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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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Abstract


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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