Monitoring multidimensional phenomena with a multicriteria composite performance interval approach

[EN] In the last two decades, the construction of composite indicators to measure and compare multidimensional phenomena in a broad spectrum of domains has increased considerably. Different methodological approaches are used to summarise huge datasets of information in a single figure. This paper proposes a new approach that consists in computing a multicriteria composite performance interval based on different aggregation rules. The suggested approach provides an additional layer of information as the performance interval displays a lower bound from a non-compensability perspective, and an upper bound allowing for full-compensability. The outstanding features of this proposal are: 1) a distance-based multicriteria technique is taken as the baseline to construct the multicriteria performance interval; 2) the aggregation of distances/separation measures is made using particular cases of Minkowski Lp metric; 3) the span of the multicriteria performance interval can be considered as a sign of the dimensions or indicators balance.Garcia-Bernabeu, A.; Hilario Caballero, A.; Pla Santamaría, D.; Salas-Molina, F. (2021). Monitoring multidimensional phenomena with a multicriteria composite performance interval approach. International Journal of Multicriteria Decision Making (Online). 8(4):368-385. https://doi.org/10.1504/IJMCDM.2021.120760S3683858

A Process Oriented MCDM Approach to Construct a Circular Economy Composite Index

[EN] The purpose of this contribution is to develop a Circular Economy Composite indicator to benchmark EU countries performance. Europe is at the forefront of the global transition towards a sustainable and circular economy. To this end, the European Commission has launched in 2015 a Circular Economy Action Plan including a monitoring framework to measure progress and to assess the effectiveness of initiatives towards the circular economy in the European Union (EU) and Member States. Still, this monitoring framework lacks a composite indicator at the national level to aggregate the circular economy dimensions into a single summary indicator. Although there is a wide range of sustainability composite indicators, no aggregate circular economy index exits to this date. We use a multi-criteria approach to construct a circular economy composite index based on TOPSIS (Technique for Order Preferences by Similarity to Ideal Solutions) methodology. In addition, we introduce a novel aggregation methodology for building a composite indicator where different levels of compensability for the distances to the ideal and anti-ideal (or negative-ideal) values of each indicator are considered. In order to illustrate the advantages of this proposal, we have applied it to evaluate the Circular Economy performance of EU Member States for the year 2016. This proposal can be a valuable tool for identifying areas in which the countries need to concentrate their efforts to boost their circular economy performance.Garcia-Bernabeu, A.; Hilario Caballero, A.; Pla Santamaría, D.; Salas-Molina, F. (2020). A Process Oriented MCDM Approach to Construct a Circular Economy Composite Index. Sustainability. 12(2):1-14. https://doi.org/10.3390/su12020618S114122Genovese, A., Acquaye, A. A., Figueroa, A., & Koh, S. C. L. (2017). Sustainable supply chain management and the transition towards a circular economy: Evidence and some applications. Omega, 66, 344-357. doi:10.1016/j.omega.2015.05.015Di Maio, F., & Rem, P. C. (2015). A Robust Indicator for Promoting Circular Economy through Recycling. Journal of Environmental Protection, 06(10), 1095-1104. doi:10.4236/jep.2015.610096Geng, Y., Sarkis, J., Ulgiati, S., & Zhang, P. (2013). Measuring China’s Circular Economy. Science, 339(6127), 1526-1527. doi:10.1126/science.1227059Geng, Y., Fu, J., Sarkis, J., & Xue, B. (2012). Towards a national circular economy indicator system in China: an evaluation and critical analysis. Journal of Cleaner Production, 23(1), 216-224. doi:10.1016/j.jclepro.2011.07.005Elia, V., Gnoni, M. G., & Tornese, F. (2017). Measuring circular economy strategies through index methods: A critical analysis. Journal of Cleaner Production, 142, 2741-2751. doi:10.1016/j.jclepro.2016.10.196Huijbregts, M. A. J., Rombouts, L. J. A., Hellweg, S., Frischknecht, R., Hendriks, A. J., van de Meent, D., … Struijs, J. (2006). 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F., Bonilla, S. H., Silva, C. C., & Almeida, C. M. V. B. (2009). The reliability of experts’ opinions in constructing a composite environmental index: The case of ESI 2005. Journal of Environmental Management, 90(8), 2448-2459. doi:10.1016/j.jenvman.2008.12.018Makkonen, T., & van der Have, R. P. (2012). Benchmarking regional innovative performance: composite measures and direct innovation counts. Scientometrics, 94(1), 247-262. doi:10.1007/s11192-012-0753-2Mazziotta, M., & Pareto, A. (2015). On a Generalized Non-compensatory Composite Index for Measuring Socio-economic Phenomena. Social Indicators Research, 127(3), 983-1003. doi:10.1007/s11205-015-0998-2Greco, M., Mazziotta, M., & Pareto, A. (2016). A Composite Index to Measure the Italian «Enological Vocation». Agriculture and Agricultural Science Procedia, 8, 691-697. doi:10.1016/j.aaspro.2016.02.045Greco, S., Ishizaka, A., Tasiou, M., & Torrisi, G. (2018). On the Methodological Framework of Composite Indices: A Review of the Issues of Weighting, Aggregation, and Robustness. Social Indicators Research, 141(1), 61-94. doi:10.1007/s11205-017-1832-9Attardi, R., Cerreta, M., Sannicandro, V., & Torre, C. M. (2018). Non-compensatory composite indicators for the evaluation of urban planning policy: The Land-Use Policy Efficiency Index (LUPEI). European Journal of Operational Research, 264(2), 491-507. doi:10.1016/j.ejor.2017.07.064Angilella, S., Catalfo, P., Corrente, S., Giarlotta, A., Greco, S., & Rizzo, M. (2018). Robust sustainable development assessment with composite indices aggregating interacting dimensions: The hierarchical-SMAA-Choquet integral approach. Knowledge-Based Systems, 158, 136-153. doi:10.1016/j.knosys.2018.05.041Greco, S., Ishizaka, A., Tasiou, M., & Torrisi, G. (2019). Sigma-Mu efficiency analysis: A methodology for evaluating units through composite indicators. 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Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach

