Linguistic temporal discrete Z-numbers and its application

The concepts of temporal intuitionistic fuzzy set and temporal fuzzy set were introduced by earlier researchers to model Spatio-temporal and dynamic motions of complex physical systems, respectively. However, the temporal intuitionistic fuzzy set has not been properly applied to solve systems with t...

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Main Author: Abdullahi, Mujahid
Format: Thesis
Language:English
Published: 2020
Subjects:
Online Access:http://eprints.utm.my/id/eprint/102253/1/MujahidAbdullahiPFS2020.pdf.pdf
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spelling my-utm-ep.1022532023-08-13T06:15:02Z Linguistic temporal discrete Z-numbers and its application 2020 Abdullahi, Mujahid QA Mathematics The concepts of temporal intuitionistic fuzzy set and temporal fuzzy set were introduced by earlier researchers to model Spatio-temporal and dynamic motions of complex physical systems, respectively. However, the temporal intuitionistic fuzzy set has not been properly applied to solve systems with temporal information. Furthermore, both concepts do not address the problem of uncertainty with respect to the time of occurrence. In this thesis, the discrete and continuous Z-numbers are proven to be ordered by employing a linear ordering relation. This new concept of ordered discrete Z-number leads to the development of two families of temporal Z-number, namely, linguistic temporal discrete Z-number (LTDZ) and temporal discrete Z-number (TDZ). Some of the basic arithmetic operations for LTDZ are introduced and their properties are proven in this thesis. In relation to that, a method for measuring uncertainty for LTDZ with respect to its time of occurrence is proposed by modifying the method for measuring the uncertainty of discrete Z-number. The temporal discrete Z-number is developed for the purpose of analyzing the electroencephalographic (EEG) signal of an epileptic seizure. Numerical examples are included to show the feasibility of the proposed concepts. 2020 Thesis http://eprints.utm.my/id/eprint/102253/ http://eprints.utm.my/id/eprint/102253/1/MujahidAbdullahiPFS2020.pdf.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:145953 phd doctoral Universiti Teknologi Malaysia Faculty of Science
institution Universiti Teknologi Malaysia
collection UTM Institutional Repository
language English
topic QA Mathematics
spellingShingle QA Mathematics
Abdullahi, Mujahid
Linguistic temporal discrete Z-numbers and its application
description The concepts of temporal intuitionistic fuzzy set and temporal fuzzy set were introduced by earlier researchers to model Spatio-temporal and dynamic motions of complex physical systems, respectively. However, the temporal intuitionistic fuzzy set has not been properly applied to solve systems with temporal information. Furthermore, both concepts do not address the problem of uncertainty with respect to the time of occurrence. In this thesis, the discrete and continuous Z-numbers are proven to be ordered by employing a linear ordering relation. This new concept of ordered discrete Z-number leads to the development of two families of temporal Z-number, namely, linguistic temporal discrete Z-number (LTDZ) and temporal discrete Z-number (TDZ). Some of the basic arithmetic operations for LTDZ are introduced and their properties are proven in this thesis. In relation to that, a method for measuring uncertainty for LTDZ with respect to its time of occurrence is proposed by modifying the method for measuring the uncertainty of discrete Z-number. The temporal discrete Z-number is developed for the purpose of analyzing the electroencephalographic (EEG) signal of an epileptic seizure. Numerical examples are included to show the feasibility of the proposed concepts.
format Thesis
qualification_name Doctor of Philosophy (PhD.)
qualification_level Doctorate
author Abdullahi, Mujahid
author_facet Abdullahi, Mujahid
author_sort Abdullahi, Mujahid
title Linguistic temporal discrete Z-numbers and its application
title_short Linguistic temporal discrete Z-numbers and its application
title_full Linguistic temporal discrete Z-numbers and its application
title_fullStr Linguistic temporal discrete Z-numbers and its application
title_full_unstemmed Linguistic temporal discrete Z-numbers and its application
title_sort linguistic temporal discrete z-numbers and its application
granting_institution Universiti Teknologi Malaysia
granting_department Faculty of Science
publishDate 2020
url http://eprints.utm.my/id/eprint/102253/1/MujahidAbdullahiPFS2020.pdf.pdf
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