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Fuzzy Logic and Arithmetical Hierarchy III

Studia Logica, 1997
[For Part I see Fuzzy Sets Syst. 73, No. 3, 359-363 (1995; Zbl 0857.03011).] Fuzzy logic RQL here means an extension of Łukasiewicz's infinite-valued first-order logic by graded notions of provability and of consequence together with (truth degree) constants for all rationals of the truth degree set \([0,1]\).
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Fuzzy arithmetic with requisite constraints

Fuzzy Sets and Systems, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On constrained fuzzy arithmetic

Proceedings of IEEE 5th International Fuzzy Systems, 2002
Basic principles of constrained fuzzy arithmetic are introduced as generalizations of the usual (unconstrained) fuzzy arithmetic. It is shown that these principles are applicable to both crisp and fuzzy constraints. The significance of constrained fuzzy arithmetic is illustrated by a few simple examples.
G.J. Klir, J.A. Cooper
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Implementing fuzzy arithmetic

Fuzzy Sets and Systems, 1995
This paper presents the authors' efforts towards the development of an effective and friendly working tool for fuzzy arithmetic. It describes the two programming libraries currently produced. The first, implemented using the Fortran language, provides high precision computational capabilities, to demonstrate the feasibility and the correctness of a ...
A.M. Anile, S. Deodato, G. Privitera
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Fuzzy arithmetic on LR fuzzy numbers with applications to fuzzy programming

Journal of Intelligent & Fuzzy Systems, 2015
In practice, some special LR fuzzy numbers, like the triangular fuzzy number, the Gaussian fuzzy number and the Cauchy fuzzy number, are widely used in many areas to deal with various vague information. With regard to these special LR fuzzy numbers, called regular LR fuzzy numbers in this paper, an operational law is proposed for fuzzy arithmetic ...
Jian Zhou 0003, Fan Yang, Ke Wang 0004
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Gradual interval arithmetic and fuzzy interval arithmetic

Granular Computing, 2019
This paper proposes an analysis of and a reflection on interval arithmetic (IA) and its extension to gradual interval arithmetic (GIA). Through this reflection, an overview of a part of IA that is directly related to fuzzy interval arithmetic (FIA) is analyzed, compared, and categorized according to two main families of IA: standard interval arithmetic
Reda Boukezzoula, Laurent Foulloy, Didier Coquin, Sylvie Galichet   +3 more
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On the Weighted Arithmetic Mean Fuzzy Filter

2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2015
Noise reduction is a fundamental step in many image processing and computer vision applications. In recent years, several noise filters especially devoted to the removal of high density salt and pepper noise, as a particular case of impulse noise, have been proposed.
Manuel González Hidalgo, Sebastia Massanet, Arnau Mir 0001, Daniel Ruiz-Aguilera   +3 more
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Fuzzy Set Transformation and Fuzzy Arithmetic

2020
The chapter elaborates on the ways of transforming fuzzy sets through functions: one of the fundamental concepts of processing fuzzy sets. The extension principle is discussed in detail. Two key ways of mapping fuzzy sets are discussed: the one based on the representation theorem (which directly links to the mapping realized in interval analysis) and ...
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Type-2 fuzzy variables and their arithmetic

Soft Computing, 2009
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Zhi-Qiang Liu, Yan-Kui Liu
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Fuzzy Arithmetic for Uncertainty Analysis

2013
When the theory of fuzzy sets arose as a new mathematical concept in the field of information processing some 50 years ago, it rapidly advanced to becoming a well-established scientific discipline and a challenging object of both theoretical research and practical application. Since its introduction by Lotfi A.
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