Two dimensional fuzzy context-free languages and tiling patterns

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2024-03-28 DOI:10.1016/j.fss.2024.108961

A. John Kaspar , D.K. Sheena Christy , V. Masilamani , D.G. Thomas

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引用次数: 0

Abstract

Fuzzy context-free languages are powerful compared to fuzzy regular languages as they are generated by fuzzy context-free grammars and fuzzy pushdown automata, which follow an enhanced computational mechanism. A two dimensional language (picture language) is a collection of two dimensional words, which are a rectangular array of symbols made up of finite alphabets. Two dimensional automata can recognize two dimensional languages that could not be recognized by one dimensional automata. In this paper, we introduce two dimensional fuzzy context-free languages generated by the two dimensional fuzzy context-free grammars and accepted by the two dimensional fuzzy pushdown automata in order to deal with the vagueness that arises in two dimensional context-free languages. We can construct a two dimensional fuzzy context free grammar from the given two dimensional fuzzy pushdown automata and vice versa. In addition, we prove that two dimensional fuzzy context-free languages are closed under union, column concatenation, column star, homomorphism, inverse homomorphism, reflection about right-most vertical, reflection about base, conjugation and half-turn and also show that two dimensional fuzzy context-free languages are not closed under matrix homomorphism, quarter-turn and transpose. Further, we have given the applications and the uses of closure properties in the formation of tiling patterns.

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二维模糊无上下文语言和平铺模式

与模糊规则语言相比，模糊无上下文语言功能强大，因为它们是由模糊无上下文语法和模糊下推自动机生成的，遵循一种增强的计算机制。二维语言（图像语言）是二维单词的集合，是由有限字母组成的矩形符号阵列。二维自动机可以识别一维自动机无法识别的二维语言。本文介绍了由二维模糊无上下文语法生成并被二维模糊下推自动机接受的二维模糊无上下文语言，以解决二维无上下文语言中出现的模糊性问题。我们可以根据给定的二维模糊下推自动机构建二维模糊无上下文语法，反之亦然。此外，我们还证明了二维模糊无上下文语言在联合、列并集、列星形、同态、逆同态、最右垂直反射、基底反射、共轭和半转下是封闭的，并证明了二维模糊无上下文语言在矩阵同态、四分之一转和转置下是不封闭的。此外，我们还给出了封闭属性在形成平铺模式中的应用和使用。

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

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.