Series based on the new order in intuitionistic fuzzy environment

Article type: Research Article

Authors: Ma, Rufei^a | Liu, Shousheng^a | Xu, Zeshui^{b; *} | Lei, Qian^c

Affiliations: [a] The Army Engineering University of PLA, Nanjing Jiangsu, China | [b] Business School, Sichuan University, Chengdu, China | [c] Nanyang Technological University, Singapore

Correspondence: [*] Corresponding author. Zeshui Xu, Business School, Sichuan University, Chengdu 610064, China. E-mail: xuzeshui@263.net.

Abstract: Intuitionistic fuzzy number (IFN) is an effective tool for dealing with the uncertain information, and it has been applied to various fields. According to IFNs, the intuitionistic fuzzy calculus has been developed, which can effectively integrate the continuous uncertain information. Series in intuitionistic fuzzy environment is a part of the intuitionistic fuzzy calculus theory, of which core idea is limit. However, the order used in the existing limit theory is not the one used in intuitionistic fuzzy calculus, causing the separation of the limit theory and intuitionistic fuzzy calculus. Thus, series in intuitionistic fuzzy environment is not closely related to the intuitionistic fuzzy calculus. In order to solve the above problem, we construct the related theories. There are mainly the following three aspects: (1) the limit theory including the sequence limit and the function limit is studied based on the new order. (2) we re-examine the numerical series according to the new tool of researching IFNs: the basis and the coordinates. (3) we discuss the function series and put forward the uniform convergence in intuitionistic fuzzy environment.

Keywords: Intuitionistic fuzzy number (IFN), intuitionistic fuzzy calculus, complementary operation, limit, series, uniform convergence

DOI: 10.3233/JIFS-191679

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 1, pp. 319-330, 2021