Data mining nowadays belongs to the most prominent Information
technologies, experiencing a boom of interest from users and software producers. Traditionally, extracting knowledge from data has been a domain of statisticians, and the largest variety of rnethods encountered in commercial data mining systems are actually methods for statistical data analysis tasks. One of the most important ones among them is testing hypotheses about the probability distribution underlying the data. Basically, it consists in checking the null hypothesis that the probability distribution, a priori cissumed to belong to a broad set of distributions, actually belongs to one of its narrow subsets, which must be precisely delimited in advance. However, in a situation in which the data mining is performed, there are seldom enough clues for such a precise delimitation. That is why the generalizations of statistical hypotheses testing to vague hypotheses háve been investigated for more than a decade, so far following the most straightforward way - to replace the set defining the null hypothesis by a fuzzy set. In this páper, a principally different generalization is proposed, based on the observational-logic approach to data mining, and in particular to hypotheses testing. Its key idea is to view statistical testing of a fuzzy hypothesis cis an application of an appropriate generalized quantifier of a fuzzy predicate calculus to predicates describing the data. The theoretical principles of the approach are elaborated for both crisp and fuzzy significance levels, and illustrated on the quantifier lower critical implication, well known from the data mining system Guha. Finally, the implementation of the approach is briefly sketched.
Over the years, one of the challenges of a rule based expert system is the possibility of evolving a compact and consistent knowledge-base with a fewer numbers of rules that are relevant to the application domain, in order to enhance the comprehensibility of the expert system. In this paper, the hybrid of fuzzy rule mining interestingness measures and fuzzy expert system is exploited as a means of solving the problem of unwieldiness and maintenance complication in the rule based expert system. This negatively increases the knowledge-base space complexity and reduces rule access rate which impedes system response time. To validate this concept, the Coronary Heart Disease risk ratio determination is used as the case study. Results of fuzzy expert system with a fewer numbers of rules and fuzzy expert system with a large numbers of rules are presented for comparison. Moreover, the effect of fuzzy linguistic variable risk ratio is investigated. This makes the expert system recommendation close to human perception.
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set S and inequality relations on Xs = S × R. Moreover, we also investigate a relationship between the functions of S and Xs.
A class of functional equations with nonlinear iterates is discussed on the unit circle ${\mathbb{T}}^1$. By lifting maps on ${\mathbb{T}}^1$ and maps on the torus ${\mathbb{T}}^n$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions.
A general synchronization method is proposed for a class of nonlinear chaotic systems involving uncertain parameters and nonlinear transmitted signals. Under some mild conditions, it shows that the class of nonlinear chaotic systems can be treated as linear time-varying systems driven by the additive white noise contaminated at the receiver, or the observed output. Synchronization can be achieved by using Kalman filtering technology. We present some sufficient conditions under which the states of the driven system are able to track the states of the drive system asymptotically, and good tracking performance can be obtained in the presence of the additive white noise involved in the observed output.
We generalize a Theorem of Koldunov [2] and prove that a disjointness proserving quasi-linear operator between Resz spaces has the Hammerstein property.
In this paper, a family of hybrid control algorithms is presented; where it is merged a free camera-calibration image-based control scheme and a direct force controller, both with the same priority level. The aim of this generalised hybrid controller is to regulate the robot-environment interaction into a two-dimensional task-space. The design of the proposed control structure takes into account most of the dynamic effects present in robot manipulators whose inputs are torque signals. As examples of this generalised structure of hybrid force/vision controllers, a linear proportional-derivative structure and a nonlinear proportional-derivative one (based on the hyperbolic tangent function) are presented. The corresponding stability analysis, using Lyapunov's direct method and invariance theory, is performed to proof the asymptotic stability of the equilibrium vector of the closed-loop system. Experimental tests of the control scheme are presented and a suitable performance is observed in all the cases. Unlike most of the previously presented hybrid schemes, the control structure proposed herein achieves soft contact forces without overshoots, fast convergence of force and position error signals, robustness of the controller in the face of some uncertainties (such as camera rotation), and safe operation of the robot actuators when saturating functions (non-linear case) are used in the mathematical structure. This is one of the first works to propose a generalized structure of hybrid force/vision control that includes a closed loop stability analysis for torque-driven robot manipulators.
Let $G$ be a locally compact group. We continue our work [A. Ghaffari: $\Gamma $-amenability of locally compact groups, Acta Math. Sinica, English Series, 26 (2010), 2313–2324] in the study of $\Gamma $-amenability of a locally compact group $G$ defined with respect to a closed subgroup $\Gamma $ of $G\times G$. In this paper, among other things, we introduce and study a closed subspace $A_\Gamma ^p(G)$ of $L^\infty (\Gamma )$ and then characterize the $\Gamma $-amenability of $G$ using $A_\Gamma ^p(G)$. Various necessary and sufficient conditions are found for a locally compact group to possess a $\Gamma $-invariant mean.
There is a classical result known as Baer's Lemma that states that an $R$-module $E$ is injective if it is injective for $R$. This means that if a map from a submodule of $R$, that is, from a left ideal $L$ of $R$ to $E$ can always be extended to $R$, then a map to $E$ from a submodule $A$ of any $R$-module $B$ can be extended to $B$; in other words, $E$ is injective. In this paper, we generalize this result to the category $q_{\omega }$ consisting of the representations of an infinite line quiver. This generalization of Baer's Lemma is useful in proving that torsion free covers exist for $q_{\omega }$.