Properties Of Generalized K-Generated Implications And Their Applications

This thesis generalize the κ-implication into a new class of fuzzy implication,namely（φ,k）-implication,discusses the ordering property,T-conditionality,the law of importation and the distributivity over triangular norms（t-norm for short）and triangular conorms（tconorm for short）,and obtains the logic inference solutions.First,it gives the concept of（φ,k）implication and some examples of（φ,k）-implications,discusses some properties related to the natural negation and continuity of（φ,k）-implications,and proves that a（φ,k）-implication is determined by k-generators and the strictly increasing continuous function φ.Next,it presents the connection between a（φ,k）-implication and other implications,i.e.,it shows that a（φ,k）－implication is a k-implication if φ（x）=x for all x∈[0,1];a（φ,k）-implication is an（f,g）－implication if Ran（g）={0,1};a（φ,k）-implication is a（g,f）-implication if g（1）<∞;a（φ,k）-implication is an（h,l）-implication if h（1）>0.Then,it investigates the relationships between（φ,k）-implications and two classes of classical implications,i.e.,it verifies that a（φ,k）-implication is an（S,N）-implication when k（0）>0,and a（φ,k）-implication is an R-implication if and only if a（m,k）-implication is a φ-conjugate of the implication I_GG.In addition,it discusses the functional equations of（φ,k）-implication which satisfies the Tconditionality,the law of importation and the distributivity over t-norms and t-conorm.Finally,this thesis supplies the solutions of FMP triple I.