Intuitionistic fuzzy hyperalgebra based on intuitionistic fuzzy space

Karema Saleh Ali Abdulmula

Please use this identifier to cite or link to this item: https://ptsldigital.ukm.my/jspui/handle/123456789/519523

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DC Field	Value	Language
dc.contributor.advisor	Abdul Razak Salleh, Prof. Dato Dr	-
dc.contributor.author	Karema Saleh Ali Abdulmula	-
dc.date.accessioned	2023-10-17T08:12:38Z	-
dc.date.available	2023-10-17T08:12:38Z	-
dc.date.issued	2013-04-04	-
dc.identifier.other	ukmvital:76442	-
dc.identifier.uri	https://ptsldigital.ukm.my/jspui/handle/123456789/519523	-
dc.description	Hyperstructure theory was introduced by the French mathematician F. Marty in 1934. Since the introduction of intuitionistic fuzzy set by Atanassov in 1986 as a generalisation of fuzzy set of Zadeh, many mathematicians turned their attention towards intuitionizing fuzzifying ordinary algebra and tried to link between the concepts of hyperstructure and intuitionistic fuzzy algebra. The main problem in fuzzy hyperalgebra and intuitionistic fuzzy hyperalgebra is how to find or pick a rational and applicable approach to fuzzify ordinary algebra and intuitionize fuzzify ordinary algebraic concepts. The approach used in fuzzy hyperalgebra through fuzzy subgroups and fuzzy subrings is referred to as Rosenfeld's approach. Another approach of fuzzifying hyperalgebra as a generalisation of fuzzy algebra, relies on the notion of fuzzy space introduced by Dib. Using fuzzy space Fathi introduced and studied the concept of fuzzy hyperalgebra, namely fuzzy hypergroup and fuzzy hyperring. In 201 0 Fathi generalised the concept of fuzzy space to intuitionistic fuzzy space and studied the theory of intuitionistic fuzzy groups and intuitionistic fuzzy rings. In this thesis, using Fathi's intuitionistic fuzzy space we generalise his fuzzy hyperalgebra and intuitionistic fuzzy algebra to intuitionistic fuzzy hyperalgebra. Concepts of intuitionistic fuzzy hypergroup and intuitionistic fuzzy hyperring are introduced and studied. Moreover, intuitionistic fuzzy hyperideals and intuitionistic fuzzy bi-hyperideals in fuzzy semihypergroups of Davvaz are redefined based on intuitionistic fuzzy space of Fathi. The concept of intuitionistic fuzzy function having onto comembership and cononmembership functions (referred to as an intuitionistic fuzzy hyperoperation) and the notion of intuitionistic fuzzy hyperalgebra are studied by using intuitionistic fuzzy binary hyperoperation. In particular some concepts related to intuitionistic fuzzy hyperalgebra such as intuitionistic fuzzy subhypergroup induced by intuitionistic fuzzy subsets are obtained. Furthermore, concepts of intuitionistic fuzzy normal subhypergroup by using the notion of associated intuitionistic fuzzy subhypergroup, intuitionistic fuzzy hyperhomomorphism, intuitionistic fuzzy subhyperring and intuitionistic fuzzy (left, right) hyperideals induced by intuitionistic fuzzy subsets are discussed. At the end of each chapter a relationship between intuitionistic fuzzy hyperalgebra based on intuitionistic fuzzy space and fuzzy hyperalgebra based on fuzzy space is also given. The concept of intuitionistic fuzzy hyperalgebra based on intuitionistic fuzzy space is proved to be a general case of intuitionistic fuzzy hyperalgebra of Davvaz.,PhD	-
dc.language.iso	eng	-
dc.publisher	UKM, Bangi	-
dc.relation	Faculty of Science and Technology / Fakulti Sains dan Teknologi	-
dc.rights	UKM	-
dc.subject	Intuitionistic fuzzy hyperalgebra	-
dc.subject	Intuitionistic fuzzy space	-
dc.subject	Fuzzy arithmetic	-
dc.subject	Fuzzy sets	-
dc.subject	Fuzzy mathematics	-
dc.subject	Hypergroups	-
dc.title	Intuitionistic fuzzy hyperalgebra based on intuitionistic fuzzy space	-
dc.type	theses	-
dc.format.pages	159	-
dc.identifier.callno	QA248.5.A236 2013 tesis	-
dc.identifier.barcode	000297	-
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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