International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Liu's inference is a process of deriving consequences from uncertain knowledge or evidence via the tool of conditional uncertainty. Using membership functions, this paper derives some expressions of Liu's inference rule for uncertain systems. This paper also discusses Liu's inference rule with multiple antecedents and with multiple if-then rules.

One of the most important issues in the field of fuzzy preference modelling is the construction of a fuzzy strict preference relation and a fuzzy indifference relation from a fuzzy weak preference relation. Here, we focus on a particular class of fuzzy weak preference relations, the so-called fuzzy orderings. The definition of a fuzzy ordering involves a fuzzy equivalence relation and, in this paper, the latter will be considered as the corresponding fuzzy indifference relation. We search for fuzzy strict preference relations compatible with a given fuzzy ordering and its fuzzy indifference relation. In many situations, depending on the t-norm and t-conorm used, this quest results in a unique fuzzy strict preference relation. Our aim is to characterize these fuzzy strict preference relations and to study their transitivity.

Synthetic data generators are one of the methods used in privacy preserving data mining for ensuring the privacy of the individuals when their data are published. Synthetic data generators construct artificial data from some models obtained from the original data. Such models are mainly based on statistics and, typically, do not take into account other aspects of interest in artificial intelligence.

In this paper we study whether one family of such synthetic data generators (the IPSO family) preserves the properties of the data that are of interest when users plan to apply clustering techniques. In particular, we study the effect of such synthetic data generators on fuzzy clustering. That is, we study the information loss data suffer when the original data are replaced by the synthetic ones.

The stability of discrete universal integrals based on copulas is discussed and examined, both with respect to the norms L₁ (Lipschitz stability) and L_∞ (Chebyshev stability). Each of these integrals is shown to be 1-Lipschitz. Exactly the discrete universal integrals based on a copula which is stochastically increasing in its first coordinate turn out to be 1-Chebyshev. A new characterization of stochastically increasing Archimedean copulas is also given.

A generalized Bayesian inference nets model (GBINM) and a new approach for internal fault detection and diagnosis of three-phase induction motor is proposed. The input data set for designing and testing the fault diagnostic system are acquired through on-site experiment. The preprocessed input data and experts' rich diagnostic experience/knowledge are used to define the membership functions and fault fuzzy sets. With GBINM and the defined fault fuzzy sets, the hierarchical Bayesian fuzzy inference nets are constructed to carry out the complex motor fault diagnostic procedure. The propagation of probability is used to address the uncertainties involved in detecting and diagnosing the motor incipient faults. The immense difficulties of defining and assigning statistical parameters, required for calculating the propagation of probability are effectively solved. The validity and effectiveness of the proposed approach is witnessed clearly from the testing results obtained.

In this paper we address the problem of inducing Bayesian network models for regression from incomplete databases. We use mixtures of truncated exponentials (MTEs) to represent the joint distribution in the induced networks. We consider two particular Bayesian network structures, the so-called naïve Bayes and TAN, which have been successfully used as regression models when learning from complete data. We propose an iterative procedure for inducing the models, based on a variation of the data augmentation method in which the missing values of the explanatory variables are filled by simulating from their posterior distributions, while the missing values of the response variable are generated using the conditional expectation of the response given the explanatory variables. We also consider the refinement of the regression models by using variable selection and bias reduction. We illustrate through a set of experiments with various databases the performance of the proposed algorithms.

Many papers have addressed the task of proposing a set of convenient axioms that a good rule interestingness measure should fulfil. We provide a new study of the principles proposed until now by means of the logic model proposed by Hájek et al.¹⁴ In this model association rules can be viewed as general relations of two itemsets quantified by means of a convenient quantifier.²⁸ Moreover, we propose and justify the addition of two new principles to the three proposed by Piatetsky-Shapiro.²⁷ We also use the logic approach for studying the relation between the different classes of quantifiers and these axioms. We define new classes of quantifiers according to the notions of strong and very strong rules, and we present a quantifier based on the certainty factor measure,³¹⁷ studying its most salient features.

This section is maintained by Vladik Kreinovich. Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@utep.edu, or by regular mail to: Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.