Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables

Abstract

This paper considers linear programming problems (LPPs) where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables). New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.

A Multistage Distribution-Generation Planning Model for Clean Power Generation under Multiple Uncertainties—A Case Study of Urumqi, China

“…Therefore, as an extension of previous research, the objective of this study is to develop a multistage distribution-generation planning (MDGP) model for supporting DG systems planning with clean energy substitution; the proposed MDGP will be applied to the city of Urumqi for supporting DG systems planning with emission mitigation, clean energy substitution and power-structure adjustment [22,23]. The MDGP model was formulated by integration of multistage stochastic programming method (MSP) [24,25], fuzzy-random interval programming (FRIP) [25][26][27], and stochastic robust optimization method (SRO) [28][29][30].…”