Research On Differently Implicational Universal Triple I Method Of (1,2,2) Type And Its Applications

Nowadays fuzzy reasoning plays a significant role in artificial intelligence, fuzzy control, fuzzy expert system and so on. The basic problems of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). As for these problems, the broadly used method is the CRI (Compositional Rule of Inference) method proposed by Zadeh in1973. Later, Guojun Wang pointed out that there were some disadvantages in the CRI method, and proposed the triple I method in1999, which has attracted rapidly growing interests in this research field.Although the triple I method possesses many acknowledged advantages such as excellent reversibility property, strong logic basis, the property of pointwise optimization and so on, it is imperfect from the viewpoint of fuzzy systems, which is embodied as inferior response ability and practicability. For this problem, the triple I method is generalized to differently implicational universal triple I method of (1,2,2) type (universal triple I method for short) in the present dissertation; moreover, systematic researches are carried through revolving around the universal triple I methods. The main works of the present dissertation are as follows:(1) Solutions of universal triple I methodsAs a fuzzy reasoning method, the chief task is to accomplish its solving. For three kinds of universal triple I methods (including basic universal triple I method, α-universal triple I method, and α-universal triple I restriction method), the strict definitions of all kinds of universal triple I solutions are given, and following that, the existence (or the condition of existence) of solution is respectively discussed, and finally the unified forms of solutions of these universal triple I methods are obtained revolving around residual implication operators. Meanwhile, as special cases of the universal triple I solutions, related results of corresponding triple I solutions are achieved. Furthermore, the optimal solutions of related universal triple I methods and triple I methods are provided for some specific implication operators.(2) Rationality of universal triple I methods The reversibility property is a recognized basic demand of fuzzy reasoning method. Aiming at the basic universal triple I method, its reversibility property is analyzed with the conclusion that it seems excellent, while the reversibility property of corresponding triple I method and CRI method are obtained. Moreover, for the interpretation of universal triple I formula, it is pointed out that the first implication and second implication (in the universal triple I method) respectively embody the function of rule base and reasoning mechanism. Lastly, from the viewpoint of universal triple I method, a rationality interpretation is given for a sort of CRI method.(3) Fuzzy systems based on universal triple I methodsTo apply fuzzy reasoning to practical problems, fuzzy reasoning often needs to be investigated as a part of fuzzy system. The fuzzy systems via universal triple I methods (i.e., the universal triple I systems) are established, and then response abilities of related universal triple I systems are investigated, and finally190usable fuzzy systems are obtained. It is achieved that the universal triple I method can provide bigger choosing space and get more usable fuzzy systems by contrast with the triple I method and CRI method.(4) Applications of universal triple I methods in innovative conceptual designBased on the related research results of universal triple I methods, applications of universal triple I methods in innovative conceptual design are researched for the function solving of and/or/not function trees in the field of innovative conceptual design. First, some related definitions of and/or/not function trees are introduced, and then the concept of function tree is generalized to the one of fuzzy function tree. Second, focusing on a key step of the process of function solving (that is, function-structure mapping), the function-structure mapping method based on the universal triple I method are put forward. Lastly, the concepts of four-valued matrix (FVM) and extended four-valued matrix (EFVM) are given, and then the FVM system and disjunctive normal form system are constructed while these two algebra systems are proved to be isomorphic; furthermore, the expanding and elaborating strategy of FVM are provided, and based on them, three function solving methods via EFVM are brought forward.What is more, the product concept's fuzzy reasoning and generation system is designed and realized. Moreover, by this system, two examples of multi-function travel cup and magnetically levitated train, illustrate the whole process of function solving in detail, demonstrating that the related results of universal triple I methods are effective.