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Omitting types in fuzzy logic with evaluated syntax

MATHEMATICAL logic QUARTERLY 2006年第3期52卷 259-268页

作者： Murinova, Petra Novak, Vilem Univ Ostrava Inst Res & Appl Fuzzy Modeling Ostrava Czech Republic

This paper is a contribution to the development of model theory of fuzzy logic in narrow sense. We consider a formal system Ev(L) of fuzzy logic that has evaluated syntax, i.e. axioms need not be fully convincing and so, they form a fuzzy set only. Consequently, formulas are provable in some general degree. A generalization of Godel's completeness theorem does hold in Ev(L). The truth values form an MV-algebra that is either finite or Lukasiewicz algebra on [0, 1]. The classical omitting types theorem states that given a formal theory T and a set Sigma(x(1),...,x(n)) of formulas with the same free variables, we can construct a model of T which omits Sigma, i.e. there is always a formula from Sigma not true in it. In this paper, we generalize this theorem for Ev(L), that is, we prove that if T is a fuzzy theory and Sigma(x(1),..., x(n)) forms a fuzzy set, then a model omitting E also exists. We will prove this theorem for two essential cases of Ev(L): either EVL has logical (truth) constants for al I truth values, or it has these constants for truth values from[0, 1] boolean AND Q only. (c) 2006 WILEYNCH Verlag GmbH & Co. KGaA, Weinheim.

关键词： model theory Lukasiewicz MV-algebra fuzzy logic with evaluated syntax

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Recognition of damaged letters based on mathematical fuzzy logic analysis

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JOURNAL OF APPLIED logic 2015年第2期13卷 94-104页

作者： Novak, Vilem Hurtik, Petr Habiballa, Hashim Stepnicka, Martin Univ Ostrava Inst Res & Applicat Fuzzy Modeling NSC CZ-70103 Ostrava 1 Czech Republic

This paper reports a real application whose task was to recognize characters printed on metal ingots. The problem is that surface of ingots is very uneven - ingots are hot or cold, cut by rough instrument, the printing machine can be worn down, etc. In this paper, we present two original recognition methods: the first one is based on application of mathematical fuzzy logic and the second one is based on representation of an image by a fuzzy-valued function. Results of these methods are compared with a simple neural network classifier and few other common methods. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Mathematical fuzzy logic fuzzy logic with evaluated syntax Optical character recognition OCR Pattern recognition CAPTCHA

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Which logic is the real fuzzy logic?

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fuzzy SETS AND SYSTEMS 2006年第5期157卷 635-641页

作者： Novák, V Univ Ostrava Inst Res & Applicat Fuzzy Modeling Ostrava 70103 1 Czech Republic Acad Sci Czech Republic Inst Informat & Automat Theory Prague 18602 8 Czech Republic

This paper is a contribution to the discussion of the problem, whether there is a fuzzy logic that can be considered as the real fuzzy logic. We give reasons for taking IMTL, BL, L Pi and Ev(L) (fuzzy logic with evaluated syntax) as those fuzzy logics that should be indeed taken as the real fuzzy logics. (c) 2005 Elsevier B.V. All rights reserved.

关键词： mathematical fuzzy logic fuzzy type theory fuzzy logic with evaluated syntax algebra of truth values

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Which logic is the real fuzzy logic?

Which logic is the real fuzzy logic?

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26th Linz Seminar on fuzzy Set Theory

作者： Novák, V Univ Ostrava Inst Res & Applicat Fuzzy Modeling Ostrava 70103 1 Czech Republic Acad Sci Czech Republic Inst Informat & Automat Theory Prague 18602 8 Czech Republic

关键词： mathematical fuzzy logic fuzzy type theory fuzzy logic with evaluated syntax algebra of truth values

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