Some characteristics of matroids through rough sets

At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid, as a branch of mathematics, is a structure that generalizes linear independence in vector spaces. Further, matroid theory borrows extensively from the terminology of linear algebra and graph theory. We can combine rough set theory with matroid theory through using rough sets to study some characteristics of matroids. In this paper, we apply rough sets to matroids through defining a family of sets which are constructed from the upper approximation operator with respect to an equivalence relation. First, we prove the family of sets satisfies the support set axioms of matroids, and then we obtain a matroid. We say the matroids induced by the equivalence relation and a type of matroid, namely support matroid, is induced. Second, through rough sets, some characteristics of matroids such as independent sets, support sets, bases, hyperplanes and closed sets are investigated.Comment: 13 page

Solution Approaches for the Management of the Water Resources in Irrigation Water Systems with Fuzzy Costs

[EN] Currently, the management of water networks is key to increase their sustainability. This fact implies that water managers have to develop tools that ease the decision-making process in order to improve the efficiency of irrigation networks, as well as their exploitation costs. The present research proposes a mathematical programming model to optimize the selection of the water sources and the volume over time in water networks, minimizing the operation costs as a function of the water demand and the reservoir capacity. The model, which is based on fuzzy methods, improves the evaluation performed by water managers when they have to decide about the acquisition of the water resources under uncertain costs. Different fuzzy solution approaches have been applied and assessed in terms of model complexity and computational efficiency, showing the solution accomplished for each one. A comparison between different methods was applied in a real water network, reaching a 20% total cost reduction for the best solution.Sanchis, R.; Díaz-Madroñero Boluda, FM.; López Jiménez, PA.; Pérez-Sánchez, M. (2019). Solution Approaches for the Management of the Water Resources in Irrigation Water Systems with Fuzzy Costs. Water. 11(12):1-22. https://doi.org/10.3390/w11122432S1221112Biswas, A. K. (2004). Integrated Water Resources Management: A Reassessment. Water International, 29(2), 248-256. doi:10.1080/02508060408691775Pahl-Wostl, C. (2006). Transitions towards adaptive management of water facing climate and global change. Water Resources Management, 21(1), 49-62. doi:10.1007/s11269-006-9040-4Wu, K., & Zhang, L. (2014). Progress in the Development of Environmental Risk Assessment as a Tool for the Decision-Making Process. Journal of Service Science and Management, 07(02), 131-143. doi:10.4236/jssm.2014.72011Hernández-Bedolla, J., Solera, A., Paredes-Arquiola, J., Pedro-Monzonís, M., Andreu, J., & Sánchez-Quispe, S. (2017). The Assessment of Sustainability Indexes and Climate Change Impacts on Integrated Water Resource Management. Water, 9(3), 213. doi:10.3390/w9030213Hunink, J., Simons, G., Suárez-Almiñana, S., Solera, A., Andreu, J., Giuliani, M., … Bastiaanssen, W. (2019). A Simplified Water Accounting Procedure to Assess Climate Change Impact on Water Resources for Agriculture across Different European River Basins. Water, 11(10), 1976. doi:10.3390/w11101976Pérez-Sánchez, M., Sánchez-Romero, F., Ramos, H., & López-Jiménez, P. (2016). Modeling Irrigation Networks for the Quantification of Potential Energy Recovering: A Case Study. Water, 8(6), 234. doi:10.3390/w8060234Corominas, J. (2010). Agua y energía en el riego, en la época de la sostenibilidad. Ingeniería del agua, 17(3). doi:10.4995/ia.2010.2977Romero, L., Pérez-Sánchez, M., & Amparo López-Jiménez, P. (2017). Improvement of sustainability indicators when traditional water management changes: a case study in Alicante (Spain). AIMS Environmental Science, 4(3), 502-522. doi:10.3934/environsci.2017.3.502Davies, E. G. R., & Simonovic, S. P. (2011). Global water resources modeling with an integrated model of the social–economic–environmental system. Advances in Water Resources, 34(6), 684-700. doi:10.1016/j.advwatres.2011.02.010ALCAMO, J., DÖLL, P., HENRICHS, T., KASPAR, F., LEHNER, B., RÖSCH, T., & SIEBERT, S. (2003). Development and testing of the WaterGAP 2 global model of water use and availability. Hydrological Sciences Journal, 48(3), 317-337. doi:10.1623/hysj.48.3.317.45290Sanchis, R., & Poler, R. (2019). Enterprise Resilience Assessment—A Quantitative Approach. Sustainability, 11(16), 4327. doi:10.3390/su11164327Rahaman, M. M., & Varis, O. (2005). Integrated water resources management: evolution, prospects and future challenges. Sustainability: Science, Practice and Policy, 1(1), 15-21. doi:10.1080/15487733.2005.11907961Markantonis, V., Reynaud, A., Karabulut, A., El Hajj, R., Altinbilek, D., Awad, I. M., … Bidoglio, G. (2019). Can the Implementation of the Water-Energy-Food Nexus Support Economic Growth in the Mediterranean Region? The Current Status and the Way Forward. Frontiers in Environmental