A Study on Two Dimensional Fuzzy Languages

Abstract

The aim of this thesis to introduce the notion of fuzziness in two dimensional languages newlineto overcome the issues of vagueness and ambiguity occurring in two dimensional languages. newlineTwo-dimensional languages are composed of digital images that are constructed using a finite newlinenumber of elements, also known as picture elements, image elements, pels, or pixels, each of newlinewhich has a specific location and value. Each element or pixel of an image, whether grayscale or newlinecolor, has its own color or intensity. However, it is difficult to determine if a given pixel is bright newlineor light compared to its neighboring pixels. In an image processing like image enhancement, newlinedenoising, image segmentation etc., the major concerns are to distinguish the object from its newlinebackground and to determine the intensity or color scale of the pixel which are ambiguous newlineand uncertain. Therefore, the concept of fuzziness is used in two dimensional grammars, two newlinedimensional automata and Petri nets. newlineIn this present work, we introduce two dimensional fuzzy right linear grammar, isometric newlinefuzzy regular array grammar, two dimensional fuzzy finite state automata, boustrophedon fuzzy newlinefinite automata, returning fuzzy finite automata and regular array token fuzzy Petri nets and their newlinerespective two dimensional fuzzy regular languages. Also, study the equivalence between these newlinegenerative tools. Discuss the closure properties of two dimensional fuzzy regular languages. newlineFurther, we discuss the applications of two dimensional fuzzy regular language with respect newlineto kolam patterns. Moreover (Likewise), we introduce two dimensional fuzzy context-free newlinegrammar and two dimensional fuzzy pushdown automata to generate two dimensional fuzzy newlinecontext-free languages and prove the equivalence between these generative tools newline