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Generalised interval-valued fuzzy ideals and filters in ordered semigroups

As a generalisation of fuzzy set, interval-valued fuzzy set has been formed by extending the grade of fuzzy membership function from a point to an interval. This concept has been applied to several algebraic structures, especially in semigroups and ordered semigroups. The importance of the ideas of...

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Main Author: Ullah Khan, Hidayat
Format: Thesis
Language:English
Published: 2015
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/54752/1/HidayatUllahKhanPFS2015.pdf
http://eprints.utm.my/id/eprint/54752/
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spelling my.utm.547522020-11-05T06:32:55Z http://eprints.utm.my/id/eprint/54752/ Generalised interval-valued fuzzy ideals and filters in ordered semigroups Ullah Khan, Hidayat QA Mathematics As a generalisation of fuzzy set, interval-valued fuzzy set has been formed by extending the grade of fuzzy membership function from a point to an interval. This concept has been applied to several algebraic structures, especially in semigroups and ordered semigroups. The importance of the ideas of “belongs to” (E) and “quasi coincident with” ( q ) relations between a fuzzy point and fuzzy set is evident from the volume of researches conducted during the past two decades relating to these concepts. Some researchers employed these concepts in various algebraic structures like BCI-algebra, MV-algebra, semigroups and ordered semigroups by using interval-valued fuzzy set. However, it appears that ordered semigroups and their classification by the properties of interval-valued. Fuzzy concepts are not yet in the literature. In this research, for the concept of “ k ~, quasi coincident with” ( k q~ ) relation between interval-valued fuzzy point and intervalvalued fuzzy subset is used to define the notions of interval-valued. Fuzzy ideal theory and interval-valued. Fuzzy filters in ordered semigroups. Interval-valued. Fuzzy ideal theory refers to interval-valued. Fuzzy ideals, generalised bi-ideal and bi-ideal. These generalised concepts are then linked with ordinary ideals, generalised bi-ideal, bi-ideal and filters by means of level subsets. Furthermore, characterisations of ordered semigroups are studied by the properties of generalised interval-valued fuzzy ideal theory and generalised intervalvalued fuzzy filters. Finally, the notions of t ~ -implication based interval-valued fuzzy ideals and filters are introduced. Thereafter implication based interval-valued fuzzy ideal theory and filters are linked with interval-valued fuzzy ideal theory and filters by using implication operators. 2015-07 Thesis NonPeerReviewed application/pdf en http://eprints.utm.my/id/eprint/54752/1/HidayatUllahKhanPFS2015.pdf Ullah Khan, Hidayat (2015) Generalised interval-valued fuzzy ideals and filters in ordered semigroups. PhD thesis, Universiti Teknologi Malaysia, Faculty of Science. http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:94319
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Ullah Khan, Hidayat
Generalised interval-valued fuzzy ideals and filters in ordered semigroups
description As a generalisation of fuzzy set, interval-valued fuzzy set has been formed by extending the grade of fuzzy membership function from a point to an interval. This concept has been applied to several algebraic structures, especially in semigroups and ordered semigroups. The importance of the ideas of “belongs to” (E) and “quasi coincident with” ( q ) relations between a fuzzy point and fuzzy set is evident from the volume of researches conducted during the past two decades relating to these concepts. Some researchers employed these concepts in various algebraic structures like BCI-algebra, MV-algebra, semigroups and ordered semigroups by using interval-valued fuzzy set. However, it appears that ordered semigroups and their classification by the properties of interval-valued. Fuzzy concepts are not yet in the literature. In this research, for the concept of “ k ~, quasi coincident with” ( k q~ ) relation between interval-valued fuzzy point and intervalvalued fuzzy subset is used to define the notions of interval-valued. Fuzzy ideal theory and interval-valued. Fuzzy filters in ordered semigroups. Interval-valued. Fuzzy ideal theory refers to interval-valued. Fuzzy ideals, generalised bi-ideal and bi-ideal. These generalised concepts are then linked with ordinary ideals, generalised bi-ideal, bi-ideal and filters by means of level subsets. Furthermore, characterisations of ordered semigroups are studied by the properties of generalised interval-valued fuzzy ideal theory and generalised intervalvalued fuzzy filters. Finally, the notions of t ~ -implication based interval-valued fuzzy ideals and filters are introduced. Thereafter implication based interval-valued fuzzy ideal theory and filters are linked with interval-valued fuzzy ideal theory and filters by using implication operators.
format Thesis
author Ullah Khan, Hidayat
author_facet Ullah Khan, Hidayat
author_sort Ullah Khan, Hidayat
title Generalised interval-valued fuzzy ideals and filters in ordered semigroups
title_short Generalised interval-valued fuzzy ideals and filters in ordered semigroups
title_full Generalised interval-valued fuzzy ideals and filters in ordered semigroups
title_fullStr Generalised interval-valued fuzzy ideals and filters in ordered semigroups
title_full_unstemmed Generalised interval-valued fuzzy ideals and filters in ordered semigroups
title_sort generalised interval-valued fuzzy ideals and filters in ordered semigroups
publishDate 2015
url http://eprints.utm.my/id/eprint/54752/1/HidayatUllahKhanPFS2015.pdf
http://eprints.utm.my/id/eprint/54752/
http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:94319
_version_ 1683230737748197376
score 13.211869

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