Different Representations of Fuzzy Vectors

  • Authors:

  • Jiuzhen Liang;Mirko Navara;Thomas Vetterlein

  • Affiliations:

  • School of Information Technology, Jiangnan University, Wuxi, Jiangsu Province, China 214122;Center for Machine Perception, Department of Cybernetics Faculty of Electrical Engineering, Czech Technical University in Prague, Praha, Czech Republic CZ-166 27;Section on Medical Expert and Knowledge-Based Systems, Medical University of Vienna, Wien, Austria A-1090

  • Venue:
  • ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
  • Year:
  • 2009

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Abstract

Fuzzy vectors were introduced as a description of imprecise quantities whose uncertainty originates from vagueness, not from a probabilistic model. Support functions are a classical tool for representation and computation with compact convex sets. The combination of these two techniques--support functions of fuzzy vectors--has been proposed by Puri and Ralescu. Independently, Bobylev proposed another type of support functions which allows a more economical representation. However, the form of the functions is not very intuitive. We suggest a new type of support functions which combines the advantages of both preceding approaches. We characterize the functions which are support functions of fuzzy vectors in the new sense.