由矩阵生成的n维区间上可容许阶的等价刻画

IF 3.2 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

International Journal of Approximate Reasoning Pub Date : 2025-04-02 DOI:10.1016/j.ijar.2025.109438

Wei Zhang

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引用次数: 0

摘要

n维区间是区间的一种推广，也是n维模糊集的隶属度。它们可以用来表示高维数据。本文首先用矩阵定义了n维区间上的二元关系。然后，证明了该二元关系是n维区间上的可容许阶当且仅当对应矩阵的行列式不等于零，且对于矩阵的每一列，第一个非零元素大于零。最后，我们将这种允许顺序应用到一个具体的多准则群体决策案例中。

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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An equivalent characterization for admissible orders on n-dimensional intervals generated by matrices

The n-dimensional intervals are a generalization of intervals, and they are also the membership degrees of n-dimensional fuzzy sets. They can be used to represent high-dimensional data. This paper first defines a binary relation on n-dimensional intervals using a matrix. Then, we prove that this binary relation is an admissible order on n-dimensional intervals if and only if the determinant of the corresponding matrix is not equal to zero, and for each column of the matrix, the first non-zero element is greater than zero. Finally, we apply this type of admissible order to a specific multi-criteria group decision-making case.

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来源期刊

International Journal of Approximate Reasoning 工程技术-计算机：人工智能

CiteScore

6.90

自引率

12.80%

发文量

170

审稿时长

67 days

期刊介绍： The International Journal of Approximate Reasoning is intended to serve as a forum for the treatment of imprecision and uncertainty in Artificial and Computational Intelligence, covering both the foundations of uncertainty theories, and the design of intelligent systems for scientific and engineering applications. It publishes high-quality research papers describing theoretical developments or innovative applications, as well as review articles on topics of general interest. Relevant topics include, but are not limited to, probabilistic reasoning and Bayesian networks, imprecise probabilities, random sets, belief functions (Dempster-Shafer theory), possibility theory, fuzzy sets, rough sets, decision theory, non-additive measures and integrals, qualitative reasoning about uncertainty, comparative probability orderings, game-theoretic probability, default reasoning, nonstandard logics, argumentation systems, inconsistency tolerant reasoning, elicitation techniques, philosophical foundations and psychological models of uncertain reasoning. Domains of application for uncertain reasoning systems include risk analysis and assessment, information retrieval and database design, information fusion, machine learning, data and web mining, computer vision, image and signal processing, intelligent data analysis, statistics, multi-agent systems, etc.