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The fuzzy topological space was introduced by Dip in 1999 depending on the notion of the fuzzy space (X, I). In this paper, further definitions, and theorems on fuzzy topological space (X, I), τ) fill the lack in Dip's article. Different types of the fuzzy topology τ are investigated and illustrated such as co-finite fuzzy topology, co-countable fuzzy topology, right ray (or left ray) fuzzy topology, and standard (usual) fuzzy topology. Furthermore, boundary, exterior, dense, and isolated fuzzy point of a fuzzy subspace are presented based on the fuzzy space (X, I). Finally, fuzzy separation axioms on the fuzzy space (X, I) are introduced. [ABSTRACT FROM AUTHOR]

Fuzzy Topographic Topological Mapping (FTTM) is a model for solving neuromagnetic inverse problem. FTTM consists of four components and connected by three algorithms. FTTM version 1 and FTTM version 2 were designed to present 3D view of an unbounded single current and bounded multicurrent sources, respectively. In 2008, Suhana introduced some definitions on sequence ofFTTM. One ofthe features produced from the sequences ofFTTM is Cube of FTTM. A cube ofFTTM is a combination of two or more FTTM in FTTM«. In this paper, cube of finite vertices ofFTTM, namely FKn are discussed. Consequently, some theorems are proven in order to describe patterns for sequence of cubes for FKn based on this k-Fibonacci sequence. Interestingly, the cube oí FKn appears to be an example ofgeneralized Fibonacci sequence, namely the k-Fibonacci sequence. [ABSTRACT FROM AUTHOR]

Fuzzy topological topographic mapping (FTTM) is developed to solve neuro magnetic inverse problem. Due to its special characteristics, namely the homeomorphism between its components, new elements can be generated using components of different version. The generated element can be depicted as a graph. A graph of pseudo degree zero is generated by FTTM with isolated component. The amount of data generated is categorized as a big data since the number of FTTM raise exponentially as the number of components rises. In this paper a sequential algorithm in generating FTTM of pseudo degree zero is presented. The results show the runtime of the algorithm also rises exponentially as the number of components increase. A GPU-CPU parallel algorithm is proposed to cut the runtime. This algorithm succeeded in increasing the speed up to 363% for data with large number of components but decrease the speed for data with low number of components. This slowdown is due to the communication time between the CPU and GPU. [ABSTRACT FROM AUTHOR]

In an early paper, we prove that a Smarandache's definition of neutrosophic paraconsistent topology is neither a generalization of Çoker's intuitionistic fuzzy topology nor a Smarandache's general neutrosophic topology. Recently, Salama and Alblowi have given a new definition of neutrosophic topology, that generalizes Çoker's intuitionistic fuzzy topology. Here, we study this new definition and its relation with Smarandache's paraconsistent neutrosophic sets. [ABSTRACT FROM AUTHOR]

In this work, the parameterized degree of compactness of a lattice valued fuzzy soft set is described in a fuzzy soft topological space. The extended versions of the basic compactness properties known in general topology are investigated for the given notion and some other characterizations of parameterized degree of compactness are specified. Further, a generalized version of Tychonoff Theorem is proved in the product fuzzy soft topological space. [ABSTRACT FROM AUTHOR]

Epilepsy disease occurs because of there is a temporary electrical disturbance in a group of brain cells (nurons). The recording of electrical signals come from the human brain which can be collected from the scalp of the head is called Electroencephalography (EEG). EEG then considered in digital format and in fuzzy form makes it a fuzzy digital space data form. The purpose of research is to identify the area (curve and surface) in fuzzy digital space affected by inside epilepsy seizure in epileptic patient's brain. The main focus for this research is to generalize fuzzy topological digital space, definition and basic operation also the properties by using digital fuzzy set and the operations. By using fuzzy digital space, the theory of digital fuzzy spline can be introduced to replace grid data that has been use previously to get better result. As a result, the flat of EEG can be fuzzy topological digital space and this type of data can be use to interpolate the digital fuzzy spline. [ABSTRACT FROM AUTHOR]