corresponding the optimal grey Game strategies of player 1 and 2 separately.

  • SMC - Study on Matrix Solution Method of Grey Matrix Game Based on Full Rank Grey Payoff Matrix
    2006 IEEE International Conference on Systems Man and Cybernetics, 2006
    Co-Authors: Zhigeng Fang, Sifeng Liu, Haowei Zhang
    Abstract:

    Game theory based on the theory and thought of classical math has brought far-reaching affects in the field of economics, sociology, and so on. However, classical Game theory can find no way out when Game circumstance faces to uncertainty condition, such as finite logos, finite knowledge, small sample, and inadequate information, the payoff value of Game can only be described with grey number. So study on grey Matrix Game has the most important theoretic value and actualistic meaning. How to solve the grey Matrix Game with high efficiency is the key problem which must be solved in the theory research and application of this field. Matrix solution method of grey Matrix Game is simple and effective. This paper has defined grey full rank payoff value expansion square Matrix of grey Matrix Game, and has also proved that besides the value of grey element at the right and bottom edge of inverse Matrix of grey full rank expansion square Matrix, the value of grey element at its last line and right column is corresponding the optimal grey Game strategies of player 1 and 2 separately.

  • Study on optimum value of Grey Matrix Game Based on Token of Grey Interval Number
    2006 6th World Congress on Intelligent Control and Automation, 2006
    Co-Authors: Zhigeng Fang, Sifeng Liu
    Abstract:

    Profit and loss Matrix in the Matrix Game is made up of grey interval number because of that there are unsymmetrical information, finite knowledge and rational. This kind of Game is called grey Matrix Game. Using thoughts of grey systems and theories of systems engineering, the paper studies pure strategy optimum grey Game value and its solution, defines the concept of grey pure strategy solution, proves the sufficient and necessary condition of profit and loss relation and grey pure strategy solution. And based on this, studies the problems of optimum grey Game value and it's solution under mixed strategy condition, sets up concepts of the most optimism and pessimism profit and loss Matrix, and the concept of the optimization grey Game value, studies the solution algorithm of max (min) grey Game value. In the end, taking the decision-making of coal stores for winter warm as an example, the results show that it acquires well effect with the theories above.

Sifeng Liu - One of the best experts on this subject based on the ideXlab platform.

  • Study on the model of grey Matrix Game based on grey mixed strategy—properties of grey mixed strategy and model of linear program
    2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 2008
    Co-Authors: Hongxing Shi, Sifeng Liu, Zhigeng Fang, Yong Zhao
    Abstract:

    Model of grey linear program is one of good methods on the process of finding the solution of grey Matrix Game. Studying interchangeabilities of grey mixed optimal strategy, we certify necessary and sufficient condition that there is grey mixed optimal strategy in the grey Matrix Game, which the grey Game value between player 1 and 2 is equality in the grey saddle point. Based on these, we prove that grey mixed optimal strategy of grey Matrix Game can be found by the way of the grey linear program model. And, we build up the solution framework system of grey linear program on the program of grey Matrix Game by using of the grey system and operation research theories.

  • FUZZ-IEEE - Study on the model of grey Matrix Game based on grey mixed strategy—properties of grey mixed strategy and model of linear program
    2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence), 2008
    Co-Authors: Hongxing Shi, Sifeng Liu, Zhigeng Fang, Yong Zhao
    Abstract:

    Model of grey linear program is one of good methods on the process of finding the solution of grey Matrix Game. Studying interchangeabilities of grey mixed optimal strategy, we certify necessary and sufficient condition that there is grey mixed optimal strategy in the grey Matrix Game, which the grey Game value between player 1 and 2 is equality in the grey saddle point. Based on these, we prove that grey mixed optimal strategy of grey Matrix Game can be found by the way of the grey linear program model. And, we build up the solution framework system of grey linear program on the program of grey Matrix Game by using of the grey system and operation research theories.

