The NOWA weighted sampling type-reduction method for interval type-2 fuzzy sets and its application

Issue title: Some highlights on fuzzy systems and data mining

Guest editors: Shilei Sun, Silviu Ionita, Eva Volná, Andrey Gavrilov and Feng Liu

Article type: Research Article

Authors: Gong, Yanbing^* | Yang, Sunxin | Dai, Liangliang

Affiliations: School of Enterprise Management, Hohai University, Changzhou, Jiangsu, P.R. China

Correspondence: [*] Corresponding author. Yanbing Gong, School of Enterprise Management, Hohai University, Changzhou, Jiangsu 213022, P.R. China. Tel.: +86 51981230713; Fax: +86 5198519; E-mail: [email protected].

Abstract: In order to aggregate all uncertain information of the footprint of uncertainty (FOU) and improve the speed of defuzzification for interval type-2 fuzzy sets (IT2 FS), the normal ordered weighted averaging (NOWA) weighted sampling method is proposed to transform an IT2 FS into a type-1 fuzzy set (T1 FS), whose defuzzified values closely approximate those of the expected values of all embedded T1 FSs. Compared with the existing methods, the proposed method is more simple and practical, and the result is mainly determined by the numbers and weights of random samples in each vertical slice of FOU. Finally, based on the NOWA weighted sampling method, a new possibility degree is introduced to solve multi-attribute decision-making problems in which the attribute values take the form of interval type-2 fuzzy numbers.

Keywords: Interval type-2 fuzzy set, type-reduction, normal OWA weight, sampling

DOI: 10.3233/JIFS-169176

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 6, pp. 2927-2933, 2016