(2103-6517)基于可拓原理的犹豫模糊数的算术运算与排序

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-08-13 DOI:10.22111/IJFS.2021.6282

M. Ranjbar, S. M. Miri, S. Effati

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引用次数: 3

摘要

在犹豫模糊分析中，犹豫模糊数作为模糊数的一种推广，具有重要的应用价值，近年来已有文献对此进行了讨论。本文基于犹豫模糊集的可拓原理，提出了犹豫模糊算法。利用这一原理，将模糊数的标准算术运算推广到HFN上，并证明了这些运算在两个HFN上的结果是一个HFN。此外，我们还利用hfs中的扩展原理对hfs进行排序，这可能是一个有趣的话题。在本文中，我们证明了hfn可以以自然的方式排序。为了引入有意义的HFNs排序，我们在HFNs上使用了一种新的基于可拓原理的格运算，并定义了HFNs上的Hamming距离。最后，说明了它们在优化和决策问题上的应用。

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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(2103-6517) Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle

A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN.Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic. In this paper, we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a newlattice operation on HFNs based upon extension principle and defining the Hamming distance on them. Finally, the applications of them are explained on optimization and decision-making problems.

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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.