On categories associated with crisp deterministic automata with fuzzy rough outputs and fuzzy rough languages

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE Soft Computing Pub Date : 2024-08-05 DOI:10.1007/s00500-024-09818-5

Mausam Kumari, Vijay K. Yadav, Shainky Ruhela, S. P. Tiwari

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Abstract

The categorical concepts, tools, and techniques advanced not only the theory of automata and languages but also developed the theory of fuzzy automata and languages and played a significant role in many other branches of theoretical computer science. Unlike theory of classical/fuzzy automata with output and their languages, this paper aims to incorporate the concept of fuzziness and roughness together in the theory of automata with output and their languages, to introduce the concepts of crisp deterministic automata with fuzzy rough output, and fuzzy rough language and study their categorical aspects. We have shown that the crisp deterministic automata with fuzzy rough outputs and fuzzy rough languages, along with their morphisms, respectively, form categories CDAFRO and FRL. We have also shown the existence of a functor between the categories CDAFRO and FRL. The categorical concepts of product and coproduct of a subfamily of object-class, equalizer, and coequalizer of a pair of parallel morphisms in category CDAFRO are studied. Finally, for a given fuzzy rough language, a minimal crisp deterministic automaton having fuzzy rough output recognizing it is constructed using the fuzzy generalization of foremost Myhill–Nerode’s theory of automata and languages.

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论与具有模糊粗糙输出和模糊粗糙语言的简明确定性自动机相关的范畴

分类概念、工具和技术不仅推动了自动机和语言理论的发展，还发展了模糊自动机和语言理论，并在理论计算机科学的许多其他分支中发挥了重要作用。与经典/模糊有输出自动机及其语言理论不同，本文旨在将模糊性和粗糙度的概念一并纳入有输出自动机及其语言理论，引入模糊粗糙输出的简明确定性自动机和模糊粗糙语言的概念，并对其进行分类研究。我们证明了具有模糊粗糙输出的简明确定性自动机和模糊粗糙语言以及它们的变形分别构成了 CDAFRO 和 FRL 两类。我们还证明了 CDAFRO 和 FRL 这两个范畴之间存在一个函数。我们还研究了 CDAFRO 类别中对象类子族的乘积和共乘积、一对平行形态的均衡器和共均衡器等分类概念。最后，对于给定的模糊粗略语言，利用最前沿的迈希尔-内罗德自动机和语言理论的模糊广义，构建了具有模糊粗略输出识别的最小简明确定性自动机。

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来源期刊

Soft Computing 工程技术-计算机：跨学科应用

CiteScore

8.10

自引率

9.80%

发文量

927

审稿时长

7.3 months

期刊介绍： Soft Computing is dedicated to system solutions based on soft computing techniques. It provides rapid dissemination of important results in soft computing technologies, a fusion of research in evolutionary algorithms and genetic programming, neural science and neural net systems, fuzzy set theory and fuzzy systems, and chaos theory and chaotic systems. Soft Computing encourages the integration of soft computing techniques and tools into both everyday and advanced applications. By linking the ideas and techniques of soft computing with other disciplines, the journal serves as a unifying platform that fosters comparisons, extensions, and new applications. As a result, the journal is an international forum for all scientists and engineers engaged in research and development in this fast growing field.