Some Generalized T-norms And Their Related Fuzzy Logic Systems

The fuzzy logic systems based on t-norms had many results, at the same time, the fuzzy logic systems based on pseudo- t-norms got much attention, such as proposed the non-commutative fuzzy logic systems psBL, psMTL, pL* and so on. However, we have finite result about fuzzy logic based on non-associative t-norms.The thesis deeply studies some generalized t-norms(particularly non-associative t-norms and on non-associative, non-commutative t-norms) and related algebra structure, specifically implication lattices and its non-commutative promotion(that is pseudo-implication lattices). On this basis, give some fuzzy logic based on generalized t-norms.The main results of the thesis are as follows:(1) Reveal internal links of non-associative t-norms and implication lattices. All low order implication lattices (the order is less than or equal to 8) are obtained by using mathematics software and inference. Illustrate the existence of proper implication lattice and well implication lattice, point out some mistakes of references; introduce the note of locally finite implication lattice and sub-associative implication lattice, proof they are all well implication lattice.(2) Propose the notion of gt-norms (non-commutative and non-associative), discuss the character of the residuated implication. Introduce the concept of pseudo-implication lattices as non-commutative promotion of implication lattices, construct binary operator ? on it, prove binary operator ? is gt-norms, give the examples. Propose the notion of pseudo-MP*-fliters, study the theory of pseudo-MP*-fliters, thus obtain the homomorphism theorem of normal pseudo-MP*-fliters.(3) The fuzzy logic system IL is established, the soundness of IL is be proved. The fuzzy logic system PIL is established, the soundness of PIL is being proved.