| Uninorm is a special aggregation operators. As is needed in the applica-tion, manv kinds of extensions of uninorms were introduced. Semi-uninorm which doesn’t satisfy commutativity and associativity is one of the extension-s. Two kinds of residual operators of semi-uninorms were dicussed and the conditions such that the operators are implications were given. Two class-es of induced operators by implications on a complete lattice were defined and conditions such that they are semi-uninorms were given. Based on this, this paper studies some properties of (US, N)-, QL-implications and residual coimplications induced by semi-uninorms. The paper contains four chapters as follows:Chapter1presents the concepts and properties of triangular norms, fuzzy implications and fuzzy coimplications. Situations of extensions of uninorms fuzzy implications and fuzzy coimplications are reviewed.Chapter2gives an overview of some basic results concerning uninorms. Their structure and the main classes characterized so far are revised. Several typical extensions of uninorms are summerized. And the relations among them are dicussed.Chapter3introduces (US,N)-opevsitor((IUS.N(x,y)=US(N(x),y))) in-duced by semi-uninorm Us and QL-operator (IQL(x,y)=U’S(N(x), US(x,y))) of a conjunctive semi-uninorms US and a disjunctive semi-uninorm U’S. Con-ditions such that the operators are implications are given. And the properties of the two operators are discussed. The main conclusion can be summarized as follows:(US,N)-perator is an implication if and only if US is disjunc- tive; If QL-operator is an implication, then US’ is a t-semiconorm and satisfies US’(x,N(x))=1,x∈[0,1], and US’ satisfies law of excluded middle w.r.t a strong negation N.Chapter4introduces two kinds of operators of semi-uninorms on a com-plete lattice and give conditions such that the operators arc complications. Two kinds of operators of coimplications are introduced and the conditions such that the operators are semi-uninorms were given. The main conclusion is summarized as follows:JiUS(i=1,2) induced by right(left)-disjunctive semi-uninorms is coimplication. A series of basic properties are given.The innovations in this paper can be summarized as follows:(1) The concepts of (Us, N)-operator((IUS,N=Us(N(x),y))) and QL-operator(IQ(x,y)=US’(N(x), US(x,y))) of semi-uninorms are introduced. Con-ditions such that the operators are implications are discussed. And the prop-erties of two operators are discussed.(2) Two kinds of residual operators of semi-uninorms are introduced. Conditions such that the operators are coimplications are given. And the basic properties of the residual coimplications of infinitely Λ-distributive semi-uninorms are discussed.(3) Two kinds of operators induced by coimplications are introduced. Con-ditions such that the operators are semi-uninorms are discussed. And the properties of two operators are discussed. |
