Antonin Dvorak | University of Ostrava (original) (raw)

Papers by Antonin Dvorak

Soft Computing, Sep 23, 1999

This paper presents a new linguistic approximation algorithm and its implementation in the frame ... more 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).

Insight into Fuzzy Modeling, 2016

Advances in Fuzzy Logic and Technology 2017, 2017

Recently an order induced by t-norms, uninorms and nullnorms have been investigated. This paper i... more Recently an order induced by t-norms, uninorms and nullnorms have been investigated. This paper is mainly devoted to defining and investigating the set of incomparable elements with respect to the order induced by a uninorm. Also, by defining such an order, an equivalence relation on the class of uninorms is defined and this equivalence is deeply investigated.

… doctoral dissertation, University of Ostrava, Ostrava, 2003

An important role in fuzzy logic and fuzzy control is played by linguistic descriptions, ie finit... more An important role in fuzzy logic and fuzzy control is played by linguistic descriptions, ie finite sets of IF-THEN rules. These rules often include so-called evaluating linguistic expressions – natural language expressions which characterize a position on an ordered scale, usually on a ...

We discuss so-called relativization of various classes of generalized quantifiers (bivalent, fuzz... more We discuss so-called relativization of various classes of generalized quantifiers (bivalent, fuzzy, semi-fuzzy). We show that for fuzzy quantifiers, relativization cannot be defined in a satisfactory way. Hence we provide a generalization of fuzzy quantifiers consisting of use of a fuzzy set as a universe for quantification. Relativization of these fuzzy quantifiers fulfills intuitive requirements.

We introduce two variants of first-order fuzzy logic that can deal with non-denoting terms, or te... more We introduce two variants of first-order fuzzy logic that can deal with non-denoting terms, or terms that lack existing referents, e.g., Pegasus, the current king of France, the largest number, or 0/0. Logics designed for this purpose in the classical setting are known as free logics. In this paper we discuss the features of free logics and select the options best suited for fuzzification, deciding on the so-called dual-domain semantics for positive free logic with truth-value gaps and outer quantifiers. We fuzzify the latter semantics in two levels of generality, first with a crisp and subsequently with a fuzzy predicate of existence. To accommodate truth-valueless statements about nonexistent objects, we employ a recently proposed first-order partial fuzzy logic with a single undefined truth value. Combining the dual-domain semantics with partial fuzzy logic, we define several kinds of ‘inner-domain’ quantifiers, relativized by the predicate of existence. Finally, we make a few ob...

We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at... more We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at the treatment of fuzzy IF-THEN rules as linguis-tically expressed genuine logical implications. Be-sides the original PbLD, we propose a new balanc-ing variant of PbLD, introduce both variants with fuzzy inputs and study them from the point of view of the interpolativity property.

Fuzzy rules and fuzzy inference systems have become the central point of fuzzy modeling since the... more Fuzzy rules and fuzzy inference systems have become the central point of fuzzy modeling since the early beginnings of fuzzy systems. Hence, distinct desirable properties of the rules, their models, and the whole systems are studied. The non-conflictness of rules and/or the preservation of modus ponens seem to be considered the most crucial one(s). However, under the standard setting, such properties are semantically equivalent to the continuity of the modeled dependency. A natural question arises whether such a requirement is consistent with semantics of fuzzy rules. While the answer is positive in the case of implicative rules, in the case of the more often used Mamdani-Assilian rules, we may consider another perspective. This article foreshadows another perspective that could lead to the investigation of a desirable property of the Mamdani-Assilian model that is different from continuity.

This paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy ... more 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.

2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2021

In this paper, we investigate qualitative integrals (generalizations of Sugeno integral) acting o... more In this paper, we investigate qualitative integrals (generalizations of Sugeno integral) acting on recently introduced Dragonfly algebras. These algebras are designed for applications in data analysis (based on fuzzy relational compositions) when some data are unknown (e.g., missing). Unknown data are represented by the additional dummy value. Definitions of operations on Dragonfly algebras follow lower estimation strategy, i.e., results of operations can be interpreted as lower estimations of results obtained when unknown values are replaced by known ones. We define qualitative integrals on Dragonfly algebras and show their monotonicity. We also prove results characterizing when these integrals return known (or unknown) values. We also present an illustrative example and hint directions of further research.

Fuzzy Sets and Systems, 2020

Abstract In this paper, we introduce a generalization of the concept of fuzzy quantifier called f... more Abstract In this paper, we introduce a generalization of the concept of fuzzy quantifier called fuzzy quantifiers over fuzzy domains. The development of this generalization is motivated by the impossibility to satisfactorily define the important operation of relativization for standard fuzzy quantifiers. We provide basic examples of these quantifiers and define and investigate also several semantic properties of them. Finally, we prove a theorem saying, among other things, that all these two argument fuzzy quantifiers that possess properties of extension and conservativity are relativizations of one-argument fuzzy quantifiers of this kind.

Insight into Fuzzy Modeling, 2016

In this paper, we present an application of perception-based logical deduction in the modeling of... more In this paper, we present an application of perception-based logical deduction in the modeling of an economic analysis given in natural language. We use fuzzy IF-THEN rules and the theory of evaluative linguistic expressions in the frame of fuzzy type theory. We outline a description of our formal tools and discuss our methodology as well as its relations to other approaches. Finally, we present an example taken from free economic analysis on the Internet.

