A Constraint-Softened Interval-Fuzzy Linear Programming Approach for Environmental Management Under Uncertainty

In this study, a constraint-softened interval-fuzzy linear programming (CS-IFLP) method is developed for violation analysis of environmental management systems under uncertainty. CS-IFLP can deal with uncertainties presented in terms of fuzzy sets and intervals. Moreover, a number of fuzzy relaxation levels for system constraints are allowed, such that the relevant decision space can be expanded. This can help generate a range of decision alternatives under various system conditions, and facilitate in-depth analyses of tradeoffs among economic objective, satisfaction degree, and constraint-violation risk. The developed method is applied to a case study of long-term municipal solid waste management planning. Results indicate that reasonable solutions for both binary and continuous variables have been generated. A higher relaxation level could result in a lower system cost and a higher satisfaction degree, but with a higher constraint-violation risk. Results of the sensitivity analyses demonstrate that violated system constraints have various effects on the system cost and satisfaction degree.