Metrics and orders in space of fuzzy numbers
Fuzzy Sets and Systems
On a canonical representation of fuzzy numbers
Fuzzy Sets and Systems
A new approach for defuzzification
Fuzzy Sets and Systems
Nearest interval approximation of a fuzzy number
Fuzzy Sets and Systems - Fuzzy intervals
A note on trapezoidal approximations of fuzzy numbers
Fuzzy Sets and Systems
Note on “Trapezoidal approximation of fuzzy numbers”
Fuzzy Sets and Systems
Trapezoidal approximations of fuzzy numbers---revisited
Fuzzy Sets and Systems
Weighted triangular approximation of fuzzy numbers
International Journal of Approximate Reasoning
On improving trapezoidal and triangular approximations of fuzzy numbers
International Journal of Approximate Reasoning
Trapezoidal and triangular approximations preserving the expected interval
Fuzzy Sets and Systems
On the nearest parametric approximation of a fuzzy number
Fuzzy Sets and Systems
Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval
Fuzzy Sets and Systems
Triangular and parametric approximations of fuzzy numbers---inadvertences and corrections
Fuzzy Sets and Systems
On the nearest parametric approximation of a fuzzy number---Revisited
Fuzzy Sets and Systems
Weighted trapezoidal and triangular approximations of fuzzy numbers
Fuzzy Sets and Systems
Reduction to least-squares estimates in multiple fuzzy regression analysis
IEEE Transactions on Fuzzy Systems
Approximation properties of piece-wise parabolic functions fuzzy logic systems
Fuzzy Sets and Systems
Trapezoidal approximations of fuzzy numbers
Fuzzy Sets and Systems
Weighted trapezoidal approximation-preserving cores of a fuzzy number
Computers & Mathematics with Applications
Trapezoidal approximation and aggregation
Fuzzy Sets and Systems
Expert Systems with Applications: An International Journal
Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity
International Journal of Approximate Reasoning
Lipschitz functions and fuzzy number approximations
Fuzzy Sets and Systems
Hi-index | 0.21 |
Recently, many scholars investigated interval, triangular, and trapezoidal approximations of fuzzy numbers. These publications can be grouped into two classes: Euclidean distance class and non-Euclidean distance class. Most approximations in Euclidean distance class can be calculated by formulas, but calculating approximations in the other class is more complicated. In the present paper, we study a special class of non-linear approximations with respect to a weighted Euclidean distance. We call it ''weighted semi-trapezoidal approximations''. The proposed approximations generalize all recent approximations in Euclidean distance class. First, we embed fuzzy numbers into a Hilbert space. Then compute weighted semi-trapezoidal approximations by means of best approximations in a closed convex subset of the Hilbert space. Finally, we propose formulas of matrix type, which is more clear than the previous contributions.