A distributionally robust credibilistic optimization method for the economic-environmental-energy-social sustainability problem

Abstract The existing literature on sustainable development problems mainly focuses on multicriteria decision analyses, and ignores the impact of uncertain information on optimal labor allocation decisions. It is necessary for sustainable development to implement suitable policies under uncertainty that integrate several competing aspects including economic, environmental, energy and social criteria. Based on type-2 fuzzy theory, this paper develops a distributionally robust optimization method for sustainable development problems. In our new model, the uncertain per capita gross domestic product (GDP), per capita electricity consumption and per capita greenhouse gas (GHG) emissions are characterized by parametric interval-valued (PIV) possibility distributions and their associated uncertainty distribution sets. Under two assumptions on the underlining decision-making environment, the robust counterpart of the original distributionally robust fuzzy sustainable development model is formally established. To solve the proposed robust sustainable development model, this paper discusses the computational issue concerning the infinitely many integral objective functions and credibilistic constraints, and turns the robust counterpart model into its computationally tractable equivalent deterministic submodels. Taking advantage of the structural characteristics of the equivalent submodels, a domain decomposition method is designed to find the robust optimal solution that can protect against distribution uncertainty. Finally, this paper applies the proposed optimization method for the key economic sectors of the United Arab Emirates (UAE) to provide quantitative justification in planning future labor and resource allocation.