A CVaR optimization method for priority of hesitant fuzzy preference relation with chance constraint

Abstract

In this paper, we establish a chance constrained model for the priority of hesitant fuzzy preference relation based on the idea of statistical distribution for preference information as stochastic variables with unknown distribution. Inspired by the idea of conditional value-at-risk (CVaR) robust optimization, a deterministic convex reformulation is proposed for tackling the chance constrained problem. The existing state-of-the-art methods usually assume that the probability density function of preference information is known a priori, such as Gaussian distribution. However, it is generally over-conservatism. On the contrary, our proposed method provides a tractable second-order cone (SOC) reformulation for the chance constrained problem with the first and second moments, which is easy to handle and calculate. We also analyze the weight acquisition problem of hesitant fuzzy preference relation with unknown distribution preference using the SOC programming method, and obtain the priority weight with its approximately equivalent computationally tractable conic optimization model. A case study is conducted which shows that the proposed method achieves a good general conclusion by comparing it with the optimization method under Gaussian distribution. In addition, this method can also get better decision support for incomplete preference information.