International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and sufficient for the vanishing of an individual tetrad difference in a recursive path model with uncorrelated errors. In this paper, we generalize their result from individual tetrad differences to sets of tetrad differences of a certain form, and we simplify their proof. The generalization allows tighter constraints to be placed on the set of models compatible with given data and thereby facilitates the search for parsimonious models for large data sets.

We give the general form of an idempotent, associative, nondecreasing and continuous binary aggregation operation in a connected order topological space. The particular case of the unit interval is studied and the choice of weights is also analized. Possible generalizations for more than two arguments are also proposed.

In this paper the equivalence between fuzzy systems and two nonparametric techniques for pattern recognition is considered. The conditions under which a fuzzy system coincides with the nearest neighbor rule, and with the Parzen’s classifier have been formulated.

The purpose of this paper is to apply fuzzy control theory in active structural control. A single-degree-of-freedom (SDOF) structure is used to develop the basic approach. The approach is then extended to multi-degree-of-freedom (MDOF) structures with the usage of weighted displacement and weighted velocity. A band-pass white noise or large amount of earthquake records are used as excitations to the structures to calculate the normalized displacements and velocities for obtaining the range of weighted displacements and velocities. Several examples are utilized to demonstrate the feasibility of fuzzy control methodology. It is shown that the fuzzy controller can achieve satisfactory results in the application of active control of structures and the feasibility is verified.

Possibility measures have been conceived by Zadeh [1], and developed by, e. g., Dubois, Prade and others, as very simple, if compared with, e.g., probability theory, but still nontrivial and reasonable uncertainty measures. The relatively poor descriptional and operational abilities of possibility measures seem to be closely related to the standard linear ordering relation and the corresponding supremum and infimum operations defined over the unit interval of real numbers. Having discussed, very briefly, the possibilities how to overcome these limitations, we propose and investigate possibility measures taking their values in the well-known Cantor subset of the unit interval but defined with respect to a nonstandard operation of supremum resulting from a nonstandard partial ordering of real numbers from the Cantor set. Such a nonstandard possibility measure is proved to be a sufficient tool to define an infinite sequence of probability measures defined over countable sets, consequently, the distribution of each continuous real-valued random variable defined over a general abstract probability space can be defined by an appropriate nonstandard possibility measure.