The chain and substitution rules of interval-valued intuitionistic fuzzy calculus

Yanmin Liu (), Hua Zhao () and Zeshui Xu ()
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Yanmin Liu: PLA University of Science and Technology
Hua Zhao: PLA University of Science and Technology
Zeshui Xu: Sichuan University

Fuzzy Optimization and Decision Making, 2018, vol. 17, issue 3, No 2, 265-285

Abstract: Abstract The interval-valued intuitionistic fuzzy set proposed by Atanassov is the extension of intuitionistic fuzzy set. It extends the membership degree and non-membership to interval values instead of a single value. So it contains more possible values and maybe more considerate. Among all the researches, the exploration on the calculus of interval-valued intuitionistic fuzzy set is entirely new. Recently, Zhao et al. (Int J Comput Intell Syst 9:36–56, 2016) proposed the concept of interval-valued intuitionistic fuzzy function (IVIFF) and gave a calculation method of derivative and differential of IVIFF. Based on this work, in this paper, firstly, we utilize a new and easier method to express the derivative and differential of IVIFF. Secondly, we propose the chain rules of derivative and the form invariance of differential in the interval-valued intuitionistic fuzzy environment. In addition, some properties of the substation rules for interval-valued intuitionistic fuzzy indefinite integrals and definite integrals are also developed.

Keywords: Interval-valued intuitionistic fuzzy function (IVIFF); Chain rule of derivatives; The invariance of differential form; Substitution rule for integrals (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10700-017-9275-y

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