Abstract
Fuzzy systems have been proven to be an effective tool for modeling and control in real applications. Fuzzy control is a well established area that is used in a large number of real systems. Fuzzy rule based systems are defined in terms of rules in which the concepts that define the rules (both in the antecedent and consequent) can be defined in terms of fuzzy sets. In applications, rules are fired and then a set of consequents need to be combined to make a final decision. This final decision is often computed by means of a defuzzification method. In this paper we discuss the defuzzification proces and propose the use of a Choquet integral for this process. In contrast with standard defuzzification methods which are based on mean operators (usually discrete), the Choquet integral permits us to have an output variable with values that have different importances and with interactions among the values themselves. To illustrate the approach, we use a numerical Choquet integral software for continuous functions that we have recently developed. We also position the application of the approach to handle the uncertainty associated to a mission-oriented Cyber-Physical System (CPS).
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The term CPS, coined in 2006 by H. Gill at the National Science Foundation [13], refers to next generation embedded ICT systems, which include monitoring and control technologies in charge of physical components for pervasive applications.
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Acknowledgments
Support from the European Commission, under grant agreement 830892 (H2020 SPARTA project), and the Cyber CNI Chair of the Institut Mines-Télécom, supported by the Center of excellence in Cybersecurity, Airbus Defence and Space, Amossys, EDF, Nokia, BNP Paribas and the Regional Council of Brittany.
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Torra, V., Garcia-Alfaro, J. (2019). Towards an Adaptive Defuzzification: Using Numerical Choquet Integral. In: Torra, V., Narukawa, Y., Pasi, G., Viviani, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2019. Lecture Notes in Computer Science(), vol 11676. Springer, Cham. https://doi.org/10.1007/978-3-030-26773-5_11
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