Geodesic
An approach to fuzzy modeling of digital devices
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 112-119.

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In the article the problem of fuzzy binary logic modeling for digital devices (DD) is investigated. In contrast to the similar classic problem of logical simulation, it is assumed that inputs signals of DD are fuzzy signals. In the real of DD for each input (0 or 1) there is a certain voltage range. If an input signal is out of the range, the correct signal identification is not guaranteed. The fuzziness of input signals means that there observed values can be either within of the defined range, or out of it. It is known that the logic modeling of every DD is the calculation of value of the certain logical expression. This expression is a mathematical model of DD. Also, the corresponding expression can be always represented in the terms of three logic operations, namely, AND, OR, and NOT. In article, a method of reducing the investigated problem to the problem of fuzzy modeling systems in the space of real numbers is proposed. The method is based on the presentation of logical expression using the infinite-valued (continuous) logic. The calculations in this logic are reduced to the evaluation of the expression in the space of real numbers. The proposed procedure in article is much less labor intensive than the previously known procedure for fuzzy modeling using fuzzy arithmetic in the space of real numbers. 
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D. V. Speranskiy. An approach to fuzzy modeling of digital devices. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 112-119. http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a10/

[1] Zadeh L. A., “Fuzzy sets”, Inf. Control, 1965, no. 8, 338–353 | DOI | MR | Zbl

[2] Dubois D., Prade H., “Fuzzy numbers, on overview”, Analysis of fuzzy information: Mathematics and logic, CRC Press, Boca Raton, FL, 1988, 3–39 | MR

[3] Kandel A., Fuzzy Mathematical Techniques with Applications, Addison Wesley Longman Publishing Co., Inc., Boston, MA, USA, 1986, 274 pp. | MR | Zbl

[4] Kaufman A., Gupta M. M., Introduction to fuzzy arithmetic theory and applications, Van Nostrand Reinhold Co., N.Y., 1991, 351 pp. | MR | Zbl

[5] Hanss M., Applied fuzzy arithmetic: Introduction with engineering applications, Springer Publ. Co., Inc., Berlin–Heidelberg, 2010, 274 pp.

[6] Yablonskiy S. V., Introduction to discrete mathematics, Nauka, M., 1986, 384 pp. (in Russian) | MR

[7] Skobtsov Yu. A., Speranskiy D. V., Skobtsov V. Yu., Modeling, testing and diagnostics of digital devices, National Public University “INTUIT” Publ., M., 2012, 439 pp. (in Russian)

[8] Zakrevskiy A. D., Pottosin Yu. V., Cheremisinova L. D., Logic design principles of discrete devices, Fizmatlit, M., 2007, 590 pp. (in Russian)

[9] Levin V. I., The Dynamics of Logic Units and Systems, Energiya, M., 1980, 224 pp. (in Russian)

[10] Levin V. I., Infinite-Valued Logic in Problems of Cybernetics, Radio i Svyaz', M., 1982, 176 pp. (in Russian)

[11] Ginzburg S. A., Mathematical continuous logic and the representation of functions, Energiya, M., 1968, 136 pp. (in Russian)

[12] Piegat A., Fuzzy Modeling and Control, Springer Science Business Media, 2001, 728 pp.