Research On Approximate Reasoning And Multi-attribute Decision-making Based On Intuitionistic-interval-valued Fuzzy Theory

To some extent,uncertainty exists in most of real systems.L.A.Zadeh,American electronic engineering and cybernetics scientist with profound insight,played emphasis on this kind of problems and published "Fuzzy Sets" for resolving it in 1965. He amended and extended set theory——the basis of modern mathematics with a bold hand and brought forward the thinking of using fuzzy set as a mathematical model to represent fuzzy business.It announced the birth of a new subject——fuzzy mathematics.In 1986 K.Atanassov,a famous Bulgarian scholar,introduced the concept of an intuitionistic fuzzy set which is characterized by two functions expressing the degree of belongingness and the degree of nonbelongingness,respectively.It provides more choices for the attribute description of an object and has stronger ability to express uncertainty than Zadeh's fuzzy sets,and gains extensive attention from the academic circles and circles of engineering and technology.In practice,interval-valued belongingness degree and nonbelongingness degree can be determined more easily than point-valued belongingness degree and nonbelongingness degree.So the concept of intuitionistic-interval-valued fuzzy sets was introduced by K.Atanassov and G.Gargov in 1989.In this dissertation,we will study the problems of approximate reasoning and multi-attribute decision-making by means of intuitionistic-interval-valued fuzzy sets, and we will establish a series of methods for solving above problems.The main contents and results are summarized as follows:1.The study on uncertainty measurement of intuitionistic-interval-valued fuzzy sets.Entropy,distance measure and similarity measure are three basic concepts in uncertainty measurement theory.The paper gives the axiom definitions of entropy, distance measure and similarity measure of intuitionistic-interval-valued fuzzy sets, and discusses basic relations among them.Theσ-measures and weakσ-measures are important concepts in fuzzy information measure.Entropy,distance measure and similarity measure are special cases ofσ-measures and weakσ-measures.This paper gives the definitions and properties ofσ-entropy and weakσ-entropy,σ-distance measure and weakσ-distance measure,σ-similarity measure and weakσ-similarity measure,then discusses basic relations among them.Different from the former intersection and union calculations,the paper points out the addition and multiplication calculations of intuitionistic-interval-valued fuzzy sets,and discusses the properties of entropy,distance measure and similarity measure based on these calculations.2.The investigation of intuitionistic-interval-valued fuzzy implication operator. The selection of implication operator has closely related with the result of approximate reasoning.Residual implication operator is a general implication operator and has many fine properties.In this paper,using the lattice(D,≤)triangular norm and conorm are straightforwardly extended to the intuitionistic-interval-valued fuzzy cases.And then the paper discusses the properties of intuitionistic-interval-valued fuzzy triangular norm and implication operator which satisfy residuation principle.3.The research on CRI algorithm of intuitionistic-interval-valued fuzzy reasoning.The first model of inference to handle fuzzy rules which used the compositional rule of inference(CRI)due to L.A.Zadeh,is one of the most fundamental inference mechanisms.Because any general intuitionistic-interval-valued reasoning can be transformed into the fundamental form:MP(Modus Ponens)or MT (Modus Tollens)by proper methods,this paper only discusses the two most fundamental forms of reasoning,and gives the general forms of CRI solutions for MP problem and MT problem in an intuitionistic-interval-valued environment, respectively.The reversibility conditions are attached importance in our discussion and the reversibility criteria are given.4.The discussion on TripleⅠalgorithm of intuitionistic-interval-valued fuzzy reasoning.The conventional CRI algorithm of fuzzy reasoning is short of solid logic foundation.The full implication TripleⅠalgorithm proposed recently efficiently improves CRI algorithm.This paper makes general discussion about the TripleⅠmethods for intuitionistic-interval-valued fuzzy reasoning,gives the general forms of TripleⅠsolutions for MP problem and MT problem in an intuitionistic-interval-valued environment,respectively.The existence conditions of the fully implicational solutions are discussed.Based on intuitionistic-interval-valued fuzzy implication operator satisfying residuation principle,the paper establishes the fully implicational methods for intuitionistic-interval-valued reasoning,i.e.,α-TripleⅠmethods for MP problem and MT problem.At last,the MultipleⅠmethod for intuitionistic-interval-valued reasoning is given.5.The research on intuitionistic-interval-valued fuzzy logic and its resolution principle.Based on operator lattice theory,this paper defines the operators and their composite operations in the set of intuitionistic interval values.And the operators are put in the front of formulas in the logic to get intuitionistic-interval-valued logic.It is similar to classical predicate logic,but they are different from each other essentially. The paper also discusses the truth values of the formulas,the models of the semantics, several properties,resolution principle and the proof of the resolution completeness theorem in the logic.6.The study on intuitionistic-interval-valued fuzzy multi-attribute decisionmaking. Firstly,possibility degree of intuitionistic interval values is defined.On the basis of it,a method on ordering for intuitionistic interval values is given.Secondly, the intuitionistic-interval-valued fuzzy multi-attribute decision-making methods based on possibility degree under three conditions:attribute weighting is known,attribute weighting is absolutely unknown and attribute weighting only is partially known,are discussed.Then,an intuitionistic-interval-valued fuzzy multi-attribute decisionmaking method based on intuitionistic-interval-valued fuzzy reasoning is put forward, decision-making information is turned into reasoning process by the method.