Semi-uninorms and implications on a complete lattice

Authors:
Hua-Wen Liu
Affiliations:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China
Venue:
Fuzzy Sets and Systems
Year:
2012

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Abstract

An extension of a uninorm called a semi-uninorm is introduced and discussed in this paper. First, we introduce the concept of semi-uninorms on a complete lattice. Then, we discuss two kinds of residual operators of semi-uninorms and give conditions such that the operators are implications. We also give equivalent conditions for infinitely @?-distributive left- and right-conjunctive semi-uninorms. Furthermore, we define two classes of induced operators by implications on a complete lattice and give conditions such that they are semi-uninorms. We also provide the equivalent conditions for the infinitely @?-distributive implications in their second variables.