[EN] Sustainable finance, which integrates environmental, social and governance criteria on financial decisions rests on the fact that money should be used for good purposes. Thus, the financial sector is also expected to play a more important role to decarbonise the global economy. To align financial flows with a pathway towards a low-carbon economy, investors should be able to integrate into their financial decisions additional criteria beyond return and risk to manage climate risk. We propose a tri-criterion portfolio selection model to extend the classical Markowitz's mean-variance approach to include investor's preferences on the portfolio carbon risk exposure as an additional criterion. To approximate the 3D Pareto front we apply an efficient multi-objective genetic algorithm called ev-MOGA which is based on the concept of epsilon-dominance. Furthermore, we introduce a-posteriori approach to incorporate the investor's preferences into the solution process regarding their climate-change related preferences measured by the carbon risk exposure and their loss-adverse attitude. We test the performance of the proposed algorithm in a cross-section of European socially responsible investments open-end funds to assess the extent to which climate-related risk could be embedded in the portfolio according to the investor's preferences.Hilario Caballero, A.; Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Vercher, M. (2020). Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach. International Journal of Environmental research and Public Health. 17(17):1-15. https://doi.org/10.3390/ijerph17176324S1151717Morningstar Low Carbon Designationhttps://bit.ly/2SfAFUAKrueger, P., Sautner, Z., & Starks, L. T. (2020). 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Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market. Management Science, 37(5), 519-531. doi:10.1287/mnsc.37.5.519Rockafellar, 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)00271-6Mansini, R. (2003). LP solvable models for portfolio optimization: a classification and computational comparison. IMA Journal of Management Mathematics, 14(3), 187-220. doi:10.1093/imaman/14.3.187Hirschberger, M., Steuer, R. E., Utz, S., Wimmer, M., & Qi, Y. (2013). Computing the Nondominated Surface in Tri-Criterion Portfolio Selection. Operations Research, 61(1), 169-183. doi:10.1287/opre.1120.1140Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491-498. doi:10.1016/j.ejor.2013.07.024Utz, S., Wimmer, M., & Steuer, R. E. (2015). Tri-criterion modeling for constructing more-sustainable mutual funds. European Journal of Operational Research, 246(1), 331-338. doi:10.1016/j.ejor.2015.04.035Chang, T.-J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302. doi:10.1016/s0305-0548(99)00074-xMaringer, D., & Kellerer, H. (2003). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectrum, 25(4), 481-495. doi:10.1007/s00291-003-0139-1Shaw, D. X., Liu, S., & Kopman, L. (2008). Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimization Methods and Software, 23(3), 411-420. doi:10.1080/10556780701722542Soleimani, H., Golmakani, H. R., & Salimi, M. H. (2009). Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36(3), 5058-5063. doi:10.1016/j.eswa.2008.06.007Anagnostopoulos, K. P., & Mamanis, G. (2011). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications. doi:10.1016/j.eswa.2011.04.233Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550. doi:10.1016/j.ejor.2011.03.030Meghwani, S. S., & Thakur, M. (2017). Multi-criteria algorithms for portfolio optimization under practical constraints. Swarm and Evolutionary Computation, 37, 104-125. doi:10.1016/j.swevo.2017.06.005Liagkouras, K., & Metaxiotis, K. (2016). A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Annals of Operations Research, 267(1-2), 281-319. doi:10.1007/s10479-016-2377-zMetaxiotis, K., & Liagkouras, K. (2012). Multiobjective Evolutionary Algorithms for Portfolio Management: A comprehensive literature review. Expert Systems with Applications, 39(14), 11685-11698. doi:10.1016/j.eswa.2012.04.053Silva, Y. L. T. V., Herthel, A. B., & Subramanian, A. (2019). A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems. Expert Systems with Applications, 133, 225-241. doi:10.1016/j.eswa.2019.05.018Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537. doi:10.1016/j.eswa.2009.02.062Liagkouras, K. (2019). A new three-dimensional encoding multiobjective evolutionary algorithm with application to the portfolio optimization problem. Knowledge-Based Systems, 163, 186-203. doi:10.1016/j.knosys.2018.08.025Kaucic, M., Moradi, M., & Mirzazadeh, M. (2019). Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures. Financial Innovation, 5(1). doi:10.1186/s40854-019-0140-6Babaei, S., Sepehri, M. M., & Babaei, E. (2015). Multi-objective portfolio optimization considering the dependence structure of asset returns. European Journal of Operational Research, 244(2), 525-539. doi:10.1016/j.ejor.2015.01.025Ruiz, A. B., Saborido, R., Bermúdez, J. D., Luque, M., & Vercher, E. (2019). Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences. Journal of Global Optimization, 76(2), 295-315. doi:10.1007/s10898-019-00782-1Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), 1285-1297. doi:10.1016/j.cor.2009.09.009Hu, Y., Chen, H., He, M., Sun, L., Liu, R., & Shen, H. (2019). Multi-Swarm Multi-Objective Optimizer Based on p-Optimality Criteria for Multi-Objective Portfolio Management. Mathematical Problems in Engineering, 2019, 1-22. doi:10.1155/2019/8418369Rangel-González, J. A., Fraire, H., Solís, J. F., Cruz-Reyes, L., Gomez-Santillan, C., Rangel-Valdez, N., & Carpio-Valadez, J. M. (2020). Fuzzy Multi-objective Particle Swarm Optimization Solving the Three-Objective Portfolio Optimization Problem. International Journal of Fuzzy Systems, 22(8), 2760-2768. doi:10.1007/s40815-020-00928-4Garcia-Bernabeu, A., Salcedo, J. V., Hilario, A., Pla-Santamaria, D., & Herrero, J. M. (2019). Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA. 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Measuring urban sustainability performance through composite indicators for Spanish cities

