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The Study on Bases of Quasi-Fuzzy Graph Matriods

Author: XiaJun
Tutor: WuDeZuo
School: Chongqing University
Course: Operational Research and Cybernetics
Keywords: fuzzy matriods quasi-fuzzy graph matroids regular fuzzy matroids bases fuzzy bases
CLC: O159
Type: Master's thesis
Year: 2013
Downloads: 6
Quote: 0
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On the base of the original theory of crisp matroids and fuzzy matroids,the paperstudies mainly about the properties of bases of fuzzy matroids, especially, and studiesthe properties of bases of quasi-fuzzy graph matroids.1) The paper studies the relationship between the closed or regular properties offuzzy matroids and the existence of fuzzy bases of fuzzy matroids.We have obtained amethod to structure a fuzzy base in the closed fuzzy matroid;2) The relationship between quasi-fuzzy graph matroids and closed regular fuzzymatroids had been analyzed,we have got one of sufficient conditions which quasi-fuzzygraph matroids is closed regular fuzzy matroids;3) The properties of bases of quasi-fuzzy graph matroids were studied,and wehave also obtained the structure-theorm of bases of quasi-fuzzy graph matroids.We haveproved the existence of the bijection between bases of quasi-fuzzy graph matroids andbases of induced matroids Mr1. Lastly,we have studied the symmetry-exchangeproperties of fuzzy bases of quasi-fuzzy graph matroids;4) From futher research on ordere-bases of quasi-fuzzy graph matroids, we havefound two sufficient conditions which quasi-fuzzy graph matroids is order-bases fuzzymatroids.This paper work over deeply the bases of quasi-fuzzy graph matroids,along withthe relationship between the bases of quasi-fuzzy graph matroids and its inducedmatroids Mr1.These have been important to enrich theory foundation for the researchof quasi-fuzzy graph matroids.

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Fuzzy Mathematics
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