Multipollutant Air Quality Management Strategies: T-Sets Based Optimization Technique Under Imprecise Environment

In this paper, technique to find Pareto optimal solutions to multiple objective optimization problems under imprecise environment is discussed. In 1976, Zimmermann described optimization technique under fuzzy environment. Jiménez and Bilbao (Fuzzy Sets Syst 150:2714–2721, 2009) showed that fuzzy efficient solutions may not be Pareto optimal solutions to multiple objective optimization problems in case that one of the fuzzy goals is fully achieved. Wu et al. (Fuzzy Optim Decis Mak 14:43–55, 2015) redefined membership functions of fuzzy set theory and proposed two-phase approach. But under imprecise environment, it is observed that the prime intention of maximizing up-gradation of most misfortunate is better served by removing some constraints that are obtained by applying existing fuzzy optimization technique in mathematical models. Further in existing fuzzy optimization technique, it is observed that membership functions are not utilized as per their definitions. Moreover, some constraints in existing fuzzy optimization technique may make a model infeasible. Consequently, in this paper, one new function viz. T-characteristic function is introduced to supersede membership function of fuzzy set, and subsequently, one new set viz. T-set is introduced to supersede fuzzy set for representing uncertainty. Then, one general algorithm has been developed to find Pareto optimal solutions to multiple objective optimization problems by applying newly introduced T-sets. One model on multipollutant air quality management strategies under imprecise environment illustrates the limitations of existing fuzzy optimization technique as well as advantages of using proposed algorithm. Finally, conclusions are drawn.Graphical Abstract