Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions

"This is an Accepted Manuscript of an article published in International Journal of Production Research on December 2014, available online: http://www.tandfonline.com/10.1080/00207543.2014.920115."In this paper, we formulate the material requirements planning) problem of a first-tier supplier in an automobile supply chain through a fuzzy multi-objective decision model, which considers three conflictive objectives to optimise: minimisation of normal, overtime and subcontracted production costs of finished goods plus the inventory costs of finished goods, raw materials and components; minimisation of idle time; minimisation of backorder quantities. Lack of knowledge or epistemic uncertainty is considered in the demand, available and required capacity data. Integrity conditions for the main decision variables of the problem are also considered. For the solution methodology, we use a fuzzy goal programming approach where the importance of the relations among the goals is considered fuzzy instead of using a crisp definition of goal weights. For illustration purposes, an example based on modifications of real-world industrial problems is used.This work has been funded by the Universitat Politecnica de Valencia Project: 'Material Requirements Planning Fourth Generation (MRPIV)' (Ref. PAID-05-12).Díaz-Madroñero Boluda, FM.; Mula, J.; Jiménez, M. (2014). Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions. International Journal of Production Research. 52(23):6971-6988. doi:10.1080/00207543.2014.920115S697169885223Aköz, O., & Petrovic, D. (2007). A fuzzy goal programming method with imprecise goal hierarchy. European Journal of Operational Research, 181(3), 1427-1433. doi:10.1016/j.ejor.2005.11.049Alfieri, A., & Matta, A. (2010). Mathematical programming representation of pull controlled single-product serial manufacturing systems. Journal of Intelligent Manufacturing, 23(1), 23-35. doi:10.1007/s10845-009-0371-xAloulou, M. A., Dolgui, A., & Kovalyov, M. Y. (2013). A bibliography of non-deterministic lot-sizing models. International Journal of Production Research, 52(8), 2293-2310. doi:10.1080/00207543.2013.855336Barba-Gutiérrez, Y., & Adenso-Díaz, B. (2009). Reverse MRP under uncertain and imprecise demand. The International Journal of Advanced Manufacturing Technology, 40(3-4), 413-424. doi:10.1007/s00170-007-1351-yBookbinder, J. H., McAuley, P. T., & Schulte, J. (1989). Inventory and Transportation Planning in the Distribution of Fine Papers. Journal of the Operational Research Society, 40(2), 155-166. doi:10.1057/jors.1989.20Chiang, W. K., & Feng, Y. (2007). The value of information sharing in the presence of supply uncertainty and demand volatility. International Journal of Production Research, 45(6), 1429-1447. doi:10.1080/00207540600634949Díaz-Madroñero, M., Mula, J., & Jiménez, M. (2013). A Modified Approach Based on Ranking Fuzzy Numbers for Fuzzy Integer Programming with Equality Constraints. Annals of Industrial Engineering 2012, 225-233. doi:10.1007/978-1-4471-5349-8_27DOLGUI, A., BEN AMMAR, O., HNAIEN, F., & LOULY, M. A. O. (2013). A State of the Art on Supply Planning and Inventory Control under Lead Time Uncertainty. Studies in Informatics and Control, 22(3). doi:10.24846/v22i3y201302Dubois, D. (2011). The role of fuzzy sets in decision sciences: Old techniques and new directions. Fuzzy Sets and Systems, 184(1), 3-28. doi:10.1016/j.fss.2011.06.003Grabot, B., Geneste, L., Reynoso-Castillo, G., & V�rot, S. (2005). Integration of uncertain and imprecise orders in the MRP method. Journal of Intelligent Manufacturing, 16(2), 215-234. doi:10.1007/s10845-004-5890-xGuillaume, R., Thierry, C., & Grabot, B. (2010). Modelling of ill-known requirements and integration in production planning. Production Planning & Control, 22(4), 336-352. doi:10.1080/09537281003800900Heilpern, S. (1992). The expected value of a fuzzy number. Fuzzy Sets and Systems, 47(1), 81-86. doi:10.1016/0165-0114(92)90062-9Hnaien, F., Dolgui, A., & Ould Louly, M.-A. (2008). Planned lead time optimization in material requirement planning environment for multilevel production systems. Journal of Systems Science and Systems Engineering, 17(2), 132-155. doi:10.1007/s11518-008-5072-zHung, Y.-F., & Chang, C.-B. (1999). Determining safety stocks for production planning in uncertain manufacturing. International Journal of Production Economics, 58(2), 199-208. doi:10.1016/s0925-5273(98)00124-8Inderfurth, K. (2009). How to protect against demand and yield risks in MRP systems. International Journal of Production Economics, 121(2), 474-481. doi:10.1016/j.ijpe.2007.02.005JIMÉNEZ, M. (1996). RANKING FUZZY NUMBERS THROUGH THE COMPARISON OF ITS EXPECTED INTERVALS. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 04(04), 379-388. doi:10.1142/s0218488596000226Jiménez, M., Arenas, M., Bilbao, A., & Rodrı´guez, M. V. (2007). Linear programming with fuzzy parameters: An interactive method resolution. European Journal of Operational Research, 177(3), 1599-1609. doi:10.1016/j.ejor.2005.10.002Jones, D. (2011). A practical weight sensitivity algorithm for goal and multiple objective programming. European Journal of Operational Research, 213(1), 238-245. doi:10.1016/j.ejor.2011.03.012Lage Junior, M., & Godinho Filho, M. (2010). Variations of the kanban system: Literature review and classification. International Journal of Production Economics, 125(1), 13-21. doi:10.1016/j.ijpe.2010.01.009Jung, J. Y., Blau, G., Pekny, J. F., Reklaitis, G. V., & Eversdyk, D. (2004). A simulation based optimization approach to supply chain management under demand uncertainty. Computers & Chemical Engineering, 28(10), 2087-2106. doi:10.1016/j.compchemeng.2004.06.006Koh, S. C. L. (2004). MRP-controlled batch-manufacturing environment under uncertainty. Journal of the Operational Research Society, 55(3), 219-232. doi:10.1057/palgrave.jors.2601710Lai, Y.