On fuzzification of topological categories

Solovyov, Sergey A.

doi:10.1016/j.fss.2013.05.003

Cited by 2 publications

(2 citation statements)

References 42 publications

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“…In each spatial datasets the weight value was given, to determine the level of importance/influence on the classification produced in each parameter criterion [30,31], This weighting used the fuzzification process, consisting of fuzzy sets indicators in giving a level description in the classification results [32].…”

Section: Spatial Datasetsmentioning

confidence: 99%

Spatial Data Modeling on GIS for Classification of Measles-prone Region Using Multiple Attribute Decision Making

Vitianingsih¹,

Choiron²,

Cahyono³

et al. 2019

IJIES

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Indonesia is a country that has a tropical climate, so that many typical tropical climate diseases emerge. This disease is caused by viruses and parasites that breed during the dry season or the rainy season. One typical tropical disease is measles. This paper discusses the geographical information system (GIS) technology by analyzing spatial data modeling to determine the classification of measles-prone areas based on immunization status coverage using the Simple Additive Weighting (SAW) and Weight Product Model (WPM) method. Some parameters are used consist of immunization status data for multiple attribute decision making (MADM), diseases preventable by immunization (PD3I), epidemic and nutritional status of infants. The SAW and WPM method in modeling spatial data analysis processes data according to the parameters to determine the scale in comparing all alternative data on the scope of classification of immunization status areas, namely: good, average, fair and poor. The test results with the Cohen's Kappa Method Consistency Test (MCT) is obtained an average coefficient of 0.41 for consistent measurements for the chosen method. It can be concluded that the two measurements using the SAW and WPM methods have a moderate for the strength of agreement category, for using in spatial data modeling on the GIS for classification of measles prone regions using MADM.

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Section: Spatial Datasetsmentioning

confidence: 99%

Spatial Data Modeling on GIS for Classification of Measles-prone Region Using Multiple Attribute Decision Making

Vitianingsih¹,

Choiron²,

Cahyono³

et al. 2019

IJIES

View full text Add to dashboard Cite

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“…This achievement relies on the machinery of topological theories of O. Wyler [18,19], and eventually amounts to the meta-mathematical statement that the whole theory of (fibresmall) topological categories (including, e.g., the categories of poslat topological spaces, shown to be topological over their ground categories in a series of papers of S. E. Rodabaugh) can be done in the framework of catalg topology (a similar but by far more moderate and not that well stated claim was vaguely hinted at in [11] with respect to the poslat topology). The purpose of this talk (which is a shortened version of [14]) is to show a particular development of fuzzy topology in the setting of the catalg one, thereby illustrating the convenient tools of the latter.There currently exist two popular (in the fuzzy community) approaches to lattice-valued topology (which by no means are the only available). The first one, initiated by C. L. Chang [1] and extended later on by J.…”

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confidence: 99%

On fuzzification of topological categories

Solovyov¹

EPiC Series in Computing

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Following the point-set lattice-theoretic (poslat) approach to topology of S. E. Rodabaugh [11], we introduced a more general way to do categorical (fuzzy) topology under the name of categorically-algebraic (catalg) topology [12], which unified many lattice-valued topological settings, and provided the means of intercommunication between different such frameworks. Moreover, motivated by the results of universal topology of H. Herrlich [7], we showed in [13] that a concrete category is fibre-small and topological if and only if it is concretely isomorphic to a subcategory of a category of catalg topological structures, which is definable by topological co-axioms. This achievement relies on the machinery of topological theories of O. Wyler [18,19], and eventually amounts to the meta-mathematical statement that the whole theory of (fibresmall) topological categories (including, e.g., the categories of poslat topological spaces, shown to be topological over their ground categories in a series of papers of S. E. Rodabaugh) can be done in the framework of catalg topology (a similar but by far more moderate and not that well stated claim was vaguely hinted at in [11] with respect to the poslat topology). The purpose of this talk (which is a shortened version of [14]) is to show a particular development of fuzzy topology in the setting of the catalg one, thereby illustrating the convenient tools of the latter.There currently exist two popular (in the fuzzy community) approaches to lattice-valued topology (which by no means are the only available). The first one, initiated by C. L. Chang [1] and extended later on by J. A. Goguen [6], defines a many-valued topology on a set X as a subset τ of an L-powerset L X (for some lattice-theoretic structure L, e.g., a quantale), which is closed under arbitrary joins and finite meets (or, possibly, quantale multiplication). The second approach, started by U. Höhle [8] and later on generalized independently by T. Kubiak [9] and A.Šostak [17], defines a lattice-valued topology on a set X as a map T : L X − → M (which employs an additional lattice-theoretic structure M ) satisfying the requirements i∈I T (α i ) T ( i∈I α i ) for every index set I, and ∧ j∈J T (α j ) T (∧ j∈J α j ) for every finite index set J, which provide lattice-valued analogues of the above-mentioned closure of topology under arbitrary joins and finite meets. In [15,16], we presented a convenient catalg framework for doing fuzzy topology in the sense of Höhle-Kubiak-Šostak, extending for that purpose the theory of latticevalued algebras of A. Di Nola and G. Gerla [5]. In this talk, we show that the approach to topology of Höhle-Kubiak-Šostak is just an instance of the machinery, which has been called by us the general fuzzification procedure for topological categories. More precisely, given a (fibre-small) topological category A, there exists a topological category B, which contains A as a full concretely coreflective subcategory, and which can be considered as a fuzzification of A. In particular, the classical cat...

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On fuzzification of topological categories

Cited by 2 publications

References 42 publications

Spatial Data Modeling on GIS for Classification of Measles-prone Region Using Multiple Attribute Decision Making

Spatial Data Modeling on GIS for Classification of Measles-prone Region Using Multiple Attribute Decision Making

On fuzzification of topological categories

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