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- W2897314022 abstract "Abstract Recently, in several articles related to the distributivity laws of fuzzy implications over triangular norms and conorms, the following functional equation appeared f ( min ( x + y , a ) ) = min ( f ( x ) + f ( y ) , b ) , where a , b are finite or infinite nonnegative constants. In our earlier papers we have considered a generalized version of this equation, i.e., the equation f ( m 1 ( x + y ) ) = m 2 ( f ( x ) + f ( y ) ) . Firstly, we analyzed the situation when both functions m 1 , m 2 are defined on some finite intervals of R . We also investigated the situation when both functions m 1 , m 2 have finite or infinite domains and codomains, but they satisfy several additional assumptions. In this article we consider the above equation when m 1 , m 2 are defined on some finite or infinite intervals and satisfy only one additional assumption: m 2 is injective. Our proofs are based on the Jensen equation, therefore we also present the detailed analysis of this functional equation when the domain or codomain are extended to the infinity and/or are bounded." @default.
- W2897314022 created "2018-10-26" @default.
- W2897314022 creator A5003579916 @default.
- W2897314022 creator A5058049197 @default.
- W2897314022 date "2019-03-01" @default.
- W2897314022 modified "2023-09-24" @default.
- W2897314022 title "On some equation related to the distributivity laws of fuzzy implications. Jensen equation extended to the infinity" @default.
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- W2897314022 doi "https://doi.org/10.1016/j.fss.2018.10.005" @default.
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