Fuzzy Reasoning Algorithms Based On Uninorms

In the recent years, fuzzy control theory has been widespreadinto many application fields and research domains. Fuzzy reasoning, as thebasic theory of fuzzy control, has already attracted much attention fromthe majority of scholars and researchers. In this thesis, we do some in-depth discussion and research into the fuzzy reasoning algorithms basedon uninorms. We mainly discuss the fuzzy reasoning algorithms based onuninorms from the following two aspects: one is the fuzzy reasoning al-gorithms based on commutative fuzzy logic systems, the other is the fuzzyreasoning algorithms based on non-commutative fuzzy logic systems. Theoutline of this thesis is organized as follow:First, we do the research on the formal triple I algorithms for logicsystem W UL. First, a new complete formal system W UL is proposed,which is uninorm logic system UL extended with the (W) axiom Aâ†'t.By adding universal quantifier logic axioms for system W UL, a completemany-sorted first-order formal system W UL msfor fuzzy predicate logicisstructured. ThentripleIalgorithmsandthecorrespondingexpressionsofthe solutions based on commutative logic system W UL are given, as wellas the strict logic proof of triple I algorithms. Moreover, the reductivitiesof the triple I algorithms are proved. Therefore, triple I algorithms basedon uninorms are put into the framework of fuzzy logic.Second, the forms of differently implicational triple I algorithms of(1,2,2) type are improved. Apart from that, we propose differently impli-cational triple I algorithms of (1,2,1) type, which has a broader applicationbackground. In differently implicational triple I algorithms of (1,2,1) type,both the first implication and the third one are residuated implication oper-ators induced by the same left-continuous t-norm, the middle implicationoperator is unlimited operator. Reductivities of these algorithms are also proved. In differently implicational α triple I algorithms of (1,2,1) type,thefirstimplicationandthelastoneareresiduatedimplicationoperatorsin-duced by the same left-continuous t-norm1, the second one is a differentresiduated implication operator induced by the left-continuous t-norm2.The expressions of differently implicational triple I solutions and α tripleI solutions of (1,2,1) type are given.Moreover, combining the reverse triple I algorithms and a class residu-ated implications induced by the family of Schweizer-Sklar t-norms, flex-ible fuzzy reasoning reverse triple I algorithms are provided. The reversetriple I algorithms and α reverse triple I algorithms based on a class resid-uated implications induces by the family of Schweizer-Sklar t-norms areproposed, as well as the corresponding expressions of reverse triple I so-lutions and α reverse triple I solutions. We discuss the expressions of thesolutions, when the parameter takes some special values.Finally,fromfuzzyreasoningbasedoncommutativelogicsystemstran-sitiontofuzzyreasoningbasedonnon-commutativelogicsystems,wecon-duct some discussion and investigation. An example of triple I algorithmsbased on the first residuated implication operator and the second residu-ated implication operator induced by a certain left-continuous pseudo-t-norm is provided. Moreover, we formalize triple I algorithms based on thefirst residuated implications and the second implications induced by left-continuous pseudo-t-norms. In addition, triple I solutions (FMP-solution,FMT-solution, FMP-α-solution and FMT-α-solution) are structured, re-spectively. A new model of fuzzy inference method is given for processingcomplicated problems in the real world.