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A new class of fuzzy convergence structure of

Author: WuWenChao
Tutor: FangJinMing
School: Ocean University of China
Course: Basic mathematics
Keywords: Fuzzy topology Fuzzy convergence structure L- filter Cartesian closed category Reflective subcategory
CLC: O159
Type: Master's thesis
Year: 2011
Downloads: 4
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Abstract


In this paper, a complete Heyting algebra cell value environment, proposed a new lattice-valued fuzzy convergence space concept, called lattice-ordered fuzzy convergence space, and to study the nature and the relationship between the structure and other related issues. convergence with the original structure is different fuzzy, fuzzy lattice ordered convergence structures and L-filter grid coordinate values ??contain relations. article results show that fuzzy convergence space lattice ordered category remains Cartesian closedness; its two sub-categories respectively, and fuzzy neighborhood space areas and areas of fuzzy topological spaces isomorphic; and that it converges with the original fuzzy spatial scales, fuzzy topological spaces stable contact areas, such as lattice-ordered fuzzy convergence space areas is original The fuzzy convergence space areas reflected full subcategory, fuzzy category of topological spaces can be embedded into the convergence space lattice-ordered fuzzy category. thesis consists of four parts: The first part is synthesis and preliminary knowledge of the structure introduced convergence theoretical background, research the origin, and summarizes the main work. Finally, this paper gives some preliminary knowledge of the second part is about the convergence of lattice-ordered fuzzy space research. Firstly, based on the convergence structure of L- Filter coordination between grid value contains the idea, put forward a new convergence of lattice-ordered fuzzy spatial concepts and illustrates the existence of such a lattice-ordered fuzzy convergence space. Secondly, the author discusses the convergence of lattice-ordered fuzzy space areas nature of the text than the original results show that fuzzy convergence space in the areas of \The third part is the lattice-ordered fuzzy convergence space areas subcategory Discussion In this section, the authors found that the convergence space lattice ordered fuzzy category there are two important sub-areas, namely nominative ordinal fuzzy convergence space and topological aspects type lattice ordered fuzzy convergence space category. research results show that the two sub-areas, namely nominative category ordinal fuzzy convergence space and topological lattice-ordered fuzzy convergence space areas were exactly isomorphic to the existing literature fuzzy neighborhood spatial scope and fuzzy category of topological spaces. fourth part is about the convergence space lattice-ordered fuzzy category relations with other areas discussed results showed that: (1) lattice-ordered fuzzy convergence space can be a natural way to degenerate into the original convergence space blurring the differences between them we give an example will be described. (2) lattice-ordered fuzzy convergence space categories are blurred areas of convergence space reflection full subcategory and, therefore topology. (3) fuzzy topological space lattice ordered category can be embedded into the category of fuzzy convergence space.

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