A Note on Fixed Point Theorem for Fuzzy Mappings

نویسندگان

  • Kankana Chakrabarty
  • Sudarsan Nanda
چکیده

The notion of fuzzy sets 6 relates to objects with unsharp boundaries and the degrees of membership plays a crucial role in describing them. In case of fuzzy sets, we allow the truths of propositions to be expressed in terms of degrees which offers a considerably broader framework for knowledge representation while dealing with uncertainty. In his paper , Heilpern introduced the concept of a fuzzy mapping which neccesarily implies a mapping from an arbitrary set to a subfamily of fuzzy sets in a metric linear space X . Heilpern further proved a fixed point theorem for such fuzzy mappings as a generalization of the fixed point theorem for point-to-set maps 2 arising from the set representation of fuzzy sets . The present paper extends Heilpern’s result and a generalized fixed point theorem is proved. In this context, some further characterizations are also done.

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عنوان ژورنال:
  • International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

دوره 13  شماره 

صفحات  -

تاریخ انتشار 2005