(S,N)-余蕴涵的性质及其等价刻画  

(S,N)-coimplication properties and their equivalent characterizations

作　　者：王玉焕 王小霞[1] 刘生云 WANG Yuhuan;WANG Xiaoxia;LIU Shengyun(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2024年第4期78-82,87,共6页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学地区基金项目(12261090);陕西省自然科学基础研究项目(2018JM1042)。

摘　　要：作为布尔逻辑中蕴涵的推广,模糊蕴涵的各种不同构造和等价刻画成果丰富,但对模糊蕴涵的对偶算子——模糊余蕴涵研究较少。本文首先借助三角余模S和模糊否定N构造了(S,N)-余蕴涵;其次讨论了(S,N)-余蕴涵包括输入律在内的若干性质和((J_(S,N))_(φ),S)满足输入法则LI的等价刻画;最后给出(S,N)-余蕴涵的等价刻画。研究结果完善了模糊蕴涵理论。As a generalization of implication in Boolean logic,there are abundant achievements in the construction and equivalent characterization of fuzzy implication,but there are few studies on the dual operator fuzzy coimplication of fuzzy implication.The(S,N)-coimplication is constructed by means of triangular conorm S and fuzzy negation N,and then several properties of(S,N)-coimplication including input law and the equivalent characterization of((J_(S,N))_(φ),S)satisfy the equivalent characterization of the input rule LI.Finally,equivalent characterizations of(S,N)-coimplication are given.The results improve the fuzzy implication theory.

关 键 词：模糊余蕴涵 模糊否定 三角余模 (S N)-余蕴涵 

分 类 号：O159[理学—数学]