-J., & Hwang, C.-L. (1993). Possibilistic linear programming for managing interest rate risk. Fuzzy Sets and Systems, 54(2), 135-146. doi:10.1016/0165-0114(93)90271-iLee, H. L., & Billington, C. (1993). Material Management in Decentralized Supply Chains. Operations Research, 41(5), 835-847. doi:10.1287/opre.41.5.835Lee, Y. H., Kim, S. H., & Moon, C. (2002). Production-distribution planning in supply chain using a hybrid approach. Production Planning & Control, 13(1), 35-46. doi:10.1080/09537280110061566Li, X., Zhang, B., & Li, H. (2006). Computing efficient solutions to fuzzy multiple objective linear programming problems. Fuzzy Sets and Systems, 157(10), 1328-1332. doi:10.1016/j.fss.2005.12.003Louly, M.-A., & Dolgui, A. (2011). Optimal time phasing and periodicity for MRP with POQ policy. International Journal of Production Economics, 131(1), 76-86. doi:10.1016/j.ijpe.2010.04.042Louly, M. A., Dolgui, A., & Hnaien, F. (2008). Optimal supply planning in MRP environments for assembly systems with random component procurement times. International Journal of Production Research, 46(19), 5441-5467. doi:10.1080/00207540802273827Mohapatra, P., Benyoucef, L., & Tiwari, M. K. (2013). Integration of process planning and scheduling through adaptive setup planning: a multi-objective approach. International Journal of Production Research, 51(23-24), 7190-7208. doi:10.1080/00207543.2013.853890Mula, J., & Díaz-Madroñero, M. (2012). Solution Approaches for Material Requirement Planning* with Fuzzy Costs. Industrial Engineering: Innovative Networks, 349-357. doi:10.1007/978-1-4471-2321-7_39Mula, J., Poler, R., & García, J. P. (2006). Evaluación de Sistemas para la Planificación y Control de la Producción/[title] [title language=en]Evaluation of Production Planning and Control Systems. Información tecnológica, 17(1). doi:10.4067/s0718-07642006000100004Mula, J., Poler, R., & Garcia, J. P. (2006). MRP with flexible constraints: A fuzzy mathematical programming approach. Fuzzy Sets and Systems, 157(1), 74-97. doi:10.1016/j.fss.2005.05.045Mula, J., Poler, R., & Garcia-Sabater, J. P. (2008). Capacity and material requirement planning modelling by comparing deterministic and fuzzy models. International Journal of Production Research, 46(20), 5589-5606. doi:10.1080/00207540701413912Mula, J., Poler, R., & Garcia-Sabater, J. P. (2007). Material Requirement Planning with fuzzy constraints and fuzzy coefficients. Fuzzy Sets and Systems, 158(7), 783-793. doi:10.1016/j.fss.2006.11.003Mula, J., Poler, R., García-Sabater, J. P., & Lario, F. C. (2006). Models for production planning under uncertainty: A review. International Journal of Production Economics, 103(1), 271-285. doi:10.1016/j.ijpe.2005.09.001Noori, S., Feylizadeh, M. R., Bagherpour, M., Zorriassatine, F., & Parkin, R. M. (2008). Optimization of material requirement planning by fuzzy multi-objective linear programming. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 222(7), 887-900. doi:10.1243/09544054jem1014Olhager, J. (2013). Evolution of operations planning and control: from production to supply chains. International Journal of Production Research, 51(23-24), 6836-6843. doi:10.1080/00207543.2012.761363Peidro, D., Mula, J., Alemany, M. M. E., & Lario, F.-C. (2012). Fuzzy multi-objective optimisation for master planning in a ceramic supply chain. International Journal of Production Research, 50(11), 3011-3020. doi:10.1080/00207543.2011.588267Peidro, D., Mula, J., Jiménez, M., & del Mar Botella, M. (2010). A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment. European Journal of Operational Research, 205(1), 65-80. doi:10.1016/j.ejor.2009.11.031Peidro, D., Mula, J., Poler, R., & Lario, F.-C. (2008). Quantitative models for supply chain planning under uncertainty: a review. The International Journal of Advanced Manufacturing Technology, 43(3-4), 400-420. doi:10.1007/s00170-008-1715-yPeidro, D., Mula, J., Poler, R., & Verdegay, J.-L. (2009). Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. Fuzzy Sets and Systems, 160(18), 2640-2657. doi:10.1016/j.fss.2009.02.021Sabri, E. H., & Beamon, B. M. (2000). A multi-objective approach to simultaneous strategic and operational planning in supply chain design. Omega, 28(5), 581-598. doi:10.1016/s0305-0483(99)00080-8Selim, H., & Ozkarahan, I. (2006). A supply chain distribution network design model: An interactive fuzzy goal programming-based solution approach. The International Journal of Advanced Manufacturing Technology, 36(3-4), 401-418. doi:10.1007/s00170-006-0842-6Suwanruji, P., & Enns, S. T. (2006). Evaluating the effects of capacity constraints and demand patterns on supply chain replenishment strategies. International Journal of Production Research, 44(21), 4607-4629. doi:10.1080/00207540500494527Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets and Systems, 159(2), 193-214. doi:10.1016/j.fss.2007.08.010Torabi, S. A., & Moghaddam, M. (2012). Multi-site integrated production-distribution planning with trans-shipment: a fuzzy goal programming approach. International Journal of Production Research, 50(6), 1726-1748. doi:10.1080/00207543.2011.560907Zimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55. doi:10.1016/0165-0114(78)90031-

Modelling an Industrial Robot and Its Impact on Productivity