  • study on Matrix solution method of grey Matrix Game based on full rank grey payoff Matrix
    Systems Man and Cybernetics, 2006
    Co-Authors: Zhigeng Fang, Sifeng Liu, Haowei Zhang
    Abstract:

    Game theory based on the theory and thought of classical math has brought far-reaching affects in the field of economics, sociology, and so on. However, classical Game theory can find no way out when Game circumstance faces to uncertainty condition, such as finite logos, finite knowledge, small sample, and inadequate information, the payoff value of Game can only be described with grey number. So study on grey Matrix Game has the most important theoretic value and actualistic meaning. How to solve the grey Matrix Game with high efficiency is the key problem which must be solved in the theory research and application of this field. Matrix solution method of grey Matrix Game is simple and effective. This paper has defined grey full rank payoff value expansion square Matrix of grey Matrix Game, and has also proved that besides the value of grey element at the right and bottom edge of inverse Matrix of grey full rank expansion square Matrix, the value of grey element at its last line and right column is corresponding the optimal grey Game strategies of player 1 and 2 separately.

  • SMC - Study on Matrix Solution Method of Grey Matrix Game Based on Full Rank Grey Payoff Matrix
    2006 IEEE International Conference on Systems Man and Cybernetics, 2006
    Co-Authors: Zhigeng Fang, Sifeng Liu, Haowei Zhang
    Abstract:

    Game theory based on the theory and thought of classical math has brought far-reaching affects in the field of economics, sociology, and so on. However, classical Game theory can find no way out when Game circumstance faces to uncertainty condition, such as finite logos, finite knowledge, small sample, and inadequate information, the payoff value of Game can only be described with grey number. So study on grey Matrix Game has the most important theoretic value and actualistic meaning. How to solve the grey Matrix Game with high efficiency is the key problem which must be solved in the theory research and application of this field. Matrix solution method of grey Matrix Game is simple and effective. This paper has defined grey full rank payoff value expansion square Matrix of grey Matrix Game, and has also proved that besides the value of grey element at the right and bottom edge of inverse Matrix of grey full rank expansion square Matrix, the value of grey element at its last line and right column is corresponding the optimal grey Game strategies of player 1 and 2 separately.

  • Study on optimum value of Grey Matrix Game Based on Token of Grey Interval Number
    2006 6th World Congress on Intelligent Control and Automation, 2006
    Co-Authors: Zhigeng Fang, Sifeng Liu
    Abstract:

    Profit and loss Matrix in the Matrix Game is made up of grey interval number because of that there are unsymmetrical information, finite knowledge and rational. This kind of Game is called grey Matrix Game. Using thoughts of grey systems and theories of systems engineering, the paper studies pure strategy optimum grey Game value and its solution, defines the concept of grey pure strategy solution, proves the sufficient and necessary condition of profit and loss relation and grey pure strategy solution. And based on this, studies the problems of optimum grey Game value and it's solution under mixed strategy condition, sets up concepts of the most optimism and pessimism profit and loss Matrix, and the concept of the optimization grey Game value, studies the solution algorithm of max (min) grey Game value. In the end, taking the decision-making of coal stores for winter warm as an example, the results show that it acquires well effect with the theories above.

Aiqing Ruan - One of the best experts on this subject based on the ideXlab platform.

  • study on the model of the standard grey Matrix Game based on pure strategy solution
    Systems Man and Cybernetics, 2005
    Co-Authors: Zhigeng Fang, Sifeng Liu, Aiqing Ruan
    Abstract:

    The problem of Game in the real-life is not all a simple decision-making problem, which the process of Game is only related to precision whitenization number, because of that there are a lot of uncertainty factors. This paper defines conceptions of pure-strategy solution (grey saddle-point) and optimal pure-strategy in the standard grey Matrix Game based on hypothesis of sense behavior and un-precision discursion characteristics for players, which the deduction process of players in the Game are not the same as exactness calculation of the computers. In the grey Matrix Atilde(ominus) of the grey Matrix Game Gtilde(ominus) = {S1, S2; Atilde(ominus)}, the strategies of line i* and the column j* of a grey saddle-point (i*, j*) are respectively a grey optimum pure-strategy alphai. of play-1 and betaj. of play-2, and the grey element [ai.j., bi.j.] of the grey saddle-point (i*, j*) in Atilde(ominus) is an optimum grey Game values of the Gtilde(ominus). Furthermore, the paper proves necessary and sufficient conditions of that there exit pure-strategies, and researches characters, which if there are multi-saddle of Gtilde(ominus), then there are properties of no-difference and changeable among these grey saddles. In fact, the standard grey Matrix Game Gtilde(ominus) is directly generalization of classical Matrix Game in the field of grey system, which the later is a special example of the former

