The expected value models on Sugeno measure space

  • Authors:

  • Minghu Ha;Hong Zhang;Witold Pedrycz;Hongjie Xing

  • Affiliations:

  • College of Mathematics and Computer Sciences, Hebei University, Baoding 071002, Hebei, PR China;School of Natural Science, Hebei University of Engineering, Handan 056038, PR China;Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada and Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland;College of Mathematics and Computer Sciences, Hebei University, Baoding 071002, Hebei, PR China

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2009

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Abstract

Uncertain programming is a theoretical tool to handle optimization problems under uncertain environment. The research reported so far is mainly concerned with probability, possibility, or credibility measure spaces. Up to now, uncertain programming realized in Sugeno measure space has not been investigated. The first type of uncertain programming considered in this study and referred to as an expected value model optimizes a given expected objective function subject to some expected constraints. We start with a concept of the Sugeno measure space. We revisit some main properties of the Sugeno measure and elaborate on the g"@l random variable and its characterization. Furthermore, the laws of the large numbers are discussed based on this space. In the sequel we introduce a Sugeno expected value model (SEVM). In order to construct an approximate solution to the complex SEVM, the ideas of a Sugeno random number generation and a Sugeno simulation are presented along with a hybrid approach.