Confidence Closure Operators And Interior Operators

Considering the intervention of many-valued logic structure, the conceptof many-valued confidence filter is proposed in this paper, as tools of studyingthe many-valued confidence closure, interior operators and their related theories.Based on the many-valued confidence filters, the confidence closure operators andconfidence interior operators are defined and investigated. Then confidence clo-sure system, confidence closed system, confidence interior system and confidenceinterior closed system are discussed. At the end of this paper, the confidenceGalois connections are also investigated.This paper is organized by five sections as follows:The first section is the preface and preliminaries. it mainly introduces thebackground of theories, development situation and trend, related to closure op-erators, then puts forward the problems for study, and introduces the main workthroughout the paper. Also, the author introduces some notations and reviewssome fundamental knowledge about lattice theory and fuzzy set theory.The second section focuses on the problem of fuzzy reasoning about closureoperators in the environment of the complete residuated lattice, and proposesthe many-valued confidence filter. On the basis, the author defines F-confidenceclosure operator and F-confidence interior operator, proves their equivalent de-pict conditions, and further researches mutual transformation between the twooperators.The third section studies two kinds of special L subsets related to theF-confidence closure operator closely, i.e., F-confidence closure system, F-con-fidence closed system. the author solves mutual transformation between F-confi-dence closure operator and F-confidence closure system, also, F-confidenceclosed system.The fourth section defines the F-confidence interior system and the F-con-fidence interior closed system,and discovers the methods of transformation be- tween F-confidence interior operators and F-confidence interior system, alsoF-confidence interior closed system.The fifth section discusses the confidence lattice-valued Galois connectionsbetween the power sets, with the many-valued confidence filter, and proves theirequivalent characteristic conditions.