  • SMC - Study on the model of the standard grey Matrix Game based on pure-strategy solution
    2005 IEEE International Conference on Systems Man and Cybernetics, 1
    Co-Authors: Zhigeng Fang, Sifeng Liu, Aiqing Ruan
    Abstract:

    The problem of Game in the real-life is not all a simple decision-making problem, which the process of Game is only related to precision whitenization number, because of that there are a lot of uncertainty factors. This paper defines conceptions of pure-strategy solution (grey saddle-point) and optimal pure-strategy in the standard grey Matrix Game based on hypothesis of sense behavior and un-precision discursion characteristics for players, which the deduction process of players in the Game are not the same as exactness calculation of the computers. In the grey Matrix Atilde(ominus) of the grey Matrix Game Gtilde(ominus) = {S1, S2; Atilde(ominus)}, the strategies of line i* and the column j* of a grey saddle-point (i*, j*) are respectively a grey optimum pure-strategy alphai. of play-1 and betaj. of play-2, and the grey element [ai.j., bi.j.] of the grey saddle-point (i*, j*) in Atilde(ominus) is an optimum grey Game values of the Gtilde(ominus). Furthermore, the paper proves necessary and sufficient conditions of that there exit pure-strategies, and researches characters, which if there are multi-saddle of Gtilde(ominus), then there are properties of no-difference and changeable among these grey saddles. In fact, the standard grey Matrix Game Gtilde(ominus) is directly generalization of classical Matrix Game in the field of grey system, which the later is a special example of the former

Sankar Kumar Roy - One of the best experts on this subject based on the ideXlab platform.

  • Multi-objective linguistic-neutrosophic Matrix Game and its applications to tourism management
    Journal of Dynamics & Games, 2019
    Co-Authors: Ankan Bhaumik, Sankar Kumar Roy, Gerhard-wilhelm Weber
    Abstract:

    Game theory plays an important role in numerous decision-oriented real-life problems. Nowadays, many such problems are basically characterized by various uncertainties. Uncertainties come to happen due to decision makers' collection of data, intuition, assumption, judgement, behaviour, evaluation and lastly, due to the problem itself. Fuzzy concept with membership degree made an initialization towards the treatment of uncertainty, but it was not enough. Intuitionistic fuzzy concept was evolved concerning with both membership and non-membership degrees but failed to express reality more accurately. Then, neutrosophy logic was developed with a new degree in uncertainty, say, indeterminacy degree besides membership and non-membership degrees. Multi-objective optimization is an area of multiple-criteria decision making related with mathematical optimization problems involving more than one objective function to be optimized at the same time. Game theory (Matrix Game) problems with imprecise, vague information, like neutrosophic, can be formed with multiple objective functions. We develop and analyse a Matrix Game with multiple objectives, and solve the problem under a single-valued neutrosophic environment in linguistic approach. The main achievement of our study is that we here introduce a problem-oriented example to justify our designed methodologies with a successful real-life implications using linguistic neutrosophic data rather than crisp data as used in previous researches.

  • An approach to solve fuzzy interval valued Matrix Game
    International Journal of Operational Research, 2016
    Co-Authors: Sankar Kumar Roy, Shakti Nath Mondal
    Abstract:

    The conventional Game theory is based on known payoffs. In the real situations, usually the payoffs are not known and have to be approximated. The aim of this paper is to develop a simple and an effective fuzzy multi-objective linear programming method for solving Matrix Game in which the payoffs are expressed with fuzzy intervals. Since, the payoffs of the Matrix Game are fuzzy intervals, the value of the Matrix Game is also fuzzy interval. Using upper and lower bounds of the payoffs, we obtain upper and lower bounds of the value of the Matrix Game by fuzzy multi-objective linear programming method. Lastly, a numerical example is given to illustrate the method.

