| In this thesis, the main work is to discuss the concepts and propertiesrelated with pre-open set in I-fuzzy topological. With the help of pre-open set,the thesis studies by using the semantic method of fuzzy logic researchpre-continuity, pre-separation, pre-compactness, and the relation with open setand pre-open set in I-fuzzy topological space. The primary studies are thefollowing:Fuzzifying topology, from a new direction with the semantic method ofcontinuous-valued logic that is different from Professor Guojun Wang isinquired by Professor Mingsheng Ying in1991, and introduced Bifuzzytopology that is based on fuzzy logic, that is, I-fuzzy topology. In fuzzifyingtopological space, the object of study is crisp set, but axiom system is fuzzy.As fuzzifying topology’s common situation--I-fuzzy topological space, notonly fuzzy the object, but also axiom system. In2001, K.M. Abd El-Hakeimdefined pre-open set, pre-neighborhood system, furthermore discusspre-continuity and decomposition theory in Fuzzifying topology. In2003,K.M. Abd El-Hakeim studied pre-separation Axioms in Fuzzifying topology.In2005, almost separation axioms was discussed by Doc. Wang. Based onthis results, the concepts of pre-open set, pre-neighborhood system, pre-interior and closure, pre-net convergence and pre-continuity in Fuzzifyingtopology is extended to I-fuzzy topology in this thesis.In2009, P-compactness in L-topology was given by Fugui Shi. This paperextended it to I-fuzzy topology. Then discussed the relationship among openset and pre-open set, continuity and pre-continuity,, degree of compactnessand degree of P-compactness. Last this thesis gives two counterexamples toexplain pre-open set is weaker than open set in I-fuzzy topology. |
