The method for obtaining the fuzzy estimates of regression parameters with the help of “Resolution Identity” in fuzzy sets theory is proposed. The -level least-squares estimates can be obtained from the usual linear regression model by using the -level real-valued data of the corresponding fuzzy input and output data. The membership functions of fuzzy estimates of regression parameters will be ...

Nonparametric estimation capabilities of fuzzy systems in stochastic environments are analyzed in this paper. By using ideas from sieve estimation, increasing sequences of fuzzy rule-based systems, capable of consistently estimating regression surfaces in different settings, are constructed. Results include least squares learning of a mapping perturbed by additive random noise in a static-regre...

The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. A multivalent fuzzy measure with infinitely many solutions based on Pmeasure was proposed by our previous work, called completed L-measure. In this paper, a further improved fuzzy measure, called extensional completed L-measure, is proposed. This new fuzzy measure is proved that it is not only an extension...

We propose a new specification test for assessing the validity of fuzzy regression discontinuity designs (FRD‐validity). derive set testable implications, characterized by inequality restrictions on joint distribution observed outcomes and treatment status at cut‐off. show that this characterization exploits all information in data is useful detecting violations FRD‐validity. Our approach diffe...