Innovative types of fuzzy gamma ideals in ordered gamma semigroups

The fuzzification of algebraic structures plays an important role in handling many areas of multi-disciplinary research, such as computer science, control theory, information science, topological spaces and fuzzy automata to handle many real world problems. For instance, algebraic structures are par...

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Main Author:	Gambo, Ibrahim
Format:	Thesis
Language:	English
Published:	2019
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/81030/1/IbrahimGamboPFS2019.pdf
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spelling	my-utm-ep.810302019-07-24T03:06:07Z Innovative types of fuzzy gamma ideals in ordered gamma semigroups 2019-01 Gambo, Ibrahim QA Mathematics The fuzzification of algebraic structures plays an important role in handling many areas of multi-disciplinary research, such as computer science, control theory, information science, topological spaces and fuzzy automata to handle many real world problems. For instance, algebraic structures are particularly useful in detecting permanent faults on sequential machine behaviour. However, the idea of ordered T-semigroup as a generalization of ordered semigroup in algebraic structures has rarely been studied. In this research, a new form of fuzzy subsystem in ordered T-semigroup is defined. Specifically, a developmental platform of further characterizations on ordered T-semigroups using fuzzy subsystems properties and new fuzzified ideal structures of ordered semigroups is developed based on a detailed study of ordered T-semigroups in terms of the idea of belongs to (E) and quasicoincidence with (q) relation. This idea of quasi-coincidence of a fuzzy point with a fuzzy set played a remarkable role in obtaining several types of fuzzy subgroups and subsystems based on three contributions. One, a new form of generalization of fuzzy generalized bi T-ideal is developed, and the notion of fuzzy bi T-ideal of the form (E,E Vqk) in an ordered T-semigroup is also introduced. In addition, a necessary and sufficient condition for an ordered T-semigroup to be simple T-ideals in terms of this new form is stated. Two, the concept of (E,E Vqk)-fuzzy quasi T-ideals, fuzzy semiprime T-ideals, and other characterization in terms of regular (left, right, completely, intra) in ordered T-semigroup are developed. Three, a new fuzzified T-ideal in terms of interior T-ideal of ordered T-semigroups in many classes are determined. Thus, this thesis provides the characterizations of innovative types of fuzzy T-ideals in ordered T-semigroups with classifications in terms of completely regular, intra-regular, for fuzzy generalized bi T-ideals, fuzzy bi T-ideals, fuzzy quasi and fuzzy semiprime T-ideals, and fuzzy interior T-ideals. These findings constitute a platform for further advancement of ordered T-semigroups and their applications to other concepts and branches of algebra. 2019-01 Thesis http://eprints.utm.my/id/eprint/81030/ http://eprints.utm.my/id/eprint/81030/1/IbrahimGamboPFS2019.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:124959 phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Gambo, Ibrahim Innovative types of fuzzy gamma ideals in ordered gamma semigroups
description	The fuzzification of algebraic structures plays an important role in handling many areas of multi-disciplinary research, such as computer science, control theory, information science, topological spaces and fuzzy automata to handle many real world problems. For instance, algebraic structures are particularly useful in detecting permanent faults on sequential machine behaviour. However, the idea of ordered T-semigroup as a generalization of ordered semigroup in algebraic structures has rarely been studied. In this research, a new form of fuzzy subsystem in ordered T-semigroup is defined. Specifically, a developmental platform of further characterizations on ordered T-semigroups using fuzzy subsystems properties and new fuzzified ideal structures of ordered semigroups is developed based on a detailed study of ordered T-semigroups in terms of the idea of belongs to (E) and quasicoincidence with (q) relation. This idea of quasi-coincidence of a fuzzy point with a fuzzy set played a remarkable role in obtaining several types of fuzzy subgroups and subsystems based on three contributions. One, a new form of generalization of fuzzy generalized bi T-ideal is developed, and the notion of fuzzy bi T-ideal of the form (E,E Vqk) in an ordered T-semigroup is also introduced. In addition, a necessary and sufficient condition for an ordered T-semigroup to be simple T-ideals in terms of this new form is stated. Two, the concept of (E,E Vqk)-fuzzy quasi T-ideals, fuzzy semiprime T-ideals, and other characterization in terms of regular (left, right, completely, intra) in ordered T-semigroup are developed. Three, a new fuzzified T-ideal in terms of interior T-ideal of ordered T-semigroups in many classes are determined. Thus, this thesis provides the characterizations of innovative types of fuzzy T-ideals in ordered T-semigroups with classifications in terms of completely regular, intra-regular, for fuzzy generalized bi T-ideals, fuzzy bi T-ideals, fuzzy quasi and fuzzy semiprime T-ideals, and fuzzy interior T-ideals. These findings constitute a platform for further advancement of ordered T-semigroups and their applications to other concepts and branches of algebra.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Gambo, Ibrahim
author_facet	Gambo, Ibrahim
author_sort	Gambo, Ibrahim
title	Innovative types of fuzzy gamma ideals in ordered gamma semigroups
title_short	Innovative types of fuzzy gamma ideals in ordered gamma semigroups
title_full	Innovative types of fuzzy gamma ideals in ordered gamma semigroups
title_fullStr	Innovative types of fuzzy gamma ideals in ordered gamma semigroups
title_full_unstemmed	Innovative types of fuzzy gamma ideals in ordered gamma semigroups
title_sort	innovative types of fuzzy gamma ideals in ordered gamma semigroups
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2019
url	http://eprints.utm.my/id/eprint/81030/1/IbrahimGamboPFS2019.pdf
_version_	1747818295887659008

Innovative types of fuzzy gamma ideals in ordered gamma semigroups

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