Interval valued fuzzy sets from continuous Archimedean triangular norms

Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference Pub Date : 1994-06-26 DOI:10.1109/FUZZY.1994.343895

T. Bilgiç, I. Turksen

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引用次数: 3

Abstract

Interval valued fuzzy sets are suggested in Turksen (1986) to model the situations where linguistic connectives as well as the variables are fuzzy. They are defined using the discrepancy of conjunctive and disjunctive Boolean normal forms in the fuzzy case. The discrepancy is due to relaxing some of the axioms of classical logic. The authors briefly investigate the basic operations in the unit interval. Specifically the literature on representing the negation functions and triangular norms is recalled. Archimedean triangular norms are investigated as possible candidates for the logical connective AND. De Morgan triples are constructed utilizing a general result for negations. Two broad families of De Morgan triples are identified; strict and strong, which are neither distributive nor idempotent. The authors introduce the concept of an interval valued fuzzy set and present the main results of the paper, namely for strict and strong De Morgan triples interval valued fuzzy sets are well defined. The paper is technical in nature and extends some results obtained in Turksen (1986) to more general settings using generator functions.<>

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连续阿基米德三角范数的区间值模糊集

区间值模糊集在Turksen(1986)中被建议用来模拟语言连接词和变量是模糊的情况。利用模糊情况下合取布尔范式与析取布尔范式的差异来定义它们。这种差异是由于经典逻辑的一些公理的松弛。简要探讨了单位区间内的基本运算。具体来说，回顾了关于表示否定函数和三角范数的文献。研究了阿基米德三角范数作为逻辑连接与的可能候选者。De Morgan三元组是利用否定的一般结果构造的。已经确定了德摩根三联体的两个大家族;严格而强，既不是分配律也不是幂等律。本文引入了区间值模糊集的概念，并给出了本文的主要结果，即对于严格和强De Morgan三元组，区间值模糊集得到了很好的定义。本文本质上是技术性的，并将Turksen(1986)获得的一些结果扩展到使用生成器函数的更一般设置。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference

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