Abstract. 

In fuzzy modeling, both clear and fuzzy values can be given to the inputs of the simulated systems. The computational complexity of fuzzy inference with fuzzy inputs, which are a formalization of linguistic values, corresponds to exponential complexity. This paper describes a new method of inference based on the decomposition theorem of multidimensional fuzzy implication and fuzzy truth value. This method makes it possible for fuzzy inputs to implement an inference with polynomial computational complexity, which makes it effective for modeling large-dimensional MISO structure systems. The implementation of this method using parallel computing technologies is reviewed in detail. As a result of the experiment, conclusions were made about the feasibility of using a particular implementation, depending on the amount of input data.

Keywords: 

a logical type of inference, a decomposition theorem, a fuzzy truth value, parallel computations.

DOI 10.14357/20718632200308

PP. 85-93.

 

References

1. Rutkowski L. 2009. Methods and techniques of artificial intelligence. PWN. 452 p.

2. V. G. Sinuk, M. V. Panchenko. 2017. Methody nechetkogo vivoda dlya odnogo klassa system MISO-struktury pri nechetkih vhodah [Fuzzy inference method for a one class of MISO structure systems with fuzzy in-puts.]. Iskustvenniy intellect i prinyatie resheniy [Artificial intelligence and decision making]. 4:33-39.

3. Zadeh L. 1976. Ponyatie lingvisticheskoy peremennoy i ego primenenie k prinyatiyu pribligennih resheniy [The concept of a linguistic variable and its application to approximate decision making]. Mir. 168 p.

4. V. G. Sinuk, E. V. Pivnenko. 2006. Ob analiticheskom vichislenii nechetkogo znacheniya istinnosti [On analytical calculation of a fuzzy truth value]. Sbornik trudov Vse-rossiyskoy nauchnoy konferencii po nechetkim sistemam i myagkim vichisleniyam (NSMV-2006)[Proceedings of the all-Russian scientific conference on fuzzy systems and soft computing (NSMV-2006)]. 129-133.

5. D. A. Kucenko, V. G. Sinuk. 2008. Algoritmi nahogdeni-ya CP pri kusochno-lineynom predstavlenii funkciy prinadlegnosti[Algorithms for finding CP in piecewise linear representation of membership functions]. Sbornik tru-dov vtoroy Vserossiyskoy nauchnoy konferencii po nechetkim sistemam I myagkim vichisleniyam (NSMV-2008) [Proceedings of the second all-Russian scientific conference on fuzzy systems and soft computing (NSMV-2008)]. 87-92.

6. A. N. Borisov, A. V. Alekseev, O. A. Krumberg. 1982. Decision models based on a linguistic variable. Riga: Zi-natne. 256 p.

7. D. Dobua, A. Prad. 1990. Theoriya vozmognostey. Prilogenie k predstavleniyu znaniy v informatike[Theory of possibilities. Applications to knowledge representation in computer science]. Moskow: Radio and communications. 228 p.

8. Jason Sanders, Edward Kandrot. 2010. CUDA by example: An introduction to general-purpose GPU programming. Addison-Wesley Professional. 320 p.

9. CUDA Programming Guide. Available at: https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html (accessed July 3, 2020)

10. CUDA Best Practices Guide. Available at: https://docs.nvidia.com/cuda/cuda-c-best-practices-guide/index.html (accessed July 3, 2020)

11. Bank Marketing Data Set. Available at: https://archive.ics.uci.edu/ml/datasets/Bank+Marketing (accessed July 3, 2020)