Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory

Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type-3 is one of the newly capable graphs for a breakthrough of the relationship between fuzzy graph and autocatalytic set. It was successfully used to model an incineration process of a regional clinical waste in 2005. In this research, the mathematical...

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Main Author:	Qasim, Umilkeram
Format:	Thesis
Language:	English
Published:	2016
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/81642/1/UmilkeramQasimObaidPFS2016.pdf
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id	my-utm-ep.81642
record_format	uketd_dc
spelling	my-utm-ep.816422019-09-10T01:53:02Z Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory 2016 Qasim, Umilkeram QA Mathematics Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type-3 is one of the newly capable graphs for a breakthrough of the relationship between fuzzy graph and autocatalytic set. It was successfully used to model an incineration process of a regional clinical waste in 2005. In this research, the mathematical structures of FACS and its properties were explored based on the suitable concept of fuzzy and non-fuzzy metric structure and fuzzy and non-fuzzy normed structure with the structure of its graph. In other words, the possible new structures of FACS have been explored via two new insights of its metric fuzziness and its normed fuzziness. Firstly, a fuzzy detour FT3-distance between vertices in FACS was investigated whereby a quasi-pseudo-FT3-metric fuzziness on FACS which depends on this distance was established, followed by an introduction to the concept FT3-cycle space of FACS as a vector space which is then proven as a normed space. These concepts have led to the visualization of the structure of FACS in a fuzzy norm, hence some propositions and theorems were established. In addition, the study on these structures of FACS was exploited, in particular the connection with functional analysis features and the application of these structures to the clinical incineration process. 2016 Thesis http://eprints.utm.my/id/eprint/81642/ http://eprints.utm.my/id/eprint/81642/1/UmilkeramQasimObaidPFS2016.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:126024 phd doctoral Universiti Teknologi Malaysia Mathematics
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Qasim, Umilkeram Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory
description	Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type-3 is one of the newly capable graphs for a breakthrough of the relationship between fuzzy graph and autocatalytic set. It was successfully used to model an incineration process of a regional clinical waste in 2005. In this research, the mathematical structures of FACS and its properties were explored based on the suitable concept of fuzzy and non-fuzzy metric structure and fuzzy and non-fuzzy normed structure with the structure of its graph. In other words, the possible new structures of FACS have been explored via two new insights of its metric fuzziness and its normed fuzziness. Firstly, a fuzzy detour FT3-distance between vertices in FACS was investigated whereby a quasi-pseudo-FT3-metric fuzziness on FACS which depends on this distance was established, followed by an introduction to the concept FT3-cycle space of FACS as a vector space which is then proven as a normed space. These concepts have led to the visualization of the structure of FACS in a fuzzy norm, hence some propositions and theorems were established. In addition, the study on these structures of FACS was exploited, in particular the connection with functional analysis features and the application of these structures to the clinical incineration process.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Qasim, Umilkeram
author_facet	Qasim, Umilkeram
author_sort	Qasim, Umilkeram
title	Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory
title_short	Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory
title_full	Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory
title_fullStr	Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory
title_full_unstemmed	Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory
title_sort	fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory
granting_institution	Universiti Teknologi Malaysia
granting_department	Mathematics
publishDate	2016
url	http://eprints.utm.my/id/eprint/81642/1/UmilkeramQasimObaidPFS2016.pdf
_version_	1747818378398007296

Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory

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