Sequences and cubes of finite vertices of fuzzy topographic topological mapping

Abstract

Fuzzy Topographic Topological Mapping (FTTM) was first developed by Fuzzy Research Group (FRG) of UTM. FTTM is a novel method for solving neuromagnetic inverse problems to determine the current source, i.e. epileptic foci in epilepsy disorder patient. FTTM consists of four components which are connected by three algorithms. FTTM is specially designed to have equivalent topological structures between its components. In addition, FTTM was generalized as a set of vertices which led to infinitely many forms of FTTM. This includes the possibilities of finite vertices of FTTM. In this research, the structure for finite vertices of FTTM, namely F K where K represents the number of vertices is established. Firstly, the sequences of FK, given by FKn are constructed as sequences of polygons. In this process, geometrical and algebraic structures for some FKn are obtained and proven in this thesis. Some patterns on FKn are observed and defined recursively. Several new features for sequences of FKn are introduced, such as sequence of vertices, sequence of faces, and sequence of cubes. Consequently, some theorems are proven in order to describe patterns for the sequence of cubes for FKn. Interestingly, the cube of FKn, appears to be an example of generaUzed Fibonacci sequence, namely the fc-Fibonacci sequence. Furthermore, the number of new elements produced from the combination of sequences of FK^ can be expressed as a combination of cubes of FKn