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 gλ 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. © 2009 Elsevier Inc. All rights reserved.
Ha, M., Zhang, H., Pedrycz, W., & Xing, H. (2009). The expected value models on Sugeno measure space. International Journal of Approximate Reasoning, 50(7), 1022–1035. https://doi.org/10.1016/j.ijar.2009.03.008