  • Solving Matrix Game with rough payoffs using genetic algorithm
    Operational Research, 2015
    Co-Authors: Sankar Kumar Roy, Prasanta Mula
    Abstract:

    In this paper, we analyze a Matrix Game using a rough programming approach. The combination of a Matrix Game and a rough programming approach represents a new class defined as a rough Matrix Game. The pay-off elements are characterized by rough variables, and the uncertainties of the rough variables are measured using a measure known as trust. Based on this trust measure, we defined trust equilibrium strategies and a rough expected value. We derived a series of optimal solutions to a rough Matrix Game using a genetic algorithm. We present a numerical example that illustrates the effectiveness of our rough Matrix Game.

  • Rough set approach to bi-Matrix Game
    International Journal of Operational Research, 2015
    Co-Authors: Sankar Kumar Roy, Prasanta Mula
    Abstract:

    The paper attempts to solve the bi-Matrix Game under rough set environment. The elements of the bi-Matrix Game are characterised by rough variables and defined as rough bi-Matrix Game (RBG). To handle RBG, we introduce the rough measurable function denoted as trust in it. Based on trust measure and rough expected operator, trust equilibrium strategies are defined for RBG. Then using rough set theory and Game theory, the RBG converts into crisp quadratic programming problem (QPP) which depends upon the confidence level. Finally, using Wolfe's modified simplex method, the solution of RBG is derived. The numerical examples are presented to illustrate the methodology.

  • Bi-Matrix Game in bifuzzy environment
    Journal of Uncertainty Analysis and Applications, 2013
    Co-Authors: Sankar Kumar Roy, Prasanta Mula
    Abstract:

    In this paper, a new concept of bifuzzy bi-Matrix Game is introduced where all elements of the payoff matrices are characterized by bifuzzy variables. The uncertainties of entries of payoff matrices (bifuzzy variables) are measured by bifuzzy measure known as Chance measure. Combining the bifuzzy set theory and bi-Matrix Game theory, the solution concept of bifuzzy bi-Matrix Game theory is introduced. The quadratic programming problem plays the major role to solve bifuzzy bi-Matrix Game. In order to show the applicability and feasibility of our proposed method, a real-life bi-Matrix Game problem is considered and solved.

Haowei Zhang - One of the best experts on this subject based on the ideXlab platform.

  • study on Matrix solution method of grey Matrix Game based on full rank grey payoff Matrix
    Systems Man and Cybernetics, 2006
    Co-Authors: Zhigeng Fang, Sifeng Liu, Haowei Zhang
    Abstract:

    Game theory based on the theory and thought of classical math has brought far-reaching affects in the field of economics, sociology, and so on. However, classical Game theory can find no way out when Game circumstance faces to uncertainty condition, such as finite logos, finite knowledge, small sample, and inadequate information, the payoff value of Game can only be described with grey number. So study on grey Matrix Game has the most important theoretic value and actualistic meaning. How to solve the grey Matrix Game with high efficiency is the key problem which must be solved in the theory research and application of this field. Matrix solution method of grey Matrix Game is simple and effective. This paper has defined grey full rank payoff value expansion square Matrix of grey Matrix Game, and has also proved that besides the value of grey element at the right and bottom edge of inverse Matrix of grey full rank expansion square Matrix, the value of grey element at its last line and right column is corresponding the optimal grey Game strategies of player 1 and 2 separately.

  • SMC - Study on Matrix Solution Method of Grey Matrix Game Based on Full Rank Grey Payoff Matrix
    2006 IEEE International Conference on Systems Man and Cybernetics, 2006
    Co-Authors: Zhigeng Fang, Sifeng Liu, Haowei Zhang
    Abstract:

    Game theory based on the theory and thought of classical math has brought far-reaching affects in the field of economics, sociology, and so on. However, classical Game theory can find no way out when Game circumstance faces to uncertainty condition, such as finite logos, finite knowledge, small sample, and inadequate information, the payoff value of Game can only be described with grey number. So study on grey Matrix Game has the most important theoretic value and actualistic meaning. How to solve the grey Matrix Game with high efficiency is the key problem which must be solved in the theory research and application of this field. Matrix solution method of grey Matrix Game is simple and effective. This paper has defined grey full rank payoff value expansion square Matrix of grey Matrix Game, and has also proved that besides the value of grey element at the right and bottom edge of inverse Matrix of grey full rank expansion square Matrix, the value of grey element at its last line and right column is corresponding the optimal grey Game strategies of player 1 and 2 separately.