[EN] This research aims to design an efficient algorithm leading to an improvement of productivity by posing a multi-objective optimization, in which both the time consumed to carry out scheduled tasks and the associated costs of the autonomous industrial system are minimized. The algorithm proposed models the kinematics and dynamics of the industrial robot, provides collision-free trajectories, allows to constrain the energy consumed and meets the physical characteristics of the robot (i.e., restriction on torque, jerks and power in all driving motors). Additionally, the trajectory tracking accuracy is improved using an adaptive fuzzy sliding mode control (AFSMC), which allows compensating for parametric uncertainties, bounded external disturbances and constraint uncertainties. Therefore, the system stability and robustness are enhanced; thus, overcoming some of the limitations of the traditional proportional-integral-derivative (PID) controllers. The trade-offs among the economic issues related to the assembly line and the optimal time trajectory of the desired motion are analyzed using Pareto fronts. The technique is tested in different examples for a six-degrees-of-freedom (DOF) robot system. Results have proved how the use of this methodology enhances the performance and reliability of assembly lines.Llopis-Albert, C.; Rubio Montoya, FJ.; Valero Chuliá, FJ. (2021). Modelling an Industrial Robot and Its Impact on Productivity. Mathematics. 9(7):1-13. https://doi.org/10.3390/math907076911397AOYAMA, T., NISHI, T., & ZHANG, G. (2017). Production planning problem with market impact under demand uncertainty. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 11(2), JAMDSM0019-JAMDSM0019. doi:10.1299/jamdsm.2017jamdsm0019Llopis-Albert, C., Rubio, F., & Valero, F. (2015). Improving productivity using a multi-objective optimization of robotic trajectory planning. Journal of Business Research, 68(7), 1429-1431. doi:10.1016/j.jbusres.2015.01.027Rubio, F., Valero, F., Sunyer, J., & Cuadrado, J. (2012). Optimal time trajectories for industrial robots with torque, power, jerk and energy consumed constraints. Industrial Robot: An International Journal, 39(1), 92-100. doi:10.1108/01439911211192538Llopis-Albert, C., Rubio, F., & Valero, F. (2018). Optimization approaches for robot trajectory planning. Multidisciplinary Journal for Education, Social and Technological Sciences, 5(1), 1. doi:10.4995/muse.2018.9867Yang, Y., Pan, J., & Wan, W. (2019). Survey of optimal motion planning. IET Cyber-Systems and Robotics, 1(1), 13-19. doi:10.1049/iet-csr.2018.0003Gasparetto, A., & Zanotto, V. (2008). A technique for time-jerk optimal planning of robot trajectories. Robotics and Computer-Integrated Manufacturing, 24(3), 415-426. doi:10.1016/j.rcim.2007.04.001Mohammed, A., Schmidt, B., Wang, L., & Gao, L. (2014). Minimizing Energy Consumption for Robot Arm Movement. Procedia CIRP, 25, 400-405. doi:10.1016/j.procir.2014.10.055Van den Berg, J., Abbeel, P., & Goldberg, K. (2011). LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information. The International Journal of Robotics Research, 30(7), 895-913. doi:10.1177/0278364911406562Liu, S., Sun, D., & Zhu, C. (2011). Coordinated Motion Planning for Multiple Mobile Robots Along Designed Paths With Formation Requirement. IEEE/ASME Transactions on Mechatronics, 16(6), 1021-1031. doi:10.1109/tmech.2010.2070843Plaku, E., Kavraki, L. E., & Vardi, M. Y. (2010). Motion Planning With Dynamics by a Synergistic Combination of Layers of Planning. IEEE Transactions on Robotics, 26(3), 469-482. doi:10.1109/tro.2010.2047820Rubio, F., Llopis-Albert, C., Valero, F., & Suñer, J. L. (2015). Assembly Line Productivity Assessment by Comparing Optimization-Simulation Algorithms of Trajectory Planning for Industrial Robots. Mathematical Problems in Engineering, 2015, 1-10. doi:10.1155/2015/931048Rubio, F., Llopis-Albert, C., Valero, F., & Suñer, J. L. (2016). Industrial robot efficient trajectory generation without collision through the evolution of the optimal trajectory. Robotics and Autonomous Systems, 86, 106-112. doi:10.1016/j.robot.2016.09.008Llopis-Albert, C., Valero, F., Mata, V., Pulloquinga, J. L., Zamora-Ortiz, P., & Escarabajal, R. J. (2020). Optimal Reconfiguration of a Parallel Robot for Forward Singularities Avoidance in Rehabilitation Therapies. A Comparison via Different Optimization Methods. Sustainability, 12(14), 5803. doi:10.3390/su12145803Llopis-Albert, C., Valero, F., Mata, V., Escarabajal, R. J., Zamora-Ortiz, P., & Pulloquinga, J. L. (2020). Optimal Reconfiguration of a Limited Parallel Robot for Forward Singularities Avoidance. Multidisciplinary Journal for Education, Social and Technological Sciences, 7(1), 113. doi:10.4995/muse.2020.13352Yang, J., Su, H., Li, Z., Ao, D., & Song, R. (2016). Adaptive control with a fuzzy tuner for cable-based rehabilitation robot. International Journal of Control, Automation and Systems, 14(3), 865-875. doi:10.1007/s12555-015-0049-4Zhang, G., & Zhang, X. (2016). Concise adaptive fuzzy control of nonlinearly parameterized and periodically time-varying systems via small gain theory. International Journal of Control, Automation and Systems, 14(4), 893-905. doi:10.1007/s12555-015-0054-7SUTONO, S. B., ABDUL-RASHID, S. H., AOYAMA, H., & TAHA, Z. (2016). Fuzzy-based Taguchi method for multi-response optimization of product form design in Kansei engineering: a case study on car form design. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 10(9), JAMDSM0108-JAMDSM0108. doi:10.1299/jamdsm.2016jamdsm0108DUBEY, A. K. (2009). Performance Optimization Control of ECH using Fuzzy Inference Application. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 3(1), 22-34. doi:10.1299/jamdsm.3.22Zhang, H., Fang, H., Zhang, D., Luo, X., & Zou, Q. (2020). Adaptive Fuzzy Sliding Mode Control for a 3-DOF Parallel Manipulator with Parameters Uncertainties. Complexity, 2020, 1-16. doi:10.1155/2020/2565316Markazi, A. H. D., Maadani, M., Zabihifar, S. H., & Doost-Mohammadi, N. (2018). Adaptive Fuzzy Sliding Mode Control of Under-actuated Nonlinear Systems. International Journal of Automation and Computing, 15(3), 364-376. doi:10.1007/s11633-017-1108-5Truong, H. V. A., Tran, D. T., To, X. D., Ahn, K. K., & Jin, M. (2019). Adaptive Fuzzy Backstepping Sliding Mode Control for a 3-DOF Hydraulic Manipulator with Nonlinear Disturbance Observer for Large Payload Variation. Applied Sciences, 9(16), 3290. doi:10.3390/app9163290Li, T.-H. S., & Huang, Y.-C. (2010). MIMO adaptive fuzzy terminal sliding-mode controller for robotic manipulators. Information Sciences, 180(23), 4641-4660. doi:10.1016/j.ins.2010.08.00

