Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory

作者：Asiain Maria J; Bustince Humberto; Mesiar Radko; Kolesarova Anna; Takac Zdenko

来源：IEEE Transactions on Fuzzy Systems, 2018, 26(2): 556-568.

DOI：10.1109/TFUZZ.2017.2686372

• Admissible order
• equilibrium point
• interval-valued fuzzy negations
• intervals
• strong negations on intervals
• total order

Admissible orders have brought the structure of chains in the framework of interval-valued fuzzy sets. However, a deeper study of functions monotone with respect to admissible orders is still missing in the literature. In this work, we consider the construction of negations and strong negations on intervals with respect to admissible orders, in particular, for the Xu and Yager and lexicographical orders, as well as for those based on K-alpha operators. We introduce and discuss an approach to the construction of strong negations on intervals with respect to K-alpha,(beta) orders based on an arbitrary couple of strong negations defined over the standard real interval [0, 1]. The introduced strong negations have a deep impact on all fields exploiting fuzzy methods dealing with intervals, allowing to introduce complements, dual aggregations, implications, entropies, etc.

• 出版日期2018-4
• 单位中国人民解放军信息工程大学