一类由一致模与模糊否定构造的新模糊蕴涵——(N,U)-蕴涵

doi:10.6040/j.issn.1671-9352.4.2022.3841

摘要/Abstract

摘要： 在(U,N)-蕴涵的基础上,从经典蕴涵算子p→q=p∨q的对偶形式p→q=(p∧q)出发,用合取一致模U取代(p∧q)中的∧运算,用一般模糊否定N取代(p∧q)中的运算,生成了一类新的模糊蕴涵,称为(N,U)-蕴涵。(N,U)-蕴涵是一类不同于(U,N)-蕴涵的蕴涵算子,与(U,N)-蕴涵形成了互补,丰富了蕴涵算子的生成方法。

关键词: 一致模, 模糊蕴涵, 模糊否定, (U,N)-蕴涵, 三角模

Abstract: Based on the duality principle and(U,N)-implication, we construct a new type of fuzzy implication, named(N,U)-implication, which is obtained by replacing ∧ and  operators with conjunctive uninorms and general fuzzy negations in the formula p→q=(p∧q)in classical logic system.(N,U)-implication differs from the(U,N)-implication, and can be considered its complement to a certain extent thus enriching the pool of the generating methods for fuzzy implications.

Key words: uninorms, fuzzy implication, fuzzy negation, (U,N)-implication, triangular norms

中图分类号:

O144

于鹏,李冉冉. 一类由一致模与模糊否定构造的新模糊蕴涵——(N,U)-蕴涵[J]. 《山东大学学报(理学版)》, 2023, 58(5): 1-9.

YU Peng, LI Ranran. (N,U)-implication: a kind of new fuzzy implication constructed by uninorms and fuzzy negation[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(5): 1-9.

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