In many practical applications, it is useful to represent a function f(x) by its fuzzy transform, i.e., by the “average” values Fi = f(x) · Ai(x) dx Ai(x) dx over different ...
The improper fuzzy Riemann integral and its numerical integration are proposed in this paper. Under the setting of the improper fuzzy Riemann integral, we can ®nd the expectation...
In many practical applications, it turns out to be useful to use the notion of fuzzy transform: once we have functions A1(x) ≥ 0, . . . , An ≥ 0, with n∑ i=1 Ai(x) = 1, we c...
The combination of fuzzy set and rough set theories lead to various models. Functional and set approaches are two categories based on different fuzzy representations. In this pape...