Robust control design for vehicle active suspension systems with uncertainty

A vehicle active suspension system, in comparison with its counterparts, plays a crucial role in adequately guarantee the stability of the vehicle and improve the suspension performances. With a full understanding of the state of the art in vehicle control systems, this thesis identifies key issues in robust control design for active suspension systems with uncertainty, contributes to enhance the suspension performances via handling tradeoffs between ride comfort, road holding and suspension deflection. Priority of this thesis is to emphasize the contributions in handing actuator-related challenges and suspension model parameter uncertainty. The challenges in suspension actuators are identified as time-varying actuator delay and actuator faults. Time-varying delay and its effects in suspension actuators are targeted and analyzed. By removing the assumptions from the state of the art methods, state-feedback and output-feedback controller design methods are proposed to design less conservative state-feedback and output-feedback controller existence conditions. It overcomes the challenges brought by generalized timevarying actuator delay. On the other hand, a novel fault-tolerant controller design algorithm is developed for active suspension systems with uncertainty of actuator faults. A continuous-time homogeneous Markov process is presented for modeling the actuator failure process. The fault-tolerant H∞ controller is designed to guarantee asymptotic the stability, H∞ performance, and the constrained performance with existing possible actuator failures. It is evident that vehicle model parameter uncertainty is a vital factor affecting the performances of suspension control system. Consequently, this thesis presents two robust control solutions to overcome suspension control challenges with nonlinear constraints. A novel fuzzy control design algorithm is presented for active suspension systems with uncertainty. By using the sector nonlinearity method, Takagi-Sugeno (T-S) fuzzy systems are used to model the system. Based on Lyapunov stability theory, a new reliable fuzzy controller is designed to improve suspension performances. A novel adaptive sliding mode controller design approach is also developed for nonlinear uncertain vehicle active suspension systems. An adaptive sliding mode controller is designed to guarantee the stability and improve the suspension performances. In conclusion, novel control design algorithms are proposed for active suspension systems with uncertainty in order to guarantee and improve the suspension performance. Simulation results and comparison with the state of the art methods are provided to evaluate the effectiveness of the research contributions. The thesis shows insights into practical solutions to vehicle active suspension systems, it is expected that these algorithms will have significant potential in industrial applications and electric vehicles industry.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Investigation of performance of fuzzy logic controllers optimized with the hybrid genetic-gravitational search algorithm for PMSM speed control

Fuzzy logic controllers (FLCs) are widely used to control complex systems with model uncertainty, such as alternating current motors. The design process of the FLC is generally based on the designer’s adjustments on the controller until the desired performance is achieved. However, doing the controller design in this way makes the design process quite difficult and time-consuming, so it is often impossible to make a suitable and successful design. In this study, the output membership functions of the FLC are optimized with heuristic algorithms to reach the best speed control performance of the permanent magnet synchronous motor (PMSM). This paper proposes a new hybrid algorithm called H-GA-GSA, created by combining the advantages of the Genetic Algorithm (GA) and Gravitational Search Algorithm (GSA) to optimize FLC. The paper presents a convenient adjustment and design method for optimizing FLC with heuristic algorithms considered. To evaluate the effectiveness of H-GA-GSA, the proposed hybrid algorithm has been compared with GA and GSA in terms of convergence rate, PMSM speed control performance and electromagnetic torque variations. Optimization performance and results obtained from simulation studies verify that the proposed hybrid H-GA-GSA outperforms GA and GSA

Application of fuzzy logic in performance management: a literature review

