Measurement Of Fuzzy Reasoning Methods And Knowledge Reasoning

Fuzzy reasoning is a kind of approximate reasoning models for simulating human reasoning. As the core content of the fuzzy control technology, it has gained broad attention and made great achievements in theory after being proposed. However, these achievements lack enough foundation in the sense of reliable logic. In order to implant fuzzy reasoning into the orbit of logical semantical implication, the full implication triple I method for fuzzy inference was proposed, which made it possible to provide logical basis for fuzzy reasoning. Nevertheless, this method is only the first step along this direction and our final goal is to integrate the method to the strict mathematical logic framework. This paper aims at making a further study on logical foundation of the triple I method and provides a syntactical version for the a-triple I method based on the boolean function theory in classical propositional logic system. In addition, by use of triple I method, three kinds of approaches are introduced to solve multiple multi-dimensional fuzzy inference problem. Moreover, the reductivity, continuity and the spread property for approximate errors are studied.Mathematical logic, also called symbolic logic, making focuss on the formal infer-ence of symbolization without paying attention to numerical calculation. The theory of quantitative logic brings numerical calculation into mathematical logic, hence mak-ing it more flexible and expanding the scope of its possible application. Meanwhile, the research on reasoning about knowledge can be traced back to the philosopher of ancient Greece and has already developed into a relatively perfect and mature theo-ry in the field of artificial intelligence science nowadays. This dissertation brings the graded ideas into multi-valued reasoning about knowledge. From the local angle, the notion of the localized truth degree of formulas is given, and extended later to the global truth degree of formulas gradually. Moreover, three different kinds of approx-imate reasoning mechanisms with errors for multi-valued propositional logic system are transplanted into the multi-valued reasoning about knowledge, which realizes the integrity quantitative research for multi-valued reasoning about knowledge.This paper is divided into five chapters.Chapter 1 recalls some basic knowledge about quantitative logic of classical propo-sitional logic and n-valued Lukasiewicz propositional logic, together with the full im-plication triple I method for fuzzy inference, as the preparation for our further study in the rest chapters. Chapter 2 studies the logical foundation of a-triple I method for fuzzy inference in classical prepositional logic system. The notion of minimal a formulas in (F(S).(?)) is introduced, and not only the existential condition of minimal a formulas but also the distribution of similarity degrees among minimal a formulas are given. Moreover, when a belongs to H={(?)=0.1,…,2n;n=1,2.…}, we prove that the set of all the minimal a formulas is consistent when a equals 1; otherwise, it is inconsistent. Finally, the concepts of a-triple I solution about the problems of generalized Modus Ponens and multiple generalized Modus Ponens are defined, and the formalized expression of a-triple I solution are given.Chapter 3 first introduces two kinds of methods to solve multiple multi-dimensional fuzzy inference:FITA-RO type triple I method and FATI-.Ro type triple I method, proves their continuity property, and further discusses their reductivity property. Next, the shortcomings in (p-θ) method, also the existing method to solve multiple multi-dimensional fuzzy inference, is analyzed, and the improvable method—p-Ro type triple I method is proposed which is proved to be continuous. Meanwhile, we obtain that these three kinds of methods have a good transmissible performance for approximate errors.Chapter 4 introduces truth degree of formulas based on the infinitely countable product of unevenly distributed probability space in three-valued Lukasiewicz propo-sitional logic, and offers inference rules with truth degree. Moreover, it is proved that the set of truth degrees of propositions in the three-valued (a/5.b/5.c/5) logic mea-sure is dense in unit interval [0,1], and expressions of truth degrees are constructed, which provided the possible framework in the generally uneven probability space for approximate reasoning of three-valued propositional logic.Chapter 5 first expands the classical Kripke knowledge structure to n-valued Krip-ke knowledge structure, and sets up corresponding semantic theory. Meanwhile, it is pointed out that the classical Kripke knowledge structure can be integrated into the framework of n-valued Kripke knowledge structure, thus the multi-valued knowledge reasoning semantic theory in this paper generalized to the classical knowledge reason-ing semantic theory. Secondly, the notion of (MLn.s,i)-truth degree of formulas is defined and the (MLn, s,i)-similarity degree among formulas is proposed. Further-more, a pseudo-metric is defined on the set of all formulas and hence an approximate reasoning mechanism under a given point (MLn,s.i) is established. Next, taking the difference between agents and possible states into consideration under a given n-valued Kripke knowledge structure M.Ln, the notion of the.MLn-truth degree of formulas is denned. Based on these, an approximate reasoning mechanism under a giv-en knowledge structure MLn is established. Finally, the notion of global truth degree of formulas is defined as the weighted average of all those truth degrees under dif-ferent n valued Kripke knowledge structure, and three different kinds of approximate reasoning mechanisms with errors for multi-valued propositional logic in quantitative logic are transplanted into the multi-valued reasoning about knowledge. Moreover, the approximate reasoning on the set of all formulas are expanded in the global sense, which realizes the graded research on multi-valued reasoning about knowledge.