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Natural trapezoidal approximations of fuzzy numbers
Fuzzy Sets and Systems, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Przemyslaw Grzegorzewski +1 more
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Exact and approximate spectra for trapezoidal FM
Proceedings of the IEEE, 1976The intensity spectrum for an FM signal modulated by a trapezoidal waveform is given in terms of Fresnel integrals. The numerical results, as observed with a finite resolution filter, are compared with the quasi-stationary model, which is asymptotically valid for large values of the FM index. The size of the discrepancy relative to the asymptotic model
L.H. Holway, J.A. Mullen
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The trapezoidal approximation of digitized images
Computer Vision, Graphics, and Image Processing, 1984Abstract A highly efficient process for representing and compressing scanned data is described which vectorizes black-white document symbology by approximating it by means of trapezoidal shapes. Also discussed are methods for encoding the resultant descriptions for transmission or archival storage. Test results indicate the system can be used for the
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The Symmetric Trapezoidal Approximations of Fuzzy Numbers
2010 International Conference on Computational and Information Sciences, 2010The nearest symmetric trapezoidal approximation is presented for simplifying calculations of fuzzy numbers, which possesses the following properties: the centroid point invariance, ambuguity invariance, width invariance, translation invariance, sc-ale invariance. Numerical results also show that the presented method is valid.
Zhongxing Wang, Jingcui Li
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Some approximations of trapezoidal fuzzy sets
Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569), 2002We study different approximations of fuzzy sets. In the multidimensional case we obtain the crisp approximation of a fuzzy set. In the one-dimensional case we define tame fuzzy sets and approximate them with combinations of trapezoidal ones.
E. Roventa, T. Spircu
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Nearest interval, triangular and trapezoidal approximation of a fuzzy number preserving ambiguity
International Journal of Approximate Reasoning, 2012 The ambiguity was introduced to simplify the task of representing and handling of fuzzy numbers. We find the nearest real interval, nearest triangular (symmetric) fuzzy number, nearest trapezoidal (symmetric) fuzzy number of a fuzzy number, with respect ...
Adrian I Ban, Lucian Coroianu
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Approximation of Fuzzy Sets by Interval Type-2 Trapezoidal Fuzzy Sets
IEEE Transactions on Cybernetics, 2020In this paper, we propose a gradient-based method to approximate a fuzzy set through a trapezoidal fuzzy set (TFS). By adding some constraints in the formulated optimization problem, the major characteristics of the fuzzy set such as the core, the major part of the support, and the shape of the membership function could be preserved; also the form of ...
Yinghua Shen +2 more
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Best Lipschitz constant of the trapezoidal approximation operator preserving the expected interval
Fuzzy Sets and Systems, 2011The author finds the smallest Lipschitz constant of the trapezoidal approximation operator of a fuzzy number which preserves the expected interval by using the property of continuity. Similar papers are, e.g. [\textit{A. I. Ban}, Fuzzy Sets Syst. 160, No.~21, 3027--3047 (2009; Zbl 1183.03047); ibid. 160, No.~21, 3048--3058 (2009; Zbl 1183.03048)].
Lucian Coroianu
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Weighted semi-trapezoidal approximations of fuzzy numbers
Fuzzy Sets and Systems, 2011The author embeds fuzzy numbers into a Hilbert space \(H\) for computing their weighted semi-trapezoidal approximations via best approximations in a closed convex subset of \(H\). Formulas of matricial type are given, thus improving results of \textit{A. I. Ban} [Fuzzy Sets Syst. 160, No.~21, 3027--3047 (2009; Zbl 1183.03047); ibid.
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Bi-symmetrically Weighted Trapezoidal Approximations of Fuzzy Numbers
2009 Ninth International Conference on Intelligent Systems Design and Applications, 2009Trapezoidal approximation of fuzzy numbers preserving the expected interval is considered. A general problem of the trapezoidal approximation of fuzzy numbers with respect to the distance based on bi-symmetrical weighted functions is solved. A practical algorithm for constructing approximation operator is given.
Przemyslaw Grzegorzewski +1 more
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