On permutations dependent operators

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

International Journal of Approximate Reasoning Pub Date : 2024-09-10 DOI:10.1016/j.ijar.2024.109294

Stanislav Basarik, Lenka Halčinová

引用次数: 0

Abstract

In this paper, we introduce permutations dependent operators. The motivation for studying such a concept arises from standard fuzzy integrals, where permutations play a crucial role. In contrast to standard fuzzy integrals, our construction allows any permutation of the basic set in a formula to be considered, rather than limiting it to permutations that reorder the components of the input vector monotonically. We herein present an approach to integration with respect to sets of permutation pairs, i.e., databases in which each vector has a preselected permutation. This new operator generalizes several concepts known in the literature. We investigate the properties of this new concept and highlight its practical utility in image processing.

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关于排列依存算子

本文介绍了与排列相关的算子。研究这一概念的动机来自标准模糊积分，其中排列起着至关重要的作用。与标准模糊积分不同的是，我们的构造允许考虑公式中基本集的任何排列，而不是仅限于对输入向量的分量进行单调排序的排列。在此，我们提出了一种与排列组合集（即每个向量都有一个预选排列组合的数据库）相关的积分方法。这个新算子概括了文献中已知的几个概念。我们研究了这一新概念的特性，并强调了它在图像处理中的实用性。

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

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.