Fuzzy number division and the multi-granularity phenomenon

• Autorzy: Piegat A. , Pluciński M.

Identyfikatory

DOI

10.1515/bpasts-2017-0055

• Języki publikacji: EN

Abstrakty

EN

The paper presents difficulties connected with fuzzy and interval division. If operations such as fuzzy addition, subtraction and multiplication provide as a result one compact, multidimensional granule, then a result of the fuzzy division can consists of few separated granules. Such results are more difficult to use in next calculations. The paper shows that the number of solution granules can be higher than 2 and that in certain problems division does not occur explicitly. In certain problems, separation of particular solution granules can be considerable. The paper also shows how to realize the fuzzy division when its denominator contains zero. Most types of fuzzy arithmetics forbid such operation. However, the paper shows that it is possible. Multidimensional fuzzy RDM arithmetic and horizontal membership functions which facilitate detecting of solution granules are also described. The considered problems are visualized by examples.

Słowa kluczowe

EN

granular computing; fuzzy arithmetic; fuzzy calculations; RDM fuzzy arithmetic; horizontal membership function

PL

przetwarzanie ziarniste; arytmetyka liczb rozmytych; RDM; funkcja przynależności poziomej

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2017
• Tom: Vol. 65, nr 4
• Strony: 497--511
• Opis fizyczny: Bibliogr. 29 poz., wykr.

Twórcy

autor

Piegat A.

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

autor

Pluciński M.

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

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).