Science, 7. doi:10.3389/fenvs.2019.00084Food and Agriculture Organization (FAO)www.fao.orgDirective 2000/60/EC of the European Parliament and of the Councilhttps://eur-lex.europa.eu/eli/dir/2000/60/ojNamany, S., Al-Ansari, T., & Govindan, R. (2019). Sustainable energy, water and food nexus systems: A focused review of decision-making tools for efficient resource management and governance. Journal of Cleaner Production, 225, 610-626. doi:10.1016/j.jclepro.2019.03.304Archibald, T. W., & Marshall, S. E. (2018). Review of Mathematical Programming Applications in Water Resource Management Under Uncertainty. Environmental Modeling & Assessment, 23(6), 753-777. doi:10.1007/s10666-018-9628-0Chen, S., Shao, D., Gu, W., Xu, B., Li, H., & Fang, L. (2017). An interval multistage water allocation model for crop different growth stages under inputs uncertainty. Agricultural Water Management, 186, 86-97. doi:10.1016/j.agwat.2017.03.001Xie, Y. L., Xia, D. H., Huang, G. H., Li, W., & Xu, Y. (2015). A multistage stochastic robust optimization model with fuzzy probability distribution for water supply management under uncertainty. Stochastic Environmental Research and Risk Assessment, 31(1), 125-143. doi:10.1007/s00477-015-1164-8Heumesser, C., Fuss, S., Szolgayová, J., Strauss, F., & Schmid, E. (2012). Investment in Irrigation Systems under Precipitation Uncertainty. Water Resources Management, 26(11), 3113-3137. doi:10.1007/s11269-012-0053-xPereira-Cardenal, S. J., Mo, B., Riegels, N. D., Arnbjerg-Nielsen, K., & Bauer-Gottwein, P. (2015). Optimization of Multipurpose Reservoir Systems Using Power Market Models. Journal of Water Resources Planning and Management, 141(8), 04014100. doi:10.1061/(asce)wr.1943-5452.0000500Kumari, S., & Mujumdar, P. P. (2017). Fuzzy Set–Based System Performance Evaluation of an Irrigation Reservoir System. Journal of Irrigation and Drainage Engineering, 143(5), 04017002. doi:10.1061/(asce)ir.1943-4774.0001155Jairaj, P. G., & Vedula, S. (2000). Water Resources Management, 14(6), 457-472. doi:10.1023/a:1011117918943Li, M., Guo, P., Singh, V. P., & Zhao, J. (2016). Irrigation Water Allocation Using an Inexact Two-Stage Quadratic Programming with Fuzzy Input under Climate Change. JAWRA Journal of the American Water Resources Association, 52(3), 667-684. doi:10.1111/1752-1688.12415Bozorg-Haddad, O., Malmir, M., Mohammad-Azari, S., & Loáiciga, H. A. (2016). Estimation of farmers’ willingness to pay for water in the agricultural sector. Agricultural Water Management, 177, 284-290. doi:10.1016/j.agwat.2016.08.011Raju, K. S., & Duckstein, L. (2003). Multiobjective fuzzy linear programming for sustainable irrigation planning: an Indian case study. Soft Computing - A Fusion of Foundations, Methodologies and Applications, 7(6), 412-418. doi:10.1007/s00500-002-0230-6Regulwar, D. G., & Gurav, J. B. (2012). Sustainable Irrigation Planning with Imprecise Parameters under Fuzzy Environment. Water Resources Management, 26(13), 3871-3892. doi:10.1007/s11269-012-0109-yMula, 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:10.1080/00207540701413912Díaz-Madroñero, M., Mula, J., Jiménez, M., & Peidro, D. (2016). A rolling horizon approach for material requirement planning under fuzzy lead times. International Journal of Production Research, 55(8), 2197-2211. doi:10.1080/00207543.2016.1223382Mula, 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. (2007). Material Requirement Planning with fuzzy constraints and fuzzy coefficients. Fuzzy Sets and Systems, 158(7), 783-793. doi:10.1016/j.fss.2006.11.003Díaz-Madroñero, M., 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:10.1080/00207543.2014.920115Pérez-Sánchez, M., Díaz-Madroñero, M., Díaz-Madroñero, D.-M., … Josefa, J. (2017). Mathematical Programming Model for Procurement Selection in Water Irrigation Systems. A Case Study. Journal of Engineering Science and Technology Review, 10(6), 154-162. doi:10.25103/jestr.106.19Herrera, F., & Verdegay, J. L. (1995). Three models of fuzzy integer linear programming. European Journal of Operational Research, 83(3), 581-593. doi:10.1016/0377-2217(93)e0338-xHerrera, F., & Verdegay, J. L. (1996). Fuzzy boolean programming problems with fuzzy costs: A general study. Fuzzy Sets and Systems, 81(1), 57-76. doi:10.1016/0165-0114(94)00324-6Alavidoost, M. H., Babazadeh, H., & Sayyari, S. T. (2016). An interactive fuzzy programming approach for bi-objective straight and U-shaped assembly line balancing problem. Applied Soft Computing, 40, 221-235. doi:10.1016/j.asoc.2015.11.025Torabi, 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.2007.08.010Yager, R. R. (1981). A procedure for ordering fuzzy subsets of the unit interval. Information Sciences, 24(2), 143-161. doi:10.1016/0020-0255(81)90017-7Lai, Y.-J., & Hwang, C.-L. (1992). A new approach to some possibilistic linear programming problems. Fuzzy Sets and Systems, 49(2), 121-133. doi:10.1016/0165-0114(92)90318-xZimmermann, 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)90031-3Selim, 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/s00170-006-0842-6Bellman, R. E., & Zadeh, L. A. (1970). Decision-Making in a Fuzzy Environment. Management Science, 17(4), B-141-B-164. doi:10.1287/mnsc.17.4.b14

