The quotient space theory of problem solving

  • Authors:

  • Ling Zhang;Bo Zhang

  • Affiliations:

  • Artificial Intelligence Institute, Anhui University, Hefei, Anhui, China;Department of Computer Science & Technology, Tsinghua University, Beijing, China 100084 and State Key Lab of Intelligent Technology & Systems

  • Venue:
  • Fundamenta Informaticae - Special issue on the 9th international conference on rough sets, fuzzy sets, data mining and granular computing (RSFDGrC 2003)
  • Year:
  • 2003

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Abstract

The paper introduces a framework of quotient space theory of problem solving. In the theory, a problem (or problem space) is represented as a triplet, including the universe, its structure and attributes. The problem spaces with different grain sizes can be represented by a set of quotient spaces. Given a problem, the construction of its quotient spaces is discussed. Based on the model, the computational complexity of hierarchical problem solving and the information combination are also dealt with. The model can also be extended to the fuzzy granular world.