区间2型模糊集的模糊加权平均和广义质心的随机化算法

IF 2.7 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-06-12 DOI:10.1016/j.fss.2025.109508

Xianliang Liu , Zishen Yang

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引用次数: 0

摘要

模糊加权平均是多准则决策中一种有用的聚类方法，而区间2型模糊集广义质心（IT2 FS）是区间2型模糊逻辑系统中一种重要的约简方法。它们是不同领域的两个不同概念。然而，计算模糊加权平均和广义质心几乎是相同的。传统上，模糊加权平均中的所有权重都必须是非负的。本文的主要目的是将模糊加权平均推广到具有负权的情况。首先，从数学的角度对可含负权的优化模型的最优解的性质进行了严格的分析和证明。其次，提出了两种有效的随机化算法来求解IT2 FS的负权和广义质心情况下的模糊加权平均；最后，通过数值实验和仿真验证了所提出的随机化算法的输出是最优值，并对所提出的随机化算法的效率进行了分析和验证。

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Randomized algorithms for computing the fuzzy weighted average and the generalized centroid of an interval type-2 fuzzy set

The fuzzy weighted average is an useful aggregation method in multiple criteria decision making, while the generalized centroid of an interval type-2 fuzzy set (IT2 FS) is an important type reduction method in interval type-2 fuzzy logic systems. They are two different concepts in different fields. However, computing the fuzzy weighted average and the generalized centroid of an IT2 FS are nearly identical. Traditionally, all the weights in the fuzzy weighted average must be non-negative. The main aim of this paper is to extend the fuzzy weighted average to the case with negative weights. First, it is analyzed and proven strictly from the mathematical point to the properties of optimal solutions to the optimization models which can include negative weights. Second, two efficient randomized algorithms are proposed to solve the fuzzy weighted average in the case with negative weights and the generalized centroid of an IT2 FS. Finally, the outputs of the proposed randomized algorithms are proven to be the optimal values and the efficiencies of the proposed randomized algorithms are analyzed and demonstrated by numerical experiments and simulations.

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来源期刊

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.