Abstract
Compensatory Fuzzy Logic (CFL) are fuzzy logic systems, which satisfy axiomatic properties of bivalent logic and Decision Theory simultaneously. There is a coherence between CFL and other theories like classical logic, t-norm, and t-conorm based fuzzy logic, mathematical statistics, and decision theory. Those properties are the basis of transdisciplinary interpretability in relation to natural language. Hence, CFL has the advantage to model easily the problems by using natural and professional language. The main objective of this paper is to propose a method, inspired by rough sets theory (RST), to approximate decision classes by means of two clusters, defined by logic predicates formed on condition attributes. The importance of the method is mainly that it is a compliment, and not a substitute, of other methods for forecasting, in the sense that its results are more useful in the way of linguistic values than in numerical values.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965). https://doi.org/10.2307/2272014
Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982). https://doi.org/10.1007/BF01001956
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, Springer Science and Business Media (1991)
Zadeh, L.: The concept of a Linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8(3), 199–249 (1975). https://doi.org/10.1016/0020-0255(75)90036-5
Zadeh, L.: From computing with numbers to computing with words-from manipulation of measure to manipulation of perceptions. Int. J. Appl. Math. Comput. Sci. 3, 307–324 (2002). https://doi.org/10.1007/978-3-7908-1792-8_5
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. Int. J. Gen Syst. 17(2–3), 191–209 (1990). https://doi.org/10.1080/03081079008935107
Agarwal, M., Palpanas, T.: Linguistic rough set. Int. J. Mach. Learn. Cybern. 7, 953–966 (2014). https://doi.org/10.1007/s13042-014-0297-2
Ahmadi, F., Maghooli, K.: Missing data analysis: a survey on the effect of different K-means clustering algorithms. Am. J. Signal Process. 4(3), 65–70 (2014)
Chen, M., Ludwig, S.: Fuzzy decision tree using soft discretization and a genetic algorithm based feature selection method. 2013 World Congress on Nature and Biologically Inspired Computing, pp. 238–244. IEEE, Fargo (2013). https://doi.org/10.1109/NaBIC.2013.6617869
Liang, D., Liu, D., Pedrycz, W., Hu, P.: Triangular fuzzy decision-theoretic rough sets. Int. J. Approximate Reasoning 54(8), 1087–1106 (2013). https://doi.org/10.1016/j.ijar.2013.03.014
Moewes, C., Kruse, R.: Evolutionary fuzzy rules for ordinal binary classification with monotonicity constraints. In: Soft Computing: State of the Art Theory, vol. 291. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-34922-5_8
Slowinski, R., Greco, S., Matarazzo, B.: Rough sets in decision making. In: Meyers R. (eds.). In Computational Complexity. Springer, New York (2012). https://doi.org/10.1007/978-1-4614-1800-9_168
Espín, R., González, E., Fernández, E., Martínez, M.: Compensatory fuzzy logic inference. In: Soft Computing for Business Intelligence, pp. 25–43. Springer, Heidelberg (2014)
Martínez, M., Espín, R., López, V., Rosete, A.: Discovering knowledge by fuzzy predicates in compensatory fuzzy logic using metaheuristic algorithms. In: Soft Computing for Business Intelligence, pp. 161–174. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-53737-0_11
Espín, R., Fernández, E., González, E.: Compensatory fuzzy logic: a frame for reasoning and modeling preference knowledge in intelligent systems. In: Espín, R., Pérez, R., Cobo, A., Marx, J., Valdés, A. (eds.). Soft Computing for Business Intelligence, pp. 3–23. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-53737-0_1
Yao, Y.: Combination of rough and fuzzy sets based on α-level sets. In: Rough Sets and Data Mining: Analysis for Imprecise Data, pp. 301–321. Springer, Boston (1997). https://doi.org/10.1007/978-1-4613-1461-5_15
Rivera, G., Cisneros, L., Sánchez-Solís, P., Rangel-Valdez, N., Rodas-Osollo, J.: Genetic algorithm for scheduling optimization considering heterogeneous containers: a real-world case study. Axioms 9(1), 27 (2020). https://doi.org/10.3390/axioms9010027
Alvarado, O., Castro, B., González, L., Rivera, G., Rodas-Osollo, J., Sánchez-Solís, J.: Metaheuristic-based optimization of treated water distribution in a Mexican City. Aplicaciones Recientes en la Investigación de Operaciones. Pp. 19–30. Universidad Autónoma de Coahuila, Coahuila (2020)
Rivera, G., Rodas-Osollo, J., Bañuelos, P., Quiroz, M., Lopez, M.: A genetic algorithm for surgery scheduling optimization in a Mexican public hospital. Recent advances in artificial intelligence research and development. In: Aguiló, I., Alquézar, R., Angulo, C., Ortiz, A. (eds.) Frontiers in Artificial Intelligence and Applications, vol. 300, pp. 269–274. IOS Press, Amsterdam (2017). https://doi.org/10.3233/978-1-61499-806-8-269
Rosete, A., Ceruto, T., Espín, R. Marx, J.: A general method for knowledge discovery using compensatory fuzzy logic and metaheuristics. In: Espín, R., Marx, J., Racet, A. (eds.). Towards a Transdisciplinary Technology for Business Intelligence, pp. 240–268. Shaker (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Espin-Andrade, R.A., González, E., Bello, R., Pedrycz, W. (2021). Knowledge Discovery by Compensatory Fuzzy Rough Predicates. In: Pedrycz, W., Martínez, L., Espin-Andrade, R.A., Rivera, G., Marx Gómez, J. (eds) Computational Intelligence for Business Analytics. Studies in Computational Intelligence, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-030-73819-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-030-73819-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-73818-1
Online ISBN: 978-3-030-73819-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)