Development of an interval-valued fuzzy linear-programming method based on infinite α-cuts for water resources management

An interval-valued fuzzy linear-programming (IVFL) method based on infinite α-cuts is developed for water resources management in this study. The introduction of interval parameters and interval-valued fuzzy parameters into the objective function and constraints makes it possible for dealing with individual uncertainty and dual uncertainties existing in many real-world cases. A two-step infinite α-cuts (TSI) solution method is communicated to the solution process to discretize infinite α-cuts to interval-valued fuzzy membership functions. Application to an agricultural irrigation problem indicates that interval-valued fuzzy sets can represent dual uncertainties in modeling parameters, and the solution method is able to generate decisions with enhanced reliability. It is also indicated that the objective (i.e. system net benefit) can be increased with the growth of violation risk, in association with a set of different allocation schemes. As the key segment of interval-valued fuzzy membership functions that could significantly affect system performance can be identified through the analysis of decision alternatives under different risk levels of constraint violation, the IVFL method provides decision makers flexibility in selecting an appropriate decision scheme according to their preference and practical conditions.