(2104-6613) Construction of 2-uninorms on bounded lattices

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-10-11 DOI:10.22111/IJFS.2021.6375

A. Xie, Z. Yi

引用次数: 0

Abstract

Uninorms and nullnorms are special 2-uninorms. In this work, we construct 2-uninorms on bounded lattices. Let L be a bounded lattice with a nontrivial element d. Given two uninorms U1 and U2, defined on sublattices [0, d] and [d, 1], respectively, this paper presents two methods for constructing binary operators on L which extend both U1 and U2. We show that our first construction is a 2-uninorm on L if and only if U2 is conjunctive and our second construction is a 2-uninorm on L if and only if U1 is disjunctive. Moreover, we prove that the two 2-uninorms are, respectively, the weakest and the strongest 2-uninorm among all 2-uninorms, the restrictions of which on [0, d]2 and [d, 1]2 are respectively U1 and U2.

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(2104-6613)有界格上2-一致子的构造

一致范数和零范数是特殊的2一致范数。在这项工作中，我们构造了有界格上的2-一致子。设L是一个具有非平凡元素d的有界格。给定分别定义在子格[0,d]和[d, 1]上的两个一致子格U1和U2，本文给出了在L上构造二元算子的两种方法，这两种算子扩展了U1和U2。我们证明了当且仅当U2是合取的，我们的第一个构造是L上的2一致的当且仅当U1是析取的，我们的第二个构造是L上的2一致的。进一步证明了这两个2-一致子分别是所有2-一致子中最弱和最强的2-一致子，它们在[0,d]2和[d, 1]2上的约束分别是U1和U2。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.