Anna Walaszek-Babiszewska

Stochastic-Fuzzy Knowledge-Based Approach to Temporal Data Modeling

In the chapter an advanced fuzzy modeling method has been presented which can be useful in temporal data analysis. The method joints fuzzy and probabilistic approaches. The notions of the stochastic process with fuzzy states, and linguistic random variable have been defined to create a knowledge representation of the SISO and MISO dynamic systems. As the basic description of the stochastic process with fuzzy states observed at fixed moments, the joint probability distribution of n linguistic random variables has been assumed. The joint, conditional and marginal probability distributions of the stochastic process with fuzzy states valuate weights of particular rules of the knowledge rule base. Also, the probability distributions determine the probabilistic structure of the particular steps of the tested process. A mean fuzzy conclusion (prediction) can be calculated by the proposed inference procedure.

Fuzzy knowledge-based approach to diagnosis tasks in stochastic environment

This work deals with the creating probabilistic-fuzzy knowledge-based systems by using the theory of fuzzy systems as well as the probability and stochastic processes theory. We show that such systems can be applied in different diagnostic tasks. The structure of the reason-result fuzzy model has a form of weighted rules. Weights represent empirical probabilities of fuzzy statements in antecedents and consequent parts of rules. The calculated probabilities of fuzzy events are included into inference/forecast procedures.

Takagi-Sugeno-Kang type fuzzy models with fuzzy equations in the consequence part

This paper is focused on the extending Takagi-Sugeno-Kang (TSK) types fuzzy models. The propositions of the models with a fuzzy set-valued function in the consequence part as well as the models with the fuzzy time series in the consequence part are presented. Also chosen theoretical aspects of the creating knowledge bases and the fuzzy reasoning procedure are presented.