A Study of Generalized Fuzzy Dishkant Implications

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-10-09 DOI:10.37394/23206.2023.22.78

Dimitrios S. Grammatikopoulos, Basil Papadopoulos

引用次数: 0

Abstract

In this paper, we revisit the generalized Dishkant implications and provide analytical proof that they are a new fuzzy implications’ class that contains the known class of Dishkant implications. Both classes are not always fuzzy implications. For this reason we use the term operations instead of implications in general. Nonetheless, it will be demonstrated that a necessary but not sufficient condition for a generalized Dishkant operation to be a fuzzy implication exists. Furthermore, the intersection of the sets of generalized Dishkant operations and Dishkant operations (respectively, implications) is provided. At the end, we prove a theorem for F- conjugation in GDoperations.

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广义模糊Dishkant蕴涵的研究

在本文中，我们重新审视了广义的Dishkant蕴涵，并提供了分析证明，它们是一个新的模糊蕴涵类，包含了已知的Dishkant蕴涵类。这两个类别并不总是模糊的含义。出于这个原因，我们使用术语“操作”而不是一般意义上的含义。尽管如此，我们将证明广义Dishkant运算是模糊蕴涵的必要但非充分条件的存在。此外，还提供了广义Dishkant操作集和Dishkant操作集的交集(分别，含义)。最后，我们证明了广义算子中F-共轭的一个定理。

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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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.