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Recently, Yager in the article “On some new classes of implication operators and their role in approximate reasoning” [Yager2004] has introduced two new classes of fuzzy implications called the $f$-generated and $g$-generated implications. Along similar lines, one of us has proposed another class of fuzzy implications called the $h$-generated implications. In this article we discuss in detail some properties of the above mentioned classes of fuzzy implications and we describe their relationships amongst...

Distributivity of fuzzy implications over different fuzzy logic connectives have a very important role to play in efficient inferencing in approximate reasoning, especially in fuzzy control systems (see [9, 15] and [4]). Recently in some considerations connected with these distributivity laws, the following functional equation appeared (see [5]) $$f(min(x+y,a\left)\right)=min\left(f\right(x)+f(y),b),$$ where $a,b>0$ and $f:[0,a]\to [0,b]$ is an unknown function. In this paper we consider in detail a generalized version of this equation, namely the equation $$f\left(m_1(x+y)\right)=m_2(f\left(x\right)+f\left(y\right)),$$ where $m_1,m_2$ are functions...