The Theoretical Research Of Intuitionistic Fuzzy Programming And Its Application

The theories of fuzzy sets provide a kind of efficient method to deal with fuzzyinformation. In 1983, Atanassov introduced the concept of intuitionistic fuzzy set whichextended the theories of fuzzy sets. It processes the information of membership andnon-membership, provides more choices for the attribute description of an object andexpresses uncertainty better than fuzzy sets. It has been applied in the area of patternrecognition, neural network, group decision-making, fuzzy optimization, etc. This paper aimsat studying Intuitionistic fuzzy subspace, convex intuitionistic fuzzy mappings andintuitionistic fuzzy programming on the basis of intuitionistic fuzzy set, The results obtainedin it enrich the theories of fuzzy sets and provide an efficient method for decision makerswhen they face uncertainty problem. The main results obtained in this dissertation aresummarized as follows:1. In Chapter 3, the theories of intuitionistic fuzzy subspace are studied. The concepts ofintuitionistic fuzzy point, intuitionistic fuzzy subspace and intuitioistic fuzzy affine set areproposed. The relation between intuitionistic fuzzy supspace and intuitionistic fuzzy affine setis also discussed. The paper using intuitionistic fuzzy point investigates the intuitionisticfuzzy affine sets and intuitionistic fuzzy subspaces, and proves a necessary and sufficientcondition for an intuitionistic fuzzy set is an intuitionistic fuzzy subspace or an intuitionisticfuzzy affine set of vector space E. The concepts of intuitionistic fuzzy linear transformationand intuitionistic fuzzy affine transformation are proposed and their relation is discussed too.These results further extend the theories of fuzzy sets.2. In Chapter 4, the convex intuitionistic fuzzy mappings are studied. Based on thetheories of fuzzy sets, the relations of convex intuitionistic fuzzy set, strictly convexintuitionistic fuzzy set, semi-strictly convex intuitionistic fuzzy set, quasi-convexintuitionistic fuzzy set, strictly quasi-convex intuitionistic fuzzy set and semi-strictlyquasi-convex intuitionistic fuzzy set are studied. Then the concept of intuitionistic fuzzynumber and its operations are presented based on the concept and operations of intervalnumbers and fuzzy numbers. The maximal and minimal of intuitionistic fuzzy numbers andhamming distance are proposed, a method of comparing intuitionistic fuzzy numbers is giventoo. At last, the concepts and relations of convex intuitionistic fuzzy mapping, (φ₁,φ₂)-convex intuitionistic fuzzy mapping, preinvex intuitionistic fuzzy mapping,quasi-preinvex intuitionistic fuzzy mapping are given.3. In Chapter 5, the models of intuitionistic fuzzy programming are discussed. Firstly,Applying the theory of intuitionistic fuzzy set in uncertainty problems, the paper describes theobject and constraints by membership function and non-membership function of intuitionisticfuzzy sets, extends the model of fuzzy linear programming introduced by Verdegay andWerners and gives a numerical example. Secondly, it presents the model of convexintuitionistic fuzzy programming by using convex intuitionistic fuzzy mapping and discussesits properties. These researches enrich the contents of fuzzy mathematical programming andprovide a good method for mathematical programming with uncertainty parameters.