Fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers and interval-valued fuzzy number arithmetic operators

  • Authors:

  • Shyi-Ming Chen;Jim-Ho Chen

  • Affiliations:

  • Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, R. O. C and Department of Computer Science and Information Enginee ...;Department of Computer Science and Information Engineering, National Taiwan University of Science and Technology, Taipei, Taiwan, R. O. C

  • Venue:
  • Expert Systems with Applications: An International Journal
  • Year:
  • 2009

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Abstract

In this paper, we present a new method for fuzzy risk analysis based on a new similarity measure between interval-valued fuzzy numbers and new interval-valued fuzzy number arithmetic operators. First, we present a new similarity measure between interval-valued fuzzy numbers. The proposed similarity measure considers the similarity of the gravities on the X-axis between upper fuzzy numbers, the difference of the spreads between upper fuzzy numbers, the heights of the upper fuzzy numbers, the degree of similarity on the X-axis between interval-valued fuzzy numbers, and the gravities on the Y-axis between interval-valued fuzzy numbers. We also present three properties of the proposed similarity measure between interval-valued fuzzy numbers. Then, we present new interval-valued fuzzy number arithmetic operators. Finally, we apply the proposed similarity measure between interval-valued fuzzy numbers and the proposed interval-valued fuzzy number arithmetic operators to propose a fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. The proposed method provides a useful way for handling fuzzy risk analysis problems based on interval-valued fuzzy numbers.