Fuzzy number division and the multi-granularity phenomenon

Bulletin of the Polish Academy of Sciences. Technical Sciences

M. Pluci?skiFaculty of Computer Science and Information Technology, West Pomeranian University of Technology, 49 ?o?nierska St., 71-210 Szczecin, PolandOther articles by this author:De Gruyter OnlineGoogle Scholar¹  A. PiegatCorresponding authorFaculty of Computer Science and Information Technology, West Pomeranian University of Technology, 49 ?o?nierska St., 71-210 Szczecin, PolandEmailOther articles by this author:De Gruyter OnlineGoogle Scholar¹ 

[1] Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, 49 ?o?nierska St., 71-210 Szczecin, Poland

关键词: Keywords: granular computing;    fuzzy arithmetic;    fuzzy calculations;    RDM fuzzy arithmetic;    horizontal membership function;   

DOI  :  10.1515/bpasts-2017-0055

学科分类：工程和技术（综合）

来源: Polska Akademia Nauk * Centrum Upowszechniania Nauki / Polish Academy of Sciences, Center for the Advancement of Science

【 摘 要 】

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.

【 授权许可】

Unknown