[EN] Performance management has become in a key success factor for any organization. Traditionally, performance management has focused uniquely in financial measures, mainly using quantitative measures, but two decades ago they were extended towards an integral view of the organization, appearing qualitative measures. This type of extended view and associated measures have a degree of uncertainty that needs to be bounded. One of the essential tools for uncertainty bounding is the fuzzy logic and, therefore,the main objective of this paper is the analysis of the literature about the application of fuzzy logic in performance measurement systems operating within uncertainty environments with the aim of categorizing, conceptualizing and classifying the works written so far. Finally, three categories are defined according to the different uses of fuzzy logic within performance management concluding that the most important application of fuzzy logic that counts with a higher number of studies is uncertainty bounding.Gurrea Montesinos, V.; Alfaro Saiz, JJ.; Rodríguez Rodríguez, R.; Verdecho Sáez, MJ. (2014). Application of fuzzy logic in performance management: a literature review. International Journal of Production Management and Engineering. 2(2):93-100. doi:10.4995/ijpme.2014.1859SWORD9310022Amini, S., & Jochem, R. (2011). A Conceptual Model Based on the Fuzzy Set Theory to Measure and Evaluate the Performance of Service Processes. 2011 IEEE 15th International Enterprise Distributed Object Computing Conference Workshops. doi:10.1109/edocw.2011.25Ammar, S. & Wright, R. (1995), "A Fuzzy Logic Approach to Performance Evaluation". Uncertainty Modeling and Analysis, 1995, and Annual Conference of the North American Fuzzy Information Processing Society. Proceedings of ISUMA - NAFIPS '95., pp. 246 - 251Ammar, S., & Wright, R. (2000). Applying fuzzy-set theory to performance evaluation. Socio-Economic Planning Sciences, 34(4), 285-302. doi:10.1016/s0038-0121(00)00004-5Arango, M.D., Jaimes, W.A. & Zapata, J.A. (2010) "Gestion cadena de abastecimiento - Logistica con indicadores bajo incertidumbre, caso aplicado sector panificador palmira" Ciencia e Ingeniería Neogranadina, Vol. 20-1, pp. 97-115.Beheshti, H. M., & Lollar, J. G. (2008). Fuzzy logic and performance evaluation: discussion and application. International Journal of Productivity and Performance Management, 57(3), 237-246. doi:10.1108/17410400810857248Behrouzi, F., & Wong, K. Y. (2011). Lean performance evaluation of manufacturing systems: A dynamic and innovative approach. Procedia Computer Science, 3, 388-395. doi:10.1016/j.procs.2010.12.065Chan, T.S., Ql, H.J. (2003), "An innovative performance measurement method for supply chain management". Sup-ply Chain Management: An International Journal Volume 8 Number 3, pp. 209-223.Chan, F. T. S., Qi, H. J., Chan, H. K., Lau, H. C. W., & Ip, R. W. L. (2003). A conceptual model of performance measurement for supply chains. Management Decision, 41(7), 635-642. doi:10.1108/00251740310495568Chen, C.-T., Lin, C.-T., & Huang, S.-F. (2006). A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, 102(2), 289-301. doi:10.1016/j.ijpe.2005.03.009Cheng, S., Hsu, B., & Shu, M. (2007). Fuzzy testing and selecting better processes performance. Industrial Management & Data Systems, 107(6), 862-881. doi:10.1108/02635570710758761Ferreira, A., Azevedo,S. &Fazendeiro, P. (2012) "A Linguistic Approach to Supply Chain Performance Assessment". IEEE International Conference on Fuzzy Sistems, pp.1-5.Lau, H. C. W., Kai Pang, W., & Wong, C. W. Y. (2002). Methodology for monitoring supply chain performance: a fuzzy logic approach. Logistics Information Management, 15(4), 271-280. doi:10.1108/09576050210436110Lalmazloumian M. & Yew K., (2012), "A Review of Modelling Approaches for Supply Chain Planning Under Un-certainty". 9th International Conference on Service Systems and Service Management (ICSSSM), pp. 197-203.Liao, M.-Y., & Wu, C.-W. (2010). Evaluating process performance based on the incapability index for measurements with uncertainty. Expert Systems with Applications, 37(8), 5999-6006. doi:10.1016/j.eswa.2010.02.005Lu, C. & Wei li, X. (2006), "Supply Chain Modeling Using Fuzzy Sets and Possibility Theory in an Uncertain Envi-ronment". The Sixth World Congress on Intelligent Control and Automation, Vol.2, pp. 3608-3612.Mahnam, M., Yadollahpour, M. R., Famil-Dardashti, V., & Hejazi, S. R. (2009). Supply chain modeling in uncertain environment with bi-objective approach. Computers & Industrial Engineering, 56(4), 1535-1544. doi:10.1016/j.cie.2008.09.038Muñoz, M. J., Rivera, J. M., & Moneva, J. M. (2008). Evaluating sustainability in organisations with a fuzzy logic approach. Industrial Management & Data Systems, 108(6), 829-841. doi:10.1108/02635570810884030Olugu, E. U., & Wong, K. Y. (2012). An expert fuzzy rule-based system for closed-loop supply chain performance assessment in the automotive industry. Expert Systems with Applications, 39(1), 375-384. doi:10.1016/j.eswa.2011.07.026Tabrizi, B. H., & Razmi, J. (2013). Introducing a mixed-integer non-linear fuzzy model for risk management in designing supply chain networks. Journal of Manufacturing Systems, 32(2), 295-307. doi:10.1016/j.jmsy.2012.12.001Theeranuphattana, A., & Tang, J. C. S. (2007). A conceptual model of performance measurement for supply chains. Journal of Manufacturing Technology Management, 19(1), 125-148. doi:10.1108/17410380810843480Unahabhokha, C., Platts, K., & Hua Tan, K. (2007). Predictive performance measurement system. Benchmarking: An International Journal, 14(1), 77-91. doi:10.1108/14635770710730946Van der Vorst, J. G. A. J., & Beulens, A. J. M. (2002). Identifying sources of uncertainty to generate supply chain redesign strategies. International Journal of Physical Distribution & Logistics Management, 32(6), 409-430. doi:10.1108/09600030210437951Wei, C., Liou, T., & Lee, K. (2008). An ERP performance measurement framework using a fuzzy integral approach. Journal of Manufacturing Technology Management, 19(5), 607-626. doi:10.1108/17410380810877285Xu Xiao Xia, L., Ma, B. & Lim, R. (2008) "Supplier Performance Measurement in a Supply Chain". 6th IEEE Inter-national Conference on Industrial Informatics, pp. 877-881

Adaptive Non-singleton Type-2 Fuzzy Logic Systems: A Way Forward for Handling Numerical Uncertainties in Real World Applications

