A new approach to the fuzzification of matroids

  • Authors:
  • Fu-Gui Shi

  • Affiliations:
  • Department of Mathematics, School of Sciences, Beijing Institute of Technology, Beijing 100081, PR China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2009

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Abstract

In this paper, the concept of closed fuzzy pre-matroids is generalized to L-fuzzy set theory when L is a complete lattice. It is also called an L-fuzzifying matroid. In the definition of L-fuzzifying matroids, each subset can be regarded as an independent set to some degree. When L is completely distributive, an L-fuzzifying matroid can be characterized by means of its L-fuzzifying rank function. An L-fuzzifying matroid and its L-fuzzifying rank function are one-to-one corresponding.