Antonín Dvořák

Fuzzy transform in the analysis of data

Fuzzy transform is a novel, mathematically well founded soft computing method with many applications. In this paper, we present this technique with applications to data analysis. First, we show how it can be used for detection and characterization of dependencies among attributes. Second, we apply it to mining associations that have a functional character. Moreover, the mined associations are characterized linguistically which means that their antecedent consists of fuzzy numbers and the consequent is characterized using pure evaluative linguistic expressions (i.e. expressions such as small, very big, more or less medium, etc).

Analysis of seasonal time series using fuzzy approach

A new methodology for the analysis and forecasting of time series is proposed. It directly employs two soft computing techniques: the fuzzy transform and the perception-based logical deduction. Thanks to the use of both these methods, and to the innovative approach, consisting of the construction of several independent models, the methodology is successfully applicable to robust long-time predictions.

A linguistic approach to time series modeling with the help of F-transform

In this paper, we describe an approach to modeling and forecasting time series that uses the theory of evaluative linguistic expressions, fuzzy/linguistic IF-THEN rules and the fuzzy transform method. We show that the use of a linguistic approach allows better readability and understandability without any significant deterioration in precision.

Mining pure linguistic associations from numerical data

This paper contains a method for direct search of associations from numerical data that are expressed in natural language and so, we call them “linguistic associations”. The associations are composed of evaluative linguistic expressions, for example “small, very big, roughly medium”, etc. The main idea is to evaluate real-valued data by the corresponding linguistic expressions and then search for associations using some of the standard data-mining technique (we have used the GUHA method). One of essential outcomes of our theory is high understandability of the found associations because when formulated in natural language they are much closer to the way of thinking of experts from various fields. Moreover, associations characterizing real dependencies can be directly taken as fuzzy IF--THEN rules and used as expert knowledge about the problem.

Formal theories and linguistic descriptions

Abstract In this contribution, we discuss properties which a formal logical theory (we call it the theory of evaluating expressions ) should have to serve us as a tool for modeling of the meaning of a certain class of natural language expressions called evaluating ( linguistic ) expressions . We further construct a formal theory for modeling of the meaning of sets of fuzzy IF–THEN rules (called linguistic descriptions ) and finally present a basic schema of fuzzy logic deduction. The basis for our study is first-order fuzzy logic with evaluated syntax.

The concept of LFLC 2000: its specificity, realization and power of applications

Linguistic Fuzzy Logic Controller (LFLC) 2000 is a complex tool for the design of linguistic descriptions and fuzzy control based on these descriptions. Unique methodology and theoretical results upon which is LFLC 2000 based are presented. Then, main purposes of it are sketched and some implementation aspects are discussed. Presentation of existing and perspective applications concludes the paper.

On redundancies in systems of fuzzy/linguistic IF-THEN rules under perception-based logical deduction inference

In this study, we formally investigate how to determine fuzzy/linguistic IF-THEN rules that are redundant in linguistic descriptions (systems of IF-THEN rules). We present a formal definition of redundancy and show that seemingly redundant rules can in fact be indispensable. These results apply to IF-THEN rules that use evaluative expressions (e.g., small and very big) and the inference method called perception-based logical deduction. However, they are also valid for inference systems with compatible design choices. We also describe an algorithm for the automatic detection and removal of redundant rules. Finally, we present an example of a linguistic description that is learned automatically from data and reduced using our algorithm.

Fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices

This paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set. It also presents basic ideas on fuzzy integrals defined using these fuzzy measures. Definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers. Several useful properties of fuzzy measures and fuzzy integrals are stated and proved. Definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral.

Fuzzy logic deduction with crisp observations

This paper presents an approach to approximate reasoning over a set of IF-THEN rules called fuzzy logic deduction. It understands IF-THEN rules as linguistically expressed logical implications and interprets them inside formal logical theory. Methodology and some properties are presented.

Type fuzzy quantifiers determined by fuzzy measures on residuated lattices. Part I. Basic definitions and examples

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.