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Pliant Operator System

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Recent Advances in Intelligent Engineering Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 378))

Abstract

We give a new representation theorem of negation based on the generator function of the strict operator. We study a certain class of strict monotone operators which build the DeMorgan class with infinitely many negations. We show that the necessary and sufficient condition for this operator class is f c (x) f d (x) = 1, where f c (x) and f d (x) are the generator functions of the strict t-norm and strict t-conorm. On the other hand our starting point is study of the relationship for Dombi aggregative operators, uninorms, strict t-norms and t-conorms. We present new representation theorem of strong negations where two explicitly contain the neutral value. Then relationships for aggregative operators and strong negations are verified as well as those for t-norm and t-conorm using the Pan operator concept. We will study a certain class of aggregative operators which build a self-DeMorgan class with infinitely many negation operators. We introduce the multiplicative pliant concept and characterize it by necessary and sufficient conditions.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Szeged, 6720, Szeged, Árpád tér 2., Hungary

    József Dombi

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  1. József Dombi
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Editors and Affiliations

  1. Institute of Intelligent Engineering Systems, Óbuda University, Bécsi út 96/b, H-1034, Budapest, Hungary

    János Fodor

  2. Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, 27 Wybrzeze Wyspianskiego st., 50-372, Wrocław, Poland

    Ryszard Klempous

  3. Departamento de Informática y Sistemas, Universidad de Las Palmas de Gran Canaria, Instituto Universitario de Ciencias y Tecnologías Cibernéticas, Campus Universitario de Tafira s/n, 35017, Las Palmas de Gran, Canaria, Spain

    Carmen Paz Suárez Araujo

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Dombi, J. (2012). Pliant Operator System. In: Fodor, J., Klempous, R., Suárez Araujo, C.P. (eds) Recent Advances in Intelligent Engineering Systems. Studies in Computational Intelligence, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23229-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-23229-9_2

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