A new approach to find the multi-fractal dimension of multi-fuzzy fractal attractor sets based on the iterated function system

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dc.authorid0000-0001-9641-2066en_US
dc.contributor.authorMohammed, Arkan Jassim
dc.date.accessioned2024-07-12T20:54:28Z
dc.date.available2024-07-12T20:54:28Z
dc.date.issued2019en_US
dc.departmentMaltepe Üniversitesi, İnsan ve Toplum Bilimleri Fakültesien_US
dc.description.abstractIn nature, objects are not single fractal sets but are a collection of complex multiple fractals that characterise the multifractal space, a generalisation of fractal space. While fractal space includes a fractal set, a multi-fractal space includes the union of fractals. A fuzzy fractal space is a fuzzy metric space and is an approach for the construction, analysis, and approximation of sets and images that exhibit fractal characteristics. The finite Cartesian product of fuzzy fractal spaces is called the multi-fuzzy fractal space. We propose in this paper, a theoretical proof to define the multi-fractal dimensions FD of a multi- fuzzy fractal attractor of n objects for the self-similar fractals sets A = n i=1 Ai = (A1, A2,... An) of the contraction mapping W?? : n i=1 H(F(Xi)) ? n i=1 H(F(Xi)) with contractivity factor r = max{ri, i = 1, 2,... n} where H(F(Xi) is a fuzzy fractal space for each i = 1, 2,..., n ; over a complete metric space (n i=1 H(F(Xi)), D?) then for all Bi that belong toH(F(Xi)), there exists B? belonging to (n i=1 H(F(Xi)) such that W??(B? = n i=1 Bi) = n i=1 ( n j=1 k(i, j) k=1 ??k i j (Bj) = n i=1 Wi(B?)). By supposing that M (t) = k (r?k i j ) FD n×n is the matrix associated with the the contraction mapping ??k i j with contraction factor r?k i j , ?i, j = 1, 2,..., n, ?k = 1, 2, ..., k(i, j), for all t ? 0, and h (t) = det(M (t) ? I) . Then, we prove that if there exists a FD such that; h(FD) = 0, then FD is the multi fractal dimension for the multi fuzzy-fractal sets of IFS; and M(FD) has a fixed point in Rn.en_US
dc.identifier.citationMohammed, A. J. (2019). A new approach to find the multi-fractal dimension of multi-fuzzy fractal attractor sets based on the iterated function system. Third International Conference of Mathematical Sciences, Maltepe Üniversitesi. s. 1-4.en_US
dc.identifier.endpage4en_US
dc.identifier.isbn978-0-7354-1930-8
dc.identifier.startpage1en_US
dc.identifier.urihttps://aip.scitation.org/doi/abs/10.1063/1.5136162
dc.identifier.urihttps://hdl.handle.net/20.500.12415/2763
dc.institutionauthorMohammed, Arkan Jassim
dc.language.isoenen_US
dc.publisherMaltepe Üniversitesien_US
dc.relation.ispartofThird International Conference of Mathematical Sciencesen_US
dc.relation.isversionof10.1063/1.5136162en_US
dc.relation.publicationcategoryUluslararası Konferans Öğesi - Başka Kurum Yazarıen_US
dc.rightsCC0 1.0 Universal*
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/*
dc.snmzKY08625
dc.subjectFractal spaceen_US
dc.subjectmulti-fuzzy fractal spaceen_US
dc.subjectIFSen_US
dc.subjectbox-counting dimensionen_US
dc.subjectfractal dimensionen_US
dc.titleA new approach to find the multi-fractal dimension of multi-fuzzy fractal attractor sets based on the iterated function systemen_US
dc.typeConference Object
dspace.entity.typePublication

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