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- W2008029862 abstract "Recently in some considerations connected with 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)m b). In the current paper we consider a generalized version of this equation, namely the equation f(m <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> (x + y)) = m <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> (f(x) + f(y)), where m <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> , m <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> are functions defined on some intervals of ℝ satisfying additional assumptions. We analyze the cases when m <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> is injective and when m <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sub> is not injective." @default.
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- W2008029862 date "2013-07-01" @default.
- W2008029862 modified "2023-10-16" @default.
- W2008029862 title "On a functional equation related to distributivity of fuzzy implications" @default.
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- W2008029862 doi "https://doi.org/10.1109/fuzz-ieee.2013.6622427" @default.
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