[EN] The role that cities play in the transition to more sustainable growth is gaining increasing recognition. Measuring progress towards sustainable urban development requires quantifying this multi-dimensional phenomenon with the help of composite indicators. The purpose of this study is to propose an integrated approach to build a sustainable cities' interval of composite indicators that rely on the Sustainable Development Goals (SDGs) framework. In addition, we propose to overcome the problem of calculating a single number by constructing a strong-weak sustainability performance interval depending on the choice of the compensability level in the aggregation stage of individual indicators. One of the advantages of this interval is that it provides information on both the average performance and the worst value of the set of indicators considered for each SDG. Moreover, it also extends the analysis for the people, planet, prosperity, peace, and partnership dimensions defined by the 2030 Agenda. As an example of application, we constructed these intervals for 50 Spanish cities, which are provincial capitals. This application lets us get a more accurate vision that can serve as a valuable tool for better urban planning design.Funding for open access charge: CRUE-Universitat Politècnica de València.Lo-Iacono-Ferreira, VG.; Garcia-Bernabeu, A.; Hilario Caballero, A.; Torregrosa López, JI. (2022). Measuring urban sustainability performance through composite indicators for Spanish cities. Journal of Cleaner Production. 359:1-11. https://doi.org/10.1016/j.jclepro.2022.13198211135

BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation

[EN] This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi¿Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.The authors wish to thank the Editor-in-Chief and the anonymous reviewers for their valuable comments and suggestions. This work has been funded by Ministerio de Economia y Competitividad (Spain) through the research project DPI2015-71443-R and by Generalitat Valenciana (Valencia, Spain) through the research project GV/2017/029.Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2018). BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation. International Journal of Applied Mathematics and Computer Science (Online). 28(3):457-472. https://doi.org/10.2478/amcs-2018-0035S45747228

T-S Fuzzy Bibo Stabilisation of Non-Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non-PDC Control Laws

[EN] This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi-Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum *-norm (upper bound of the 1-norm) for the T-S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.This work has been funded by Ministerio de Economia y Competitividad, Spain (research project RTI2018-096904-B-I00) and Conselleria de Educacion, Cultura y Deporte-Generalitat Valenciana, Spain (research project AICO/2019/055).Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2020). T-S Fuzzy Bibo Stabilisation of Non-Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non-PDC Control Laws. International Journal of Applied Mathematics and Computer Science (Online). 30(3):529-550. https://doi.org/10.34768/amcs-2020-0039S52955030

Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA

[EN] Despite the widespread use of the classical bicriteria Markowitz mean-variance framework, a broad consensus is emerging on the need to include more criteria for complex portfolio selection problems. Sustainable investing, also called socially responsible investment, is becoming a mainstream investment practice. In recent years, some scholars have attempted to include sustainability as a third criterion to better reflect the individual preferences of those ethical or green investors who are willing to combine strong financial performance with social benefits. For this purpose, new computational methods for optimizing this complex multiobjective problem are needed. Multiobjective evolutionary algorithms (MOEAs) have been recently used for portfolio selection, thus extending the mean-variance methodology to obtain a mean-variance-sustainability nondominated surface. In this paper, we apply a recent multiobjective genetic algorithm based on the concept of epsilon-dominance called ev-MOGA. This algorithm tries to ensure convergence towards the Pareto set in a smart distributed manner with limited memory resources. It also adjusts the limits of the Pareto front dynamically and prevents solutions belonging to the ends of the front from being lost. Moreover, the individual preferences of socially responsible investors could be visualised using a novel tool, known as level diagrams, which helps investors better understand the range of values attainable and the tradeoff between return, risk, and sustainability.This work was funded by "Ministerio de Economia y Competitividad" (Spain), research project RTI2018-096904B-I00, and "Conselleria de Educacion, Cultura y DeporteGeneralitat Valenciana" (Spain), research project AICO/2019/055Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Hilario Caballero, A.; Pla Santamaría, D.; Herrero Durá, JM. (2019). Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA. Complexity. 2019:1-12. https://doi.org/10.1155/2019/6095712S1122019Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77. doi:10.2307/2975974Hirschberger, M., Steuer, R. E., Utz, S., Wimmer, M., & Qi, Y. (2013). Computing the Nondominated Surface in Tri-Criterion Portfolio Selection. Operations Research, 61(1), 169-183. doi:10.1287/opre.1120.1140Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491-498. doi:10.1016/j.ejor.2013.07.024Utz, S., Wimmer, M., & Steuer, R. E. (2015). Tri-criterion modeling for constructing more-sustainable mutual funds. European Journal of Operational Research, 246(1), 331-338. doi:10.1016/j.ejor.2015.04.035Qi, Y., Steuer, R. E., & Wimmer, M. (2015). 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