Research On Representation Of Hybrid Uncertainties With Applications

Uncertainty is pervasive in practical information systems, and several differentkinds of uncertainty often exist simultaneously in practical situations. It is a critical andfundamental problem to effectively represent hybrid uncertainty in informationrepresentation and processing. Therefore, the representation and processing of threecommonly encountered classes of hybrid uncertainty consisting of the combinations ofthe elementary uncertainty, randomness, fuzziness and roughness, are studied in thispaper. Their applications in fields such as nonparametric regression analysis, patternclassification and evidential reasoning are also investigated.The paper is organized as follows.In the first chapter, the research background is introduced in detail at first. Then thecurrent research status of hybrid uncertainty representation and author’s primary workand main contributions are also presented subsequently.The second chapter reviews several fundamental theories for uncertaintyrepresentation, including probability theory, evidence theory, fuzzy set theory and roughset theory.In the third chapter, the rule-based fuzzy system and the form of probabilistic fuzzyrule base are firstly surveyed. Then we present two methods for generating probabilisticfuzzy rule base from data set, based on which two classes of probabilistic fuzzy systemare realized. A Mamdani type probabilistic fuzzy rule base is derived for the case thatthe consequent variable is quantitatively continuous, while a probabilistic fuzzyclassification rule base is induced for the case that the consequent variable isqualitatively discrete. These two classes of probabilistic fuzzy system are applied tononparametric regression analysis, time series prediction and pattern classificationrespectively, with which better application results are obtained as compared with that ofsimilar approaches.A fuzzy evidence theory with fuzzy-valued belief function in continuous interval isproposed in the fourth chapter. Considering that the fuzzy descriptions are pervasive andthe infinite universes of discourse are commonly encountered in practical problems,some fuzzy generalizations of evidence theory in continuous interval have beenaddressed. More or less some deficiencies occur in these generalizations, such as theinsensitivity of belief functions to the significant changes in focal elements, there is no reasonable interpretation for belief functions as lower probabilities, and resultingpoint-valued belief functions usually are not equivalent to the fuzzy bodies of evidence.Therefore, fuzzy-valued belief function in continuous interval is defined in this paper.The equivalence of such defined belief function with the fuzzy body of evidence isproved for a large class of fuzzy bodies of evidence. Moreover, the induced belieffunction and plausibility function possess corresponding probabilistic interpretations.The fifth chapter presents a method for constructing fuzzy T-similarity relationfrom fuzzy attribute data for fuzzy rough set analysis. As a fuzzy extension of rough settheory, fuzzy rough set analysis is an effective tool to discover knowledge and extractrules from data set with continuous or fuzzy attribute values. The fuzziness androughness are represented simultaneously by using fuzzy relation which is theprecondition and basis of fuzzy rough set analysis. It is generally required the fuzzyrelation to be a fuzzy T-similarity relation. The presented fuzzy T-similarity relationgeneration method lays foundation for subsequent fuzzy rough analysis.Finally, some conclusions have been drawn and the directions for future work havealso been listed in the last chapter.