Non-additive measures by interval probability functions

  • Authors:

  • Hideo Tanaka;Kazutomi Sugihara;Yutaka Maeda

  • Affiliations:

  • Department of Kansei Information, Hiroshima International University, Gakuendai, Kurose, Hiroshima 724-0695, Japan;Department of Applied Physics, Graduate School of Engineering, Osaka University, Yamadaoka 2-1, Suita, Osaka 565-0871, Japan;Department of Industrial Engineering, College of Engineering, Osaka Prefecture University, Gakuencho 1-1. Sakai, Osaka 590-8531, Japan

  • Venue:
  • Information Sciences—Informatics and Computer Science: An International Journal
  • Year:
  • 2004

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Abstract

Probability measures are well-defined ones that satisfy additivity. However, it is slightly tight, because of its condition of additivity. Fuzzy measures that do not satisfy additivity have been proposed as substitute measures. The only belief function involves a density function in finite spaces among them. In this paper, we propose two probability functions by extending values of probability functions to interval values, which do not satisfy additivity. According to the definition of interval probability functions, lower and upper probabilities are defined, respectively, as known in Dempster--Shafer Theory. A combination rule and a conditional probability can be defined well. The properties of the proposed measure are clarified. Last, a numerical example with respect to Bayes' decision problems is shown.