Hybrid fuzzy sliding mode control for motorised space tether spin-up when coupled with axial and torsional oscillation

A specialised hybrid controller is applied to the control of a motorised space tether spin-up space coupled with an axial and a torsional oscillation phenomenon. A seven-degree-of-freedom (7-DOF) dynamic model of a motorised momentum exchange tether is used as the basis for interplanetary payload exchange in the context of control. The tether comprises a symmetrical double payload configuration, with an outrigger counter inertia and massive central facility. It is shown that including axial and torsional elasticity permits an enhanced level of performance prediction accuracy and a useful departure from the usual rigid body representations, particularly for accurate payload positioning at strategic points. A simulation with given initial condition data has been devised in a connecting programme between control code written in MATLAB and dynamics simulation code constructed within MATHEMATICA. It is shown that there is an enhanced level of spin-up control for the 7-DOF motorised momentum exchange tether system using the specialised hybrid controller. hybrid controller

Time series forecasting using a TSK fuzzy system tuned with simulated annealing

In this paper, a combination of a Takagi-Sugeno fuzzy system (TSK) and simulated annealing is used to predict well known time series by searching for the best configuration of the fuzzy system. Simulated annealing is used to optimise the parameters of the antecedent and the consequent parts of the fuzzy system rules. The results of the proposed method are encouraging indicating that simulated annealing and fuzzy logic are able to combine well in time series prediction

Triangular norms which are join-morphisms in 3-dimensional fuzzy set theory

The n-dimensional fuzzy sets have been introduced as a generalization of interval-valued fuzzy sets, Atanassov's intuitionistic and interval-valued intuitionistic fuzzy sets. In this paper we investigate t-norms on 3-dimensional sets which are join-morphisms. Under some additional conditions we show that they can be represented using a representation which generalizes a similar representation for t-norms in interval-valued fuzzy set theory