Author
Irina Perfilieva
Bio: Irina Perfilieva is an academic researcher from University of Ostrava. The author has contributed to research in topics: Fuzzy logic & Fuzzy number. The author has an hindex of 34, co-authored 246 publications receiving 4675 citations.
Papers published on a yearly basis
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Book•
31 Aug 1999
TL;DR: Fuzzy Logic: What, Why, for Which?
Abstract: Preface. 1. Fuzzy Logic: What, Why, for Which? 2. Algebraic Structures for Logical Calculi. 3. Logical Calculi and Model Theory. 4. Fuzzy Logic in Narrow Sense. 5. Functional Systems in Fuzzy Logic Theories. 6. Fuzzy Logic in Broader Sense. 7. Topoi and Categories of Fuzzy Sets. 8. Few Historical and Concluding Remarks. References. Index.
898 citations
TL;DR: A method of image compression and reconstruction on the basis of the F-transform, which is a fuzzy partition of a universe into fuzzy subsets (factors, clusters, granules etc.), is presented.
548 citations
TL;DR: The results show that the PSNR obtained with the usage of direct and inverse fuzzy transforms is higher than thePSNR determined either with fuzzy relation equations method or in the DCT one and it is close to the PS NR determined in JPEG method for small values of the compression rate.
174 citations
TL;DR: The aim of this study is to show how the F-transform technique can be generalized from the cases of constant components to the case of polynomial components.
134 citations
TL;DR: This paper shows how fuzzy transform can be used for detection and characterization of dependencies among attributes and applies it to mining associations that have a functional character.
118 citations
Cited by
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TL;DR: In this paper, fuzzy logic is viewed in a nonstandard perspective and the cornerstones of fuzzy logic-and its principal distinguishing features-are: graduation, granulation, precisiation and the concept of a generalized constraint.
1,253 citations
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TL;DR: “Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas and there is no doubt that a modern treatise on “Nonlinear functional analysis” can not afford the luxury of ignoring multivalued analysis.
Abstract: “Multivalued Analysis” is the theory of set-valued maps (called multifonctions) and has important applications in many different areas. Multivalued analysis is a remarkable mixture of many different parts of mathematics such as point-set topology, measure theory and nonlinear functional analysis. It is also closely related to “Nonsmooth Analysis” (Chapter 5) and in fact one of the main motivations behind the development of the theory, was in order to provide necessary analytical tools for the study of problems in nonsmooth analysis. It is not a coincidence that the development of the two fields coincide chronologically and follow parallel paths. Today multivalued analysis is a mature mathematical field with its own methods, techniques and applications that range from social and economic sciences to biological sciences and engineering. There is no doubt that a modern treatise on “Nonlinear Functional Analysis” can not afford the luxury of ignoring multivalued analysis. The omission of the theory of multifunctions will drastically limit the possible applications.
996 citations
TL;DR: The generalized theory of uncertainty (GTU) which is outlined in this paper breaks with this tradition and views uncertainty in a much broader perspective and represents a significant change both in perspective and direction in dealing with uncertainty and information.
989 citations
TL;DR: In this article, the authors consider the problem of finding the best approximation operator for a given function, and the uniqueness of best approximations and the existence of best approximation operators.
Abstract: Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.
841 citations