Metasets: a new approach to partial membership

  • Authors:

  • Bartłomiej Starosta

  • Affiliations:

  • Polish-Japanese Institute of Information Technology, Warsaw, Poland

  • Venue:
  • ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part I
  • Year:
  • 2012

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Abstract

Metaset is a new concept of set with partial membership relation. It is designed to represent and process vague, imprecise data --- similarly to fuzzy sets. Metasets are based on the classical set theory primitive notions. At the same time they are directed towards efficient computer implementations and applications. The degrees of membership for metasets are expressed as finite binary sequences, they form a Boolean algebra and they may be evaluated as real numbers too. Besides partial membership, equality and their negations, metasets allow for expressing a hesitancy degree of membership --- similarly to intuitionistic fuzzy sets. The algebraic operations for metasets satisfy axioms of Boolean algebra.