Antonin Dvorak

Analysis and prediction of time series using fuzzy transform

A new methodology for forecasting of time series is proposed. It is based on combination of two techniques: fuzzy transform and perception-based logical deduction on the basis of learned linguistic description.

On linguistic approximation in the frame of fuzzy logic deduction

Abstract This paper presents a new linguistic approximation algorithm and its implementation in the frame of fuzzy logic deduction. The algorithm presented is designed for fuzzy logic deduction mechanism implemented in Linguistic Fuzzy Logic Controller (LFLC).

Redundancies in systems of fuzzy/linguistic IF-THEN rules

In this paper we will investigate which fuzzy/linguistic rules are redundant in systems of such rules called linguistic descriptions. We present a formal definition of redundancy and show that rules which are seemingly redundant can be in fact indispensable. These results apply for IF-THEN rules which use evaluative linguistic expressions (e.g., small, very big, etc.) and inference method called perception-based logical deduction (PbLD). However, they are also valid for inference systems which use compatible design choices with PbLD.

New results on redundancies of fuzzy/linguistic IF-THEN rules

In this paper we present new results on detection and removal of redundancies of IF-THEN rules in so-called linguistic descriptions (systems of such rules). We introduce an algorithm for removal of redundancies and describe a practical application.

Type 〈1, 1〉 fuzzy quantifiers determined by fuzzy measures

In this paper we present a new definition of fuzzy quantifiers of type 〈1, 1〉 determined by fuzzy measures and fuzzy integrals. We show basic semantic properties, namely, permutation and isomorphism invariance, extension and conservativity, of these fuzzy quantifiers.

Linguistic approach to time series analysis and forecasts

Linguistic approach of time series analysis is suggested. It adopts aspects of the decomposition and autoregression. The linguistic, i.e., interpretable and transparent, nature of the approach is emphasized. Precision of the suggested approach is demonstrated on real time series.

Object oriented implementation of fuzzy logic systems

Various aspects of implementation of fuzzy software systems are discussed. Some theoretical considerations on basic notions are introduced and also our approach to implemetation is presented.

Computational Properties of Fuzzy Logic Deduction

This paper studies computational properties of fuzzy logic deduction and compares them with the standard inference methods. The principles of deduction in fuzzy logic are explained and algorithms for its computer realization are described. Basic algorithm has exponential complexity with respect to the number of antecedent variables, and in case of fuzzy observations we are able to improve its performance only by constant factor.

Mining Pure Linguistic Associations on the Basis of Perceptions in Numerical Data

In this paper, a method for mining associations composed of evaluating linguistic expressions (expressions as small, very big, etc.) is proposed. The main idea is to evaluate real-valued data by the corresponding linguistic expressions and then search for the corresponding associations using some of the standard data-mining technique (we have used GUHA method)

On Convergence of Fuzzy Integrals over Complete Residuated Lattices

Recently we proposed a new type of fuzzy integrals defined over complete residuated lattices. These integrals are intended for the modeling of type ⟨1, 1⟩ fuzzy quantifiers. An interesting theoretical question is, how to introduce various notions of convergence of this type of fuzzy integrals. In this contribution, we would like to present some results on strong and pointwise convergence of these fuzzy integrals, where the operation of the biresiduum is used to establish the measurement how close two elements of a residuated lattice are.