q-Spherical fuzzy rough sets and their usage in multi-attribute decision-making problems

IF 1.8 3区 数学 Q1 MATHEMATICS
Ahmad Bin Azim, Ahmad Aloqaily, Asad Ali, Sumbal Ali, Nabil Mlaiki, F. Hussain
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引用次数: 1

Abstract

This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as "aggregation operators" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.
q-球面模糊粗糙集及其在多属性决策问题中的应用
本文的目的是研究和推广粗糙集的概念,除了q球模糊集,并引入一个新的概念,称为q球模糊粗糙集(q-SFRS)。这种新颖的方法避免了诸如直觉模糊粗糙集、毕达哥拉斯模糊粗糙集和q-rung正形模糊粗糙集等新近思想的复杂性。因为称为“聚合运算符”的数学运算是用来将数据集合在一起的。常用的聚合操作包括算术平均值和加权平均值。加权平均数和算术平均数之间的关键区别在于,算术平均数允许我们根据其重要性对各种值进行加权。不同的聚合操作符对输入(数据类型)和可能包含在模型中的信息类型做出不同的假设。为此,引入了新的q球模糊粗糙加权算术平均算子和q球模糊粗糙加权几何平均算子。发达的运营商更为普遍。因为图像模糊粗糙加权算术平均数(PFRWAM)算子、图像模糊粗糙加权几何平均数(PFRWGM)算子、球面模糊粗糙加权算术平均数(SFRWAM)算子和球面模糊粗糙加权几何平均数(SFRWGM)算子都是q-SFRWAM和q-SFRWGM算子的特例。当参数q = 1时,q- sfrwam算子约简PFRWAM算子,q- sfrwgm算子约简PFRWGM算子。当参数q = 2时,q-SFRWAM算子约简SFRWAM算子,q-SFRWGM算子约简SFRWGM算子。此外,我们的方法更加灵活,决策者可以根据不同的风险态度选择不同的参数q值。此外,还对这些新出现的算子的基本性质进行了深入的分析和阐述。此外,还建立了一种称为多标准决策(MCDM)的技术,并提供了一个详细的示例来支持最近介绍的工作。在文章的结论中建立了对所提供方法的评估。研究结果表明,与q球模糊集相比,我们的方法更好、更有效。
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
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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