Real world environments are characterized by high levels of linguistic and numerical uncertainties. A Fuzzy Logic System (FLS) is recognized as an adequate methodology to handle the uncertainties and imprecision available in real world environments and applications. Since the invention of fuzzy logic, it has been applied with great success to numerous real world applications such as washing machines, food processors, battery chargers, electrical vehicles, and several other domestic and industrial appliances. The first generation of FLSs were type-1 FLSs in which type-1 fuzzy sets were employed. Later, it was found that using type-2 FLSs can enable the handling of higher levels of uncertainties. Recent works have shown that interval type-2 FLSs can outperform type-1 FLSs in the applications which encompass high uncertainty levels. However, the majority of interval type-2 FLSs handle the linguistic and input numerical uncertainties using singleton interval type-2 FLSs that mix the numerical and linguistic uncertainties to be handled only by the linguistic labels type-2 fuzzy sets. This ignores the fact that if input numerical uncertainties were present, they should affect the incoming inputs to the FLS. Even in the papers that employed non-singleton type-2 FLSs, the input signals were assumed to have a predefined shape (mostly Gaussian or triangular) which might not reflect the real uncertainty distribution which can vary with the associated measurement. In this paper, we will present a new approach which is based on an adaptive non-singleton interval type-2 FLS where the numerical uncertainties will be modeled and handled by non-singleton type-2 fuzzy inputs and the linguistic uncertainties will be handled by interval type-2 fuzzy sets to represent the antecedents’ linguistic labels. The non-singleton type-2 fuzzy inputs are dynamic and they are automatically generated from data and they do not assume a specific shape about the distribution associated with the given sensor. We will present several real world experiments using a real world robot which will show how the proposed type-2 non-singleton type-2 FLS will produce a superior performance to its singleton type-1 and type-2 counterparts when encountering high levels of uncertainties.</jats:p

Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory

[EN] The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio's performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018.García García, F.; González-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J.; Tamosiuniene, R. (2020). Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory. Technological and Economic Development of Economy (Online). 26(6):1165-1186. https://doi.org/10.3846/tede.2020.13189S11651186266Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. doi:10.1016/s0378-4266(02)00283-2Ahmed, A., Ali, R., Ejaz, A., & Ahmad, I. (2018). Sectoral integration and investment diversification opportunities: evidence from Colombo Stock Exchange. Entrepreneurship and Sustainability Issues, 5(3), 514-527. doi:10.9770/jesi.2018.5.3(8)Arenas Parra, M., Bilbao Terol, A., & Rodrı́guez Urı́a, M. V. (2001). A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research, 133(2), 287-297. doi:10.1016/s0377-2217(00)00298-8Arribas, I., Espinós-Vañó, M. D., García, F., & Tamošiūnienė, R. (2019). Negative screening and sustainable portfolio diversification. Entrepreneurship and Sustainability Issues, 6(4), 1566-1586. doi:10.9770/jesi.2019.6.4(2)Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3), 203-228. doi:10.1111/1467-9965.00068Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2(1), 95-121. doi:10.1016/0304-405x(75)90025-2Bermúdez, J. D., Segura, J. V., & Vercher, E. (2012). A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection. Fuzzy Sets and Systems, 188(1), 16-26. doi:10.1016/j.fss.2011.05.013Bezoui, M., Moulaï, M., Bounceur, A., & Euler, R. (2018). An iterative method for solving a bi-objective constrained portfolio optimization problem. Computational Optimization and Applications, 72(2), 479-498. doi:10.1007/s10589-018-0052-9Bi, T., Zhang, B., & Wu, H. (2013). Measuring Downside Risk Using High-Frequency Data: Realized Downside Risk Measure. Communications in Statistics - Simulation and Computation, 42(4), 741-754. doi:10.1080/03610918.2012.655826Carlsson, C., Fullér, R., & Majlender, P. (2002). A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems, 131(1), 13-21. doi:10.1016/s0165-0114(01)00251-2Chen, W., & Xu, W. (2018). A Hybrid Multiobjective Bat Algorithm for Fuzzy Portfolio Optimization with Real-World Constraints. International Journal of Fuzzy Systems, 21(1), 291-307. doi:10.1007/s40815-018-0533-0Choobineh, F., & Branting, D. (1986). A simple approximation for semivariance. European Journal of Operational Research, 27(3), 364-370. doi:10.1016/0377-2217(86)90332-2Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. doi:10.1109/4235.996017Fang, Y., Lai, K. K., & Wang, S.-Y. (2006). Portfolio rebalancing model with transaction costs based on fuzzy decision theory. European Journal of Operational Research, 175(2), 879-893. doi:10.1016/j.ejor.2005.05.020Favre, L., & Galeano, J.-A. (2002). Mean-Modified Value-at-Risk Optimization with Hedge Funds. The Journal of Alternative Investments, 5(2), 21-25. doi:10.3905/jai.2002.319052García, F., González-Bueno, J., Guijarro, F., & Oliver, J. (2020). Forecasting the Environmental, Social, and Governance Rating of Firms by Using Corporate Financial Performance Variables: A Rough Set Approach. Sustainability, 12(8), 3324. doi:10.3390/su12083324García, González-Bueno, Oliver, & Riley. (2019). Selecting Socially Responsible Portfolios: A Fuzzy Multicriteria Approach. Sustainability, 11(9), 2496. doi:10.3390/su11092496García, F., González-Bueno, J., Oliver, J., & Tamošiūnienė, R. (2019). A CREDIBILISTIC MEAN-SEMIVARIANCE-PER PORTFOLIO SELECTION MODEL FOR LATIN AMERICA. Journal of Business Economics and Management, 20(2), 225-243. doi:10.3846/jbem.2019.8317García, F., Guijarro, F., & Moya, I. (2013). A MULTIOBJECTIVE MODEL FOR PASSIVE PORTFOLIO MANAGEMENT: AN APPLICATION ON THE S&P 100 INDEX. Journal of Business Economics and Management, 14(4), 758-775. doi:10.3846/16111699.2012.668859García, F., Guijarro, F., & Oliver, J. (2017). Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics. Neural Computing and Applications, 30(8), 2625-2641. doi:10.1007/s00521-017-2882-2García, F., Guijarro, F., Oliver, J., & Tamošiūnienė, R. (2018). HYBRID FUZZY NEURAL NETWORK TO PREDICT PRICE DIRECTION IN THE GERMAN DAX-30 INDEX. Technological and Economic Development of Economy, 24(6), 2161-2178. doi:10.3846/tede.2018.6394Goel, A., Sharma, A., & Mehra, A. (2018). Index tracking and enhanced indexing using mixed conditional value-at-risk. Journal of Computational and Applied Mathematics, 335, 361-380. doi:10.1016/j.cam.2017.12.015González-Bueno, J. (2019). Optimización multiobjetivo para la selección de carteras a la luz de la teoría de la credibilidad. Una aplicación en el mercado integrado latinoamericano. Editorial Universidad Pontificia Bolivariana.Gupta, P., Inuiguchi, M., & Mehlawat, M. K. (2011). A hybrid approach for constructing suitable and optimal portfolios. Expert Systems with Applications, 38(5), 5620-5632. doi:10.1016/j.eswa.2010.10.073Gupta, P., Inuiguchi, M., Mehlawat, M. K., & Mittal, G. (2013). Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints. Information Sciences, 229, 1-17. doi:10.1016/j.ins.2012.12.011Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014). Portfolio Optimization Using Credibility Theory. Studies in Fuzziness and Soft Computing, 127-160. doi:10.1007/978-3-642-54652-5_5Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014). Portfolio Optimization with Interval Coefficients. Studies in Fuzziness and Soft Computing, 33-59. doi:10.1007/978-3-642-54652-5_2Gupta, P., Mehlawat, M. K., Kumar, A., Yadav, S., & Aggarwal, A. (2020). A Credibilistic Fuzzy DEA Approach for Portfolio Efficiency Evaluation and Rebalancing Toward Benchmark Portfolios Using Positive and Negative Returns. International Journal of Fuzzy Systems, 22(3), 824-843. doi:10.1007/s40815-020-00801-4Gupta, P., Mehlawat, M. K., & Saxena, A. (2010). A hybrid approach to asset allocation with simultaneous consideration of suitability and optimality. Information Sciences, 180(11), 2264-2285. doi:10.1016/j.ins.2010.02.007Gupta, P., Mehlawat, M. K., Yadav, S., & Kumar, A. (2020). Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models. Soft Computing, 24(16), 11931-11956. doi:10.1007/s00500-019-04639-3Gupta, P., Mittal, G., & Mehlawat, M. K. (2013). Expected value multiobjective portfolio rebalancing model with fuzzy parameters. Insurance: Mathematics and Economics, 52(2), 190-203. doi:10.1016/j.insmatheco.2012.12.002Heidari-Fathian, H., & Davari-Ardakani, H. (2019). Bi-objective optimization of a project selection and adjustment problem under risk controls. Journal of Modelling in Management, 15(1), 89-111. doi:10.1108/jm2-07-2018-0106Hilkevics, S., & Semakina, V. (2019). The classification and comparison of business ratios analysis methods. Insights into Regional Development, 1(1), 48-57. doi:10.9770/ird.2019.1.1(4)Huang, X. (2006). Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation, 177(2), 500-507. doi:10.1016/j.amc.2005.11.027Huang, X. (2008). Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics, 217(1), 1-8. doi:10.1016/j.cam.2007.06.009Huang, X. (2009). A review of credibilistic portfolio selection. Fuzzy Optimization and Decision Making, 8(3), 263-281. doi:10.1007/s10700-009-9064-3Huang, X. (2010). Portfolio Analysis. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-642-11214-0Huang, X. (2017). A review of uncertain portfolio selection. Journal of Intelligent & Fuzzy Systems, 32(6), 4453-4465. doi:10.3233/jifs-169211Huang, X., & Di, H. (2016). Uncertain portfolio selection with background risk. Applied Mathematics and Computation, 276, 284-296. doi:10.1016/j.amc.2015.12.018Huang, X., & Wang, X. (2019). International portfolio optimization based on uncertainty theory. Optimization, 70(2), 225-249. doi:10.1080/02331934.2019.1705821Huang, X., & Yang, T. (2020). How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk. Journal of Banking & Finance, 111, 105726. doi:10.1016/j.jbankfin.2019.105726Jalota, H., Thakur, M., & Mittal, G. (2017). Modelling and constructing membership function for uncertain portfolio parameters: A credibilistic framework. Expert Systems with Applications, 71, 40-56. doi:10.1016/j.eswa.2016.11.014Jalota, H., Thakur, M., & Mittal, G. (2017). A credibilistic decision support system for portfolio optimization. Applied Soft Computing, 59, 512-528. doi:10.1016/j.asoc.2017.05.054Kaplan, P. D., & Alldredge, R. H. (1997). Semivariance in Risk-Based Index Construction. The Journal of Investing, 6(2), 82-87. doi:10.3905/joi.1997.408419Konno, H., & Yamazaki, H. (1991). Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market. Management Science, 37(5), 519-531. doi:10.1287/mnsc.37.5.519Li, B., Zhu, Y., Sun, Y., Aw, G., & Teo, K. L. (2018). Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint. Applied Mathematical Modelling, 56, 539-550. doi:10.1016/j.apm.2017.12.016Li, H.-Q., & Yi, Z.-H. (2019). Portfolio selection with coherent Investor’s expectations under uncertainty. Expert Systems with Applications, 133, 49-58. doi:10.1016/j.eswa.2019.05.008Li, X., & Qin, Z. (2014). Interval portfolio selection models within the framework of uncertainty theory. Economic Modelling, 41, 338-344. doi:10.1016/j.econmod.2014.05.036Liagkouras, K., & Metaxiotis, K. (2015). Efficient Portfolio Construction with the Use of Multiobjective Evolutionary Algorithms: Best Practices and Performance Metrics. International Journal of Information Technology & Decision Making, 14(03), 535-564. doi:10.1142/s0219622015300013Liu, B. (2004). Uncertainty Theory. