Fuzzy Sets and Systems ( IF 3.2 ) Pub Date : 2021-06-25 , DOI: 10.1016/j.fss.2021.06.009 Raquel Fernandez-Peralta , Sebastia Massanet , Andrea Mesiarová-Zemánková , Arnau Mir
The characterization of -implications when N is a non-continuous negation has remained one of the most significant open problems in fuzzy logic for the last decades. This paper constitutes the first progress in this topic. Namely, a general characterization of this family of fuzzy implication functions is presented, in which the central property is the existence of a completion of a binary function defined on a certain subregion of to a t-conorm. In this paper, the dual problem of finding a completion of a binary function defined on a subregion of to a continuous t-norm is studied and solved for the minimum and a cancellative function. These results are the basis for the novel axiomatic characterizations of -implications in the case when N has one point of discontinuity and S is equal to the maximum t-conorm in a certain subregion of or a strict t-conorm.
中文翻译:
用于治疗与非连续否定(S,N)-implications基于叔conorms的完井表征的总体框架
的表征 -implications当ñ是不连续的否定一直在模糊逻辑中最显著开放的问题,为过去的几十年之一。本文构成了这一主题的第一份进展。即,该家族的模糊蕴涵功能的通用特征被呈现,其中,所述中央属性是基于的特定子区域定义的二元函数的完成的存在到叔余模。在本文中,找到一个二进制函数的完成的对偶问题上的子区域限定到连续t-模被研究和解决的最小和一个消功能。这些结果是对的新颖公理表征的基础- 当N有一个不连续点并且S等于某个子区域中的最大 t-conorm 时的含义 或严格叔余模。