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Aggregation Operator for Ordered Fuzzy Numbers Concerning the Direction

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Artificial Intelligence and Soft Computing (ICAISC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8467))

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Abstract

Ordered Fuzzy Numbers (OFN) were proposed about 10 years ago [7,8] as a tool for the calculations of imprecise values represented by fuzzy numbers. Calculation methods based on this model shall retain properties of operations known from real numbers. In addition, in contrast to the classic operations on convex fuzzy numbers, making a series of operations in accordance with the OFN model is not doomed to greater and greater imprecision of the results.

Apart from good computational properties, OFNs also offer new possibilities for imprecise information processing by using fuzzy systems. [13,14,18] show examples of systems and the various proposals for methods based on the new model. There is a range of work [20,21,23], which focus on implications or inference operators. In the works [10,23,24,29] various aspects of defuzzification were analyzed. Little attention has been paid to aggregation of premises of rules based on OFN so far. Therefore, the aim of this paper is to propose effective aggregation operator which will generate good results as well as being intuitively consistent with the idea of the new model. Moreover, the proposed solution maintains the expected properties of the aggregate functions [6,16], it takes into account key idea of OFN the direction of components.

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Authors and Affiliations

  1. Institute of Mechanics and Applied Computer Science, Kazimierz Wielki University, Bydgoszcz, Poland

    Piotr Prokopowicz

  2. Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

    Samira Malek Mohamadi Golsefid

Authors
  1. Piotr Prokopowicz
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  2. Samira Malek Mohamadi Golsefid
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Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Computer Science Division, Department of Electrical Engineering and Computer Sciences, University of California Berkeley, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Computational Intelligence Laboratory, Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

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Prokopowicz, P., Golsefid, S.M.M. (2014). Aggregation Operator for Ordered Fuzzy Numbers Concerning the Direction. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2014. Lecture Notes in Computer Science(), vol 8467. Springer, Cham. https://doi.org/10.1007/978-3-319-07173-2_24

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  • DOI: https://doi.org/10.1007/978-3-319-07173-2_24

  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-07173-2

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