Chance-constrained programming on sugeno measure space

Uncertain programming is a theoretical tool to handle optimization problems under uncertain environment, it is mainly established in probability, possibility, or credibility measure spaces. Sugeno measure space is an interesting and important extension of probability measure space. This motivates us to discuss the uncertain programming based on Sugeno measure space. We have constructed the first type of uncertain programming on Sugeno measure space, i.e. the expected value models of uncertain programming on Sugeno measure space. In this paper, the second type of uncertain programming on Sugeno measure space, i.e. chance-constrained programming on Sugeno measure space, is investigated. Firstly, the definition and the characteristic of α-optimistic value and α-pessimistic value as a ranking measure are provided. Secondly, Sugeno chance-constrained programming (SCCP) is introduced. Lastly, in order to construct an approximate solution to the complex SCCP, the ideas of a Sugeno random number generation and a Sugeno simulation are presented along with a hybrid approach.

► Chance-constrained programming on Sugeno measure space (SCCP) is shown. ► We give the definitions of α-pessimistic and α-optimistic values. ► The definitions and properties of SCCP models are provided. ► We give algorithmic components such as the Sugeno random number generation and Sugeno simulation. ► A numeric example illustrated that the proposed hybrid approach to solve the SCCP by Sugeno simulation is feasible.