Fuzzy Multiobjective Lattice-order Decision Making And Symmetric Matrix Game

The famous axioms for rational behavior established by Von-Neumann and Morgenstern , as a sign of birth of modern decision-making, is a cornerstone of normative decision-making theory. In the past half century, the researching on the axioms and the applying them to practice have been a hot spot all the while, and numerous significant achievements have been gained. In the 1950s, Allais and Edwards with some other scholars began to do the research to check the facticity of the rational decision-making models applied to the real decision-making behavior, only to find all kinds of unsatisfying deviations. These researches mainly focused on weakening the independence axiom and transitivity axiom. But recently, some scholars such as Prof. Guo Yaohuang have pointed out that preference relation is often a lattice and developed a new set of axioms for lattice-order decision-makingbehavior. By using the modern mathematical theory--lattice theory inthis dissertation, the ordering axiom is generalized to the lattice order axiom , and the connected axiom is wakened . This dissertation introduces the lattice - order decision-making behavior axioms and their vast range of prospects. Since the 1970s, multiobjective decision-making has been developed greatly. Because of the conflicts among the objectives, the fuzzy information such as decision-maker' preference and judgment must be considered in order to choose a satisfactory scheme. Fuzzy theory has been an efficient tool to solve all kinds of multiobjective decision-making problems in a fuzzy situation.The dissertation integrates decision-making theory, lattice theory, fuzzy set theory and other related knowledge, (1) puts forward the concepts of fuzzy multiobjective lattice-order decision-making, and constructs the models of fuzzy multiobjective lattice - order decision-making models, and attains two kinds of basic methods to solve them by illustrating by example. (2) presents the concepts of fuzzy multiobjective group lattice-order decision-making, and constructs the models of fuzzy multiobjective group lattice-order decision-making models, and obtains two kinds of feasible methods tosolve them by illustrating by example. The main idea: As for decision-making whose choice sets and objective sets are finite, if two arbitrary choices have supremum and infimum, then the top element (oar the bottom element) is the optimum choice. If the condition does not exist, in order to form a lattice, the fuzzy positive and negative ideal solutions which are suppositional are respectively regarded as the top element and the bottom element. The optimum solutions or satisfying solutions are found by the comparison of the distance between every choice and the positive or negative ideal solution.Since 1912, game theory has attracted many scholars' intrest and had an extensive application in quite a few fields such as natural science and social science. Matrix game is the base of game theory , so it is of greater significance to study the properties of symmetric game. In this dissertation, the model of symmetric game is built first .A solution of symmetric game is gained by its properties .By constructing a block matrix,we can convert a general matrix game into a symmetric game, then we gain a rapid method to solve matrix game.