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The new approach to the construction of parametric membership functions for fuzzy sets with unequal supports
Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.ORCID iD: 0000-0002-9920-7946
2017 (English)In: Knowledge-Based and Intelligent Information & Engineering Systems: Proceedings of the 21st International Conference, KES-20176-8 September 2017, Marseille, France / [ed] Cecilia Zanni-Merk, Claudia Frydman, Carlos Toro, Yulia Hicks, Robert J. Howlett, Lakhmi C. Jain, Elsevier, 2017, Vol. 112, 2057-2065 p., kes17-155Conference paper, Published paper (Refereed)
Abstract [en]

The current research is devoted to developing methods of a novel mathematical interpretation of term-sets of linguistic variables. To the term-sets of the linguistic variables fuzzy sets are assigned. We intend to adopt the π-functions and the π-functions to derive formulas of membership functions of these sets. The fuzzy sets are divided in three families in the case of an odd number of the term-sets. To each family, we assign only one parametric formula, which depends on two parameters: the width of a non-fuzzy set, which contains all supports of the fuzzy sets being representatives of the term-sets, and a number of the term-sets. Provided that the supports of fuzzy sets will be unequal, the membership function of the set, belonging to one of the families, is computed by means of a functional modifier, inserted in the common equation typical of this family. Medical examples explain how to use cumulated membership functions practically. The procedure can be easily computerized.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 112, 2057-2065 p., kes17-155
Series
Procedia Computer Science, ISSN 1877-0509 ; 112
Keyword [en]
s-function; π-function; term-set of linguistic variable; variable intensity level; set-parametric boundaries; functional modifier
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:bth-15144DOI: 10.1016/j.procs.2017.08.253OAI: oai:DiVA.org:bth-15144DiVA: diva2:1141834
Conference
21st International Conference on Knowledge-Based and Intelligent Information & Engineering Systems, Marseille
Note

Open Access

Available from: 2017-09-16 Created: 2017-09-16 Last updated: 2017-09-18Bibliographically approved

Open Access in DiVA

kes17-155(226 kB)58 downloads
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Publisher's full texthttp://www.sciencedirect.com/science/article/pii/S1877050917316629

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Rakus-Andersson, Elisabeth
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CiteExportLink to record
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