Research On The Method Of Information Fusion And Knowledge Acquisition Of Multi-fuzzy Information Systems

As we move into the information age, information acquisition, information analysis andprocessing, information fusion become hot topics in the field of information technology. Andinformation system is the carrier of our most access to information resources, it will inevitablybecome the main object of information science. Information systems with huge amount of in-formation have significant uncertainties. These uncertainty measures are the important issues ofdata mining and knowledge discovery. From the probability point of view, the evidence theoryand information entropy are main theoretical bases of the uncertainty of the systems; from theset theory point of view, the information granules, rough sets, fuzzy sets and intuitionistic fuzzysets are tools to describe the uncertainty. Based on the theory of granular computing, rough sets,evidence theory, information entropy, fuzzy sets and intuitionistic fuzzy sets, this paper studythe information fusion, reduction, the uncertainty measure and knowledge acquisition problemof multiple fuzzy information systems, including knowledge fusion of multi-fuzzy coveringsystems, uncertainty measure of (intuitionistic) fuzzy covering systems, the probability of anintuitionistic fuzzy set, belief function and plausibility function of intuitionistic fuzzy informa-tion systems and their applications, the definition of information entropy of an intuitionisticfuzzy information system and being a tool to reduce an intuitionistic fuzzy information system.The main contribution of this paper can be described as follows:(1) How to fuse multi-information systems based on rough set theory is a topic worthy ofour in-depth study. Most types of fuzzy binary relation can generate a fuzzy covering on theuniverse of discourse. Therefore, we study fuzzy evidence theory based on fuzzy coverings.Firstly, we give the completion approach of an uncomplete fuzzy covering information systemand a pair of the generation of the belief and plausibility function and the homologous massfunction with respect to the lower and upper approximation operators based on a completefuzzy covering. Then we discuss the reduction of a fuzzy covering by using the plausibilityfunction in information systems and in decision tables respectively. When the belief structureis given to a fuzzy covering system, we propose an information fusion method of multi-fuzzycovering systems. We first define a new fusion mass function, and discuss the properties andapplications of the corresponding belief and plausibility function. We then give lower andupper approximation operations generated by the belief function and plausibility function ontwo special cases:(a) the number of the focal elements in a fusion mass function is smallerthan the number of the elements in U;(b) the number of the focal elements in a fusion mass function is bigger than the number of the elements in U, and the mass function values of thefocal elements, assigned to the same object, in a fusion mass function are the same.(2) Reduction is one of the important research topics in rough set theory. In this section,the research priorities are the reduction of various fuzzy covering systems. Due to the presenceof noise in information systems, in order to as far as possible to avoid the influence of noise andto achieve better approximation effect, we redefine the information granules of a fuzzy coveringsystem, that is, the most possible fuzzy description of each element with respect to fuzzy cov-ering regards as a grain. We propose a dual pair of fuzzy rough approximation operators basedon the new information granules. Hereafter, we discuss the reductions of a fuzzy covering deci-sion system. According to the consistent, we divide multi-fuzzy covering decision systems intoconsistent, β consistent and inconsistent multi-fuzzy covering decision systems. And then, weintroduce information entropy and conditional entropy of the fuzzy covering decision systemand define the reduction of the fuzzy covering system by means of conditional entropy (re-spectively, β conditional entropy and limited conditional entropy) in consistent (respectively,β consistent and inconsistent) fuzzy covering decision systems. Algorithms are designed tocompute the approximate reduction of consistent, β consistent and inconsistent fuzzy coveringdecision systems, respectively.(3) Since probability theory is the basis of the evidence theory and information entropy,we propose a new method to compute the probability of a measurable intuitionistic fuzzy setusing the integral operation for level sets of an intuitionistic fuzzy set, which is a real numberin [0,1]. We then study the evidence theory of intuitionistic fuzzy systems using our proposedprobability of an intuitionistic fuzzy set and intuitionistic fuzzy (I, T) rough approximationoperators. We propose the belief structure and belief and plausibility functions of intuitionisticfuzzy systems based on the new probability definition and discuss their properties. And, wegive an application of the decision analysis using our belief function and plausibility function.The other application of the probability is given to the definitions of intuitionistic fuzzy entropyand conditional entropy in intuitionistic fuzzy environment, and we discuss the reduction ofintuitionistic fuzzy systems using the conditional entropy.(4) When extending a fuzzy covering system to an intuitionistic fuzzy covering system, westudy intuitionistic fuzzy covering approximation operators in intuitionistic fuzzy environment.We define a new pair of induced intuitionistic fuzzy covering lower and upper approximationoperators. And propose the uncertainty measure of intuitionistic fuzzy sets reflecting the intu- itionistic fuzzy rough measure and the uncertainty measure of an intuitionistic fuzzy coveringsystem. And, when a set is a crisp and definitional set, we prove that the intuitionistic fuzzyrough measure is0. Then we discuss the properties of the construction of an intuitionistic fuzzycovering. The reductions of an intuitionistic fuzzy covering with respect to the construction andrough approximation are presented, respectively. And we analyse the relation of the two kindsof reductions. Finally, we use the conditional entropy of the intuitionistic fuzzy covering withrespect to intuitionistic fuzzy decision covering to design an algorithm to reduce intuitionisticfuzzy covering decision systems.