有界偏集上的幂等幺正和零范数

IF 1.9 4区数学 Q1 MATHEMATICS

Iranian Journal of Fuzzy Systems Pub Date : 2021-10-01 DOI:10.22111/IJFS.2021.6255

M. Kalina

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引用次数: 0

摘要

本文讨论了一致范数和零范数作为交换单调递增的基本半群运算。这些运算首先在单位区间上引入，然后推广到有界格上。在[Kalina 2019]中，它们被引入到有界偏置集上。这一贡献是对[Kalina 2019]中结果的概括和扩展。研究了有界偏集上幂等一致模和幂等零模存在的充分必要条件。最后，给出了一些应用实例。

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Idempotent uninorms and nullnorms on bounded posets

The paper deals with uninorms and nullnorms as basic semi-group operations which are commutative and monotone (increasing). These operations were first introduced on the unit interval and later generalized to bounded lattices. In [Kalina 2019], they were introduced on bounded posets. This contribution is a generalization and extension of the results in [Kalina 2019]. Some necessary and some sufficient conditions for the existence of idempotent uninorms and idempotent nullnorms on bounded posets are studied. Finally, some application examples are provided.

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来源期刊

Iranian Journal of Fuzzy Systems 数学-数学

CiteScore

3.50

自引率

16.70%

发文量

期刊介绍： The two-monthly Iranian Journal of Fuzzy Systems (IJFS) aims to provide an international forum for refereed original research works in the theory and applications of fuzzy sets and systems in the areas of foundations, pure mathematics, artificial intelligence, control, robotics, data analysis, data mining, decision making, finance and management, information systems, operations research, pattern recognition and image processing, soft computing and uncertainty modeling. Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.