Abstract
In this paper we discuss special and inversely special properties for different families of fuzzy implications. We show that a characterization of general binary operations whose residuals become special presented in [B. Jayaram, R. Mesiar, On special fuzzy implications, Fuzzy Sets and Systems 160 (2009) 2063–2085] is incorrect and we present a correct characterization with some additional assumptions. Moreover, we discuss these both properties for R-implications generated from left-continuous t-norms and representable aggregation functions, implications based on copulas, f- and g-implications.
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References
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Acknowledgment
This work was partially supported by the National Science Centre, Poland, through Project Number 2015/19/B/ST6/03259.
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Miś, K., Baczyński, M. (2018). Special and Inversely Special Properties of Fuzzy Implications. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 642. Springer, Cham. https://doi.org/10.1007/978-3-319-66824-6_47
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DOI: https://doi.org/10.1007/978-3-319-66824-6_47
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