Nearness approximation space based on axiomatic fuzzy sets

  • Authors:

  • Lidong Wang;Xiaodong Liu;Wangren Qiu

  • Affiliations:

  • Department of Mathematics, Dalian Maritime University, Dalian 116026, PR China;Department of Mathematics, Dalian Maritime University, Dalian 116026, PR China;Department of Information Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333001, PR China

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2012

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Abstract

The approximation space model was originally proposed by Pawlak (1982) [19]. It was Orlowska who first observed that approximation spaces serves as a formal counterpart of perception, or observation [16, &2, p. 8], in which approximations provide a means of approximating one set of objects with another set of objects using the indiscernibility relation. Topology has been used to enrich the original model of an approximation space as well as more recent models of generalized approximation spaces. In this paper, an extension of th e topology neighborhood based on AFS (Axiomatic Fuzzy Sets) theory is introduced, and some interesting properties are given. Furthermore, a new generalized approximation space model is established with two application examples, which can be used to deal with information tables with many category features and viewed as a multi-granulations form of nearness approximation space models.