Abstract
The existence of uncertainty is inherent and unavoidable in process systems. The sources of it might be linked, though not limited, to the estimation of model parameters through experimental/regression exercises and their related errors apart from the regular variations in the process operations. Thus, the outcomes of an optimization study by assuming uncertain parameters as non-varying one, as opposite to the actual scenario, would prompt to incorrect results and sometimes even infeasible solutions. One of the ways to handle such situations is by using intuitionistic fuzzy numbers (IFNs) to represent the uncertainty which considers both the membership and the nonmembership degree and carry out the uncertainty analysis based on the intuitionistic fuzzy logic. In this study, the above approach has been adopted to a real-life case study which contains highly nonlinear parameters named industrial grinding process considering different moods of a decision-maker under uncertain situations, i.e., optimistic, pessimistic, and mixed. Various sources of uncertainties are categorized as uncertainties related to model parameters (e.g., tuning parameters inside the model) and operational parameters (e.g., feed stream uncertainties), and their individual and amalgamated effects on the grinding process which is a multi-objective optimization problem have been analyzed. A novel way of determining the parametric sensitivity in presence of number of uncertain parameters has also been proposed. Based on the extent of non-determinacy to be resolved, the newly defined membership degree enables conducting comparative study of fuzzy and intuitionistic fuzzy robust optimization under different scenarios. Additionally, comparative analysis has been carried out for the proposed IFRO algorithm with the benchmark robust worst-case formulation (Ben-Tal and Nemirovskii 2001) and it has been observed that IFRO gives better results when compared with the worst-case formulation.
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Sahinidis, N. V. (2004). Optimization under uncertainty: State-of-the-art and opportunities. Computers & Chemical Engineering, 28, 971–983.
Ben-Tal, A., & Nemirovskii, A. (2001). Lectures on modern convex optimization: Analysis, algorithms, and engineering applications. MPS-SIAM Series on optimization. Philadelphia: MPS-SIAM.
Liu, B. (2002). Theory and practice of uncertain programming. Heidelberg: Physica-Verlag.
Liu, M. L., & Sahinidis, N. V. (1996). Optimization in process planning under uncertainty. Industrial and Engineering Chemistry Research, 35, 4154–4165.
Charnes, A., & Cooper, W. W. (1959). Chance-constrained programming. Management Science, 6, 73–79.
Gupta, A., & Maranas, C. D. (2000). A two-stage modeling and solution framework for multisite midterm planning under demand uncertainty. Industrial and Engineering Chemistry Research, 39, 3799–3813.
Ayoub, N., Martins, R., Wang, K., Seki, H., & Naka, Y. (2007). Two levels decision system for efficient planning and implementation of bioenergy production. Energy Conversion and Management, 48, 709–723.
Mitra, K., Gudi, R. D., Patwardhan, S. C., & Sardar, G. (2008). Midterm supply chain planning under uncertainty: a multi-objective chance constrained programming framework. Industrial and Engineering Chemistry Research, 47, 5501–5511.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
Palwak, Z. (1985). Rough sets and fuzzy sets. Fuzzy Sets and Systems, 17, 99–102.
Gau, W. L., & Buehrer, D. J. (1993). Vague sets. IEEE Transactions on Systems, Man and Cybernetics, 23, 610–614.
Sambuc, R. (1975). Fonctions φ-floues. Application l’aide au diagnostic en pathologie thyroidienne, Ph.D. Thesis, University of Marseille, France.
Zimmermann, H. J. (1991). Fuzzy set theory and its application. Boston: Kluwer Academic Publishers.
Dubois, D., & Prade, H. (1988). Possibility theory: An approach to computerized processing of uncertainty. New York: Plenum Press.
Virivinti, N., & Mitra, K. (2014). Fuzzy expected value analysis of an industrial grinding process. Powder Technology, 286, 9–18.
Tian, G., Chu, J., Liu, Y., Ke, H., Zhao, X., & Xu, G. (2011). Expected energy analysis for industrial process planning problem with fuzzy time parameters. Computers & Chemical Engineering, 35, 2905–2912.
Mitra, K. (2009). Multi-objective optimization of an industrial grinding operation under uncertainty. Chemical Engineering Science, 64, 5043–5056.
Virivinti, N., & Mitra, K. (2016). A comparative study of fuzzy techniques to handle uncertainty: An industrial grinding process. Chemical Engineering and Technology, 39, 1031–1039.
Marano, G. C., & Quaranta, G. (2009). Robust optimum criteria for tuned mass dampers in fuzzy environments. Applied Soft Computing, 9, 1232–1243.
Zhang, X., Huang, G. H., Chan, C. W., Liu, Z., & Lin, Q. (2010). A fuzzy-robust stochastic multiobjective programming approach for petroleum waste management planning. Applied Mathematical Modelling, 34, 2778–2788.
Diez, M., & Peri, D. (2010). Robust optimization for ship conceptual design. Ocean Engineering, 37, 966–977.
Capolei, A., Suwartadi, E., Foss, B., & Jorgensen J. B. (2015). A mean–variance objective for robust production optimization in uncertain geological scenarios. Journal of Petroleum Science and Engineering, 125, 23–37.
Atanassov, K. T. (1986). Intutionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.
Virivinti, N., & Mitra, K. (2015). Intuitionistic fuzzy chance constrained programming for handling parametric uncertainty: An industrial grinding case study. Industrial and Engineering Chemistry Research, 54, 6291–6304.
Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley.
Yager, R. R. (2009). Some aspects of intuitionistic fuzzy sets. Fuzzy Optimization and Decision Making, 8, 67–90.
Bellman, R., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Science, 17, 141–161.
Angelov, P. P. (1997). Optimization in an intuitionistic fuzzy environment. Fuzzy Sets and Systems, 86, 299–306.
Liu, B., & Liu, Y. K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10, 445–450.
Dubey, D., Chandra, S., & Mehra, A. (2012). Fuzzy linear programming under interval uncertainty based on IFS representation. Fuzzy Sets and Systems, 188, 68–87.
Petzold, L. R. (1983). A description of DASSL: A differential/algebraic system solver. In Scientific computing (pp. 65–68). North-Holland, Amsterdam.
Mitra, K., & Gopinath, R. (2004). Multiobjective optimization of an industrial grinding operation using elitist non-dominated sorting genetic algorithm. Chemical Engineering Science, 59, 385–396.
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Virivinti, N., Mitra, K. (2019). Intuitionistic Fuzzy Approach Toward Evolutionary Robust Optimization of an Industrial Grinding Operation Under Uncertainty. In: Datta, S., Davim, J. (eds) Optimization in Industry. Management and Industrial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-01641-8_10
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DOI: https://doi.org/10.1007/978-3-030-01641-8_10
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