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-540-39987-2Baoding Liu, & Yian-Kui Liu. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445-450. doi:10.1109/tfuzz.2002.800692Liu, N., Chen, Y., & Liu, Y. (2018). Optimizing portfolio selection problems under credibilistic CVaR criterion. Journal of Intelligent & Fuzzy Systems, 34(1), 335-347. doi:10.3233/jifs-171298Liu, Y.-J., & Zhang, W.-G. (2018). Multiperiod Fuzzy Portfolio Selection Optimization Model Based on Possibility Theory. International Journal of Information Technology & Decision Making, 17(03), 941-968. doi:10.1142/s0219622018500190Mansour, N., Cherif, M. S., & Abdelfattah, W. (2019). Multi-objective imprecise programming for financial portfolio selection with fuzzy returns. Expert Systems with Applications, 138, 112810. doi:10.1016/j.eswa.2019.07.027Markowitz, H. (1952). PORTFOLIO SELECTION*. The Journal of Finance, 7(1), 77-91. doi:10.1111/j.1540-6261.1952.tb01525.xMarkowitz, H., Todd, P., Xu, G., & Yamane, Y. (1993). Computation of mean-semivariance efficient sets by the Critical Line Algorithm. Annals of Operations Research, 45(1), 307-317. doi:10.1007/bf02282055Martin, R. D., Rachev, S. (Zari), & Siboulet, F. (2003). Phi-alpha optimal portfolios and extreme risk management. Wilmott, 2003(6), 70-83. doi:10.1002/wilm.42820030619Mehlawat, M. K. (2016). Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels. Information Sciences, 345, 9-26. doi:10.1016/j.ins.2016.01.042Mehlawat, M. K., Gupta, P., Kumar, A., Yadav, S., & Aggarwal, A. (2020). Multiobjective Fuzzy Portfolio Performance Evaluation Using Data Envelopment Analysis Under Credibilistic Framework. IEEE Transactions on Fuzzy Systems, 28(11), 2726-2737. doi:10.1109/tfuzz.2020.2969406Mehralizade, R., Amini, M., Sadeghpour Gildeh, B., & Ahmadzade, H. (2020). Uncertain random portfolio selection based on risk curve. Soft Computing, 24(17), 13331-13345. doi:10.1007/s00500-020-04751-9Moeini, M. (2019). Solving the index tracking problem: a continuous optimization approach. Central European Journal of Operations Research. doi:10.1007/s10100-019-00633-0Narkunienė, J., & Ulbinaitė, A. (2018). Comparative analysis of company performance evaluation methods. Entrepreneurship and Sustainability Issues, 6(1), 125-138. doi:10.9770/jesi.2018.6.1(10)Palanikumar, K., Latha, B., Senthilkumar, V. S., & Karthikeyan, R. (2009). Multiple performance optimization in machining of GFRP composites by a PCD tool using non-dominated sorting genetic algorithm (NSGA-II). Metals and Materials International, 15(2), 249-258. doi:10.1007/s12540-009-0249-7Pflug, G. C. (2000). Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk. Probabilistic Constrained Optimization, 272-281. doi:10.1007/978-1-4757-3150-7_15Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. The Journal of Risk, 2(3), 21-41. doi:10.21314/jor.2000.038Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. doi:10.1016/s0378-4266(02)00271-6Rubio, A., Bermúdez, J. D., & Vercher, E. (2016). Forecasting portfolio returns using weighted fuzzy time series methods. International Journal of Approximate Reasoning, 75, 1-12. doi:10.1016/j.ijar.2016.03.007Saborido, R., Ruiz, A. B., Bermúdez, J. D., Vercher, E., & Luque, M. (2016). Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection. Applied Soft Computing, 39, 48-63. doi:10.1016/j.asoc.2015.11.005Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(S1), 119. doi:10.1086/294846Sharpe, W. F. (1994). The Sharpe Ratio. The Journal of Portfolio Management, 21(1), 49-58. doi:10.3905/jpm.1994.409501Sortino, F. A., & Price, L. N. (1994). Performance Measurement in a Downside Risk Framework. The Journal of Investing, 3(3), 59-64. doi:10.3905/joi.3.3.59Srinivas, N., & Deb, K. (1994). Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2(3), 221-248. doi:10.1162/evco.1994.2.3.221Vercher, E., & Bermúdez, J. D. (2012). Fuzzy Portfolio Selection Models: A Numerical Study. Financial Decision Making Using Computational Intelligence, 253-280. doi:10.1007/978-1-4614-3773-4_10Vercher, E., & Bermudez, J. D. (2013). A Possibilistic Mean-Downside Risk-Skewness Model for Efficient Portfolio Selection. IEEE Transactions on Fuzzy Systems, 21(3), 585-595. doi:10.1109/tfuzz.2012.2227487Vercher, E., & Bermúdez, J. D. (2015). Portfolio optimization using a credibility mean-absolute semi-deviation model. Expert Systems with Applications, 42(20), 7121-7131. doi:10.1016/j.eswa.2015.05.020Vercher, E., Bermúdez, J. D., & Segura, J. V. (2007). Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets and Systems, 158(7), 769-782. doi:10.1016/j.fss.2006.10.026Wang, S., & Zhu, S. (2002). Fuzzy Optimization and Decision Making, 1(4), 361-377. doi:10.1023/a:1020907229361Yue, W., & Wang, Y. (2017). A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios. Physica A: Statistical Mechanics and its Applications, 465, 124-140. doi:10.1016/j.physa.2016.08.009Yue, W., Wang, Y., & Xuan, H. (2018). Fuzzy multi-objective portfolio model based on semi-variance–semi-absolute deviation risk measures. Soft Computing, 23(17), 8159-8179. doi:10.1007/s00500-018-3452-yZadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. doi:10.1016/s0019-9958(65)90241-xZhai, J., & Bai, M. (2018). Mean-risk model for uncertain portfolio selection with background risk. Journal of Computational and Applied Mathematics, 330, 59-69. doi:10.1016/j.cam.2017.07.038Zhao, Z., Wang, H., Yang, X., & Xu, F. (2020). CVaR-cardinality enhanced indexation optimization with tunable short-selling constraints. Applied Economics Letters, 28(3), 201-207. doi:10.1080/13504851.2020.174015

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered.Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 17-July-2017; Revised 18-Sept-2017; Accepted for publication 20-Sept-2017. arXiv admin note: text overlap with arXiv:1504.0515