A decomposition approach to type 2 interval arithmetic

• Autorzy: Piegat Andrzej , Dobryakova Larisa

Identyfikatory

DOI

10.34768/amcs-2020-0015

• Języki publikacji: EN

Abstrakty

EN

The classic interval has precise borders A = [a, ā] . Therefore, it can be called a type 1 interval. Because of great practical importance of such interval data, several versions of type 1 interval arithmetic have been created. However, sometimes precise borders a and ā of intervals cannot be determined in practice. If the borders are uncertain, then we have to do with type 2 intervals. A type 2 interval can be denoted as A_T2 = [a_L, a_R], [ā_L, ā_R]. The paper presents multidimensional decomposition RDM type 2 interval arithmetic (D-RDM-T2-I arithmetic), where RDM means relative-distance measure. The decomposition approach considerably simplifies calculations and is transparent for users. Apart from this arithmetic, examples of its applications are also presented. To the authors’ best knowledge, no papers on this arithmetic exist. D-RDM-T2-I arithmetic is necessary to create type 2 fuzzy arithmetic based on horizontal µ-cuts, which the authors aim to do.

Słowa kluczowe

EN

multidimensional RDM interval arithmetic; type 2 interval arithmetic; RDM type 2 interval arithmetic; decomposition type 2 interval arithmetic; interval arithmetic

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 1
• Strony: 185--201
• Opis fizyczny: Bibliogr. 23 poz., rys., tab., wykr.

Twórcy

autor

Piegat Andrzej

• Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland

autor

Dobryakova Larisa

• Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland

Bibliografia

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• [17] Piegat, A. and Pluciński, M. (2015). Fuzzy number addition with the application of horizontal membership functions, Scientific World Journal 2015, Article ID: 367214, DOI: 10.1155/2015/367214.
• [18] Piegat, A. and Pluciński, M. (2017). Fuzzy number division and the multi-granularity phenomenon, Bulletin of the Polish Academy of Sciences: Technical Sciences 65(4): 497–511.
• [19] Pluciński, M. (2015). Solving Zadeh’s challenge problems with the application of RDM-arithmetic, International Conference on Artificial Intelligence and Soft Computing, Zakopane, Poland, pp. 239–248.
• [20] Sharghi, P., Jabbarova, K. and Aliyeva, K. (2017). RDMinterval arithmetic based decision making on port selection, Procedia Computer Science 120: 572–579.
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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).