A Robust Inexact Joint-optimal α cut Interval Type-2 Fuzzy Boundary Linear Programming (RIJ-IT2FBLP) for energy systems planning under uncertainty

• Analyze multiple uncertainties within energy systems expressed as interval type-2 fuzzy sets boundaries.
• Propose a Robust Inexact Joint-optimal α Cut Interval Type-2 Fuzzy Boundary Linear Programming (RIJ-IT2FBLP) model for energy systems.
• Use a case study of energy example to illustrate superiority of RIJ-IT2FBLP method.
• Obtain optimal solutions under joint-optimal α cut degrees and system benefits.
• Provide decision makers with effective energy management schemes.

In this study, a new Robust Inexact Joint-optimal α cut Interval Type-2 Fuzzy Boundary Linear Programming (RIJ-IT2FBLP) model is developed for planning of energy systems by integrating both the interval T2 fuzzy sets and the Inexact Linear Programming (ILP) methods. It intends to find an optimal solution for energy systems under such uncertainty expressed as interval fuzzy boundary intervals that exist in the right-hand sides of model constraints. It improves the formal Fuzzy sets Linear Programming (FLP) method by using an optimal analysis in order to obtain an appropriate interpretation of type-2 fuzzy intervals and their solutions. The interval type-2 fuzzy boundary method can provide more accurate judgments to measure the dispersion of fuzzy sets. It also improves the formal interval Two-Step solving Method (TSM) by applying a Robust Two-Step algorithm (RTSM), which allows solutions to avoid absolute violation. Then, the developed model is applied to a case study of long term energy resources planning. Solutions related to interval T2 fuzzy sets linear programming are obtained. These help decision makers handle multiple ambiguity issues existing in energy demand, supply and capacity expansions. The results of the RIJ-IT2FBLP model not only deliver an optimized energy scheme, but also provide a suitable way to balance uncertain cost and profit parameters of an energy supply system. Therefore, the RIJ-IT2FBLP is considered a more practical method for energy management under multiple uncertainties.