(2103-6517)基于可拓原理的犹豫模糊数的算术运算与排序

IF 1.9 4区数学 Q1 MATHEMATICS

Iranian Journal of Fuzzy Systems 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。

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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

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 Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.