{"id":{"repo_id":"de-montfort","oai_identifier":"oai:dora.dmu.ac.uk:2086/10782"},"canonical_url":"https://search.dev.ndltd.org/etd/de-montfort/oai:dora.dmu.ac.uk:2086/10782","repository":{"repo_id":"de-montfort","name":"De Montfort University","base_url":"https://dora.dmu.ac.uk/server/oai/request"},"display":{"title":"Geometric Fuzzy Logic Systems","abstract":"There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. Type-2 fuzzy systems offer the ability to model and reason with uncertain concepts. When faced with uncertainties type-2 fuzzy systems should, theoretically, give an increase in performance over type-l fuzzy systems. However, the computational complexity of generalised type-2 fuzzy systems is significantly higher than type-l systems. A direct consequence of this is that, prior to this thesis, generalised type-2 fuzzy logic has not yet been applied in a time critical domain, such as control. Control applications are the main application area of type-l fuzzy systems with the literature reporting many successes in this area. Clearly the computational complexity oftype-2 fuzzy logic is holding the field back. This restriction on the development oftype-2 fuzzy systems is tackled in this research. This thesis presents the novel approach ofdefining fuzzy sets as geometric objects - geometric fuzzy sets. The logical operations for geometric fuzzy sets are defined as geometric manipulations of these sets. This novel geometric approach is applied to type-I, type-2 interval and generalised type-2 fuzzy sets and systems. The major contribution of this research is the reduction in the computational complexity oftype-2 fuzzy logic that results from the application of the geometric approach. This reduction in computational complexity is so substantial that generalised type-2 fuzzy logic has, for the first time, been successfully applied to a control problem - mobile robot navigation. A detailed comparison between the performance of the generalised type-2 fuzzy controller and the performance of the type-l and type-2 interval controllers is given. The results indicate that the generalised type-2 fuzzy logic controller outperforms the other robot controllers. This outcome suggests that generalised type-2 fuzzy systems can offer an improved performance over type-l and type-2 interval systems.","abstract_html":"There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. Type-2 fuzzy systems offer the ability to model and reason with uncertain concepts. When faced with uncertainties type-2 fuzzy systems should, theoretically, give an increase in performance over type-l fuzzy systems. However, the computational complexity of generalised type-2 fuzzy systems is significantly higher than type-l systems. A direct consequence of this is that, prior to this thesis, generalised type-2 fuzzy logic has not yet been applied in a time critical domain, such as control. Control applications are the main application area of type-l fuzzy systems with the literature reporting many successes in this area. Clearly the computational complexity oftype-2 fuzzy logic is holding the field back. This restriction on the development oftype-2 fuzzy systems is tackled in this research. This thesis presents the novel approach ofdefining fuzzy sets as geometric objects - geometric fuzzy sets. The logical operations for geometric fuzzy sets are defined as geometric manipulations of these sets. This novel geometric approach is applied to type-I, type-2 interval and generalised type-2 fuzzy sets and systems. The major contribution of this research is the reduction in the computational complexity oftype-2 fuzzy logic that results from the application of the geometric approach. This reduction in computational complexity is so substantial that generalised type-2 fuzzy logic has, for the first time, been successfully applied to a control problem - mobile robot navigation. A detailed comparison between the performance of the generalised type-2 fuzzy controller and the performance of the type-l and type-2 interval controllers is given. The results indicate that the generalised type-2 fuzzy logic controller outperforms the other robot controllers. This outcome suggests that generalised type-2 fuzzy systems can offer an improved performance over type-l and type-2 interval systems.","abstract_has_math":false,"creators":["Coupland, Simon"],"institution":"De Montfort University","degree_name":"PhD","degree_level":"Doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006","date_published":"2006","updated_at":"2026-07-24T06:18:31Z","subjects":[],"languages":[],"rights":[],"rights_urls":["https://dora.dmu.ac.uk/bitstreams/10f78222-c90e-4b86-86ec-0aaf74844eea/download"],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Coupland, Simon"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.issued","label":"Date","values":["2006"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["De Montfort University"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["http://hdl.handle.net/2086/10782"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or dissertation"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["https://dora.dmu.ac.uk/bitstreams/10f78222-c90e-4b86-86ec-0aaf74844eea/download"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://dora.dmu.ac.uk/bitstreams/55fc50cb-7ddc-4407-9972-aaad5e944402/download","https://dora.dmu.ac.uk/bitstreams/7eaf9aea-1bb4-484c-8621-302e620093aa/download"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. 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