Intelligent Systems for Manufacturing, 1998

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

2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

New Trends in Aggregation Theory

Lecture Notes in Computer Science, 1997

This paper studies computational properties of fuzzy logic deduction and compares them with the s... more 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

Soft Computing, Sep 23, 1999

This paper presents a new linguistic approximation algorithm and its implementation in the frame ... more 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).

Insight into Fuzzy Modeling, 2016

Advances in Fuzzy Logic and Technology 2017, 2017

Recently an order induced by t-norms, uninorms and nullnorms have been investigated. This paper i... more Recently an order induced by t-norms, uninorms and nullnorms have been investigated. This paper is mainly devoted to defining and investigating the set of incomparable elements with respect to the order induced by a uninorm. Also, by defining such an order, an equivalence relation on the class of uninorms is defined and this equivalence is deeply investigated.

… doctoral dissertation, University of Ostrava, Ostrava, 2003

An important role in fuzzy logic and fuzzy control is played by linguistic descriptions, ie finit... more An important role in fuzzy logic and fuzzy control is played by linguistic descriptions, ie finite sets of IF-THEN rules. These rules often include so-called evaluating linguistic expressions – natural language expressions which characterize a position on an ordered scale, usually on a ...

We discuss so-called relativization of various classes of generalized quantifiers (bivalent, fuzz... more We discuss so-called relativization of various classes of generalized quantifiers (bivalent, fuzzy, semi-fuzzy). We show that for fuzzy quantifiers, relativization cannot be defined in a satisfactory way. Hence we provide a generalization of fuzzy quantifiers consisting of use of a fuzzy set as a universe for quantification. Relativization of these fuzzy quantifiers fulfills intuitive requirements.

We introduce two variants of first-order fuzzy logic that can deal with non-denoting terms, or te... more We introduce two variants of first-order fuzzy logic that can deal with non-denoting terms, or terms that lack existing referents, e.g., Pegasus, the current king of France, the largest number, or 0/0. Logics designed for this purpose in the classical setting are known as free logics. In this paper we discuss the features of free logics and select the options best suited for fuzzification, deciding on the so-called dual-domain semantics for positive free logic with truth-value gaps and outer quantifiers. We fuzzify the latter semantics in two levels of generality, first with a crisp and subsequently with a fuzzy predicate of existence. To accommodate truth-valueless statements about nonexistent objects, we employ a recently proposed first-order partial fuzzy logic with a single undefined truth value. Combining the dual-domain semantics with partial fuzzy logic, we define several kinds of ‘inner-domain’ quantifiers, relativized by the predicate of existence. Finally, we make a few ob...

We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at... more We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at the treatment of fuzzy IF-THEN rules as linguis-tically expressed genuine logical implications. Be-sides the original PbLD, we propose a new balanc-ing variant of PbLD, introduce both variants with fuzzy inputs and study them from the point of view of the interpolativity property.

Fuzzy rules and fuzzy inference systems have become the central point of fuzzy modeling since the... more Fuzzy rules and fuzzy inference systems have become the central point of fuzzy modeling since the early beginnings of fuzzy systems. Hence, distinct desirable properties of the rules, their models, and the whole systems are studied. The non-conflictness of rules and/or the preservation of modus ponens seem to be considered the most crucial one(s). However, under the standard setting, such properties are semantically equivalent to the continuity of the modeled dependency. A natural question arises whether such a requirement is consistent with semantics of fuzzy rules. While the answer is positive in the case of implicative rules, in the case of the more often used Mamdani-Assilian rules, we may consider another perspective. This article foreshadows another perspective that could lead to the investigation of a desirable property of the Mamdani-Assilian model that is different from continuity.

This paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy ... more 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.

2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2021

In this paper, we investigate qualitative integrals (generalizations of Sugeno integral) acting o... more In this paper, we investigate qualitative integrals (generalizations of Sugeno integral) acting on recently introduced Dragonfly algebras. These algebras are designed for applications in data analysis (based on fuzzy relational compositions) when some data are unknown (e.g., missing). Unknown data are represented by the additional dummy value. Definitions of operations on Dragonfly algebras follow lower estimation strategy, i.e., results of operations can be interpreted as lower estimations of results obtained when unknown values are replaced by known ones. We define qualitative integrals on Dragonfly algebras and show their monotonicity. We also prove results characterizing when these integrals return known (or unknown) values. We also present an illustrative example and hint directions of further research.

Fuzzy Sets and Systems, 2020

Abstract In this paper, we introduce a generalization of the concept of fuzzy quantifier called f... more Abstract In this paper, we introduce a generalization of the concept of fuzzy quantifier called fuzzy quantifiers over fuzzy domains. The development of this generalization is motivated by the impossibility to satisfactorily define the important operation of relativization for standard fuzzy quantifiers. We provide basic examples of these quantifiers and define and investigate also several semantic properties of them. Finally, we prove a theorem saying, among other things, that all these two argument fuzzy quantifiers that possess properties of extension and conservativity are relativizations of one-argument fuzzy quantifiers of this kind.

Insight into Fuzzy Modeling, 2016

In this paper, we present an application of perception-based logical deduction in the modeling of... more In this paper, we present an application of perception-based logical deduction in the modeling of an economic analysis given in natural language. We use fuzzy IF-THEN rules and the theory of evaluative linguistic expressions in the frame of fuzzy type theory. We outline a description of our formal tools and discuss our methodology as well as its relations to other approaches. Finally, we present an example taken from free economic analysis on the Internet.

Intelligent Systems for Manufacturing, 1998

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

2020 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

New Trends in Aggregation Theory

Lecture Notes in Computer Science, 1997

This paper studies computational properties of fuzzy logic deduction and compares them with the s... more 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