Stabilization of bilinear systems by a linear feedback control
Relations of granular worlds
In this study, we are concerned with a two-objective development of information granules completed on a basis of numeric data. The first goal of this design concerns revealing and representing a structure in a data set. As such it is very much oriented towards coping with the underlying it relational aspects of the experimental data. The second goal deals with a formation of a mapping between information granules constructed in two spaces (thus it concentrates on the it directional aspect of information...
On continuity of the entropy-based differently implicational algorithm
Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity. To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous t-norms are employed. Furthermore, four numerical...
Measures of fuzziness and operations with fuzzy sets.
We discuss the effects that the usual set theoretic and arithmetic operations with fuzzy sets and fuzzy numbers have with respect to the energies and entropies of the fuzzy sets connected and of the resulting fuzzy sets, and we also compare the entropies and energies of the results of several of those operations.
Fuzzy relation equations under LSC and USC t-norms and their Boolean solutions.
This paper follows a companion paper (Stochastica 8 (1984), 99-145) in which we gave the state of the art of the theory of fuzzy relation equations under a special class of triangular norms. Here we continue this theory establishing new results under lower and upper semicontinuous triangular norms and surveying on the main theoretical results appeared in foregoing papers. Max-t fuzzy equations with Boolean solutions are recalled and studied. Many examples clarify the results established.
Fuzzy relation equation under a class of triangular norms: A survey and new results.
By substituting the classical lattice operator min of the unit real interval with a triangular norm of Schweizer and Sklar, the usual fuzzy relational equations theory of Sanchez can be generalized to wider theory of fuzzy equations. Considering a remarkable class of triangular norms, for such type of equations defined on finite sets, we characterize the upper an lower solutions. We also characterize the solutions posessing a minimal fuzziness measure of Yager valued with respect to...
Symmetric implicational restriction method of fuzzy inference
The symmetric implicational method is revealed from a different perspective based upon the restriction theory, which results in a novel fuzzy inference scheme called the symmetric implicational restriction method. Initially, the SIR-principles are put forward, which constitute optimized versions of the triple I restriction inference mechanism. Next, the existential requirements of basic solutions are given. The supremum (or infimum) of its basic solutions is achieved from some properties of fuzzy...
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