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(S,N)-余蕴涵的性质及其等价刻画

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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((JS,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.
(S,N)-coimplication properties and their equivalent characterizations
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 coimplica-tion of fuzzy implication.The(S,N)-coimplication is constructed by means of triangular conorm S and fuzzy nega-tion N,and then several properties of(S,N)-coimplication including input law and the equivalent characterization of((JS,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.

fuzzy coimplicationfuzzy negationtriangular conorm(S,N)-coimplication

王玉焕、王小霞、刘生云

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延安大学 数学与计算机科学学院,陕西 延安 716000

模糊余蕴涵 模糊否定 三角余模 (S,N)-余蕴涵

2024

延安大学学报(自然科学版)
延安大学

延安大学学报(自然科学版)

影响因子:0.238
ISSN:1004-602X
年,卷(期):2024.43(4)