Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Articles Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Two dimensional fuzzy context-free languages and tiling patterns Subject The topic of the resource Fuzzy languages; Fuzzy pushdown automata; Picture languages; Two dimensional fuzzy languages Description An account of the resource 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. 2024 Elsevier B.V. Creator An entity primarily responsible for making the resource John Kaspar A.; Sheena Christy D.K.; Masilamani V.; Thomas D.G. Source A related resource from which the described resource is derived Fuzzy Sets and Systems, Vol-485 Publisher An entity responsible for making the resource available Elsevier B.V. Date A point or period of time associated with an event in the lifecycle of the resource 2024-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1016/j.fss.2024.108961" target="_blank" rel="noreferrer noopener">https://doi.org/10.1016/j.fss.2024.108961</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85189547292&amp;doi=10.1016%2Fj.fss.2024.108961&amp;partnerID=40&amp;md5=79f445df0eb5570688ca5d0386587a3b" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85189547292&amp;doi=10.1016%2fj.fss.2024.108961&amp;partnerID=40&amp;md5=79f445df0eb5570688ca5d0386587a3b</a> Rights Information about rights held in and over the resource Restricted Access Relation A related resource ISSN: 1650114; CODEN: FSSYD Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant John Kaspar A., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bengaluru, 560 029, India; Sheena Christy D.K., Department of Mathematics, SRM Institute of Scinece and Technology, TamilNadu, Kattankulathur, Chennai, 603 203, India; Masilamani V., Department of Computer Science, Indian Institute of Information and Design Manufacturing, TamilNadu, Kancheepuram, Chennai, 600 127, India; Thomas D.G., Department of mathematics, Madras Christian College, Former Professor, Tambaram, TamilNadu, Chennai, 600 059, India