Some notes on possibilistic variances of generalized trapezoidal intuitionistic fuzzy numbers

Qiansheng Zhang; Dongfang Sun; Qiansheng Zhang; Dongfang Sun

doi:10.3934/math.2021221

AIMS Mathematics

2021, Volume 6, Issue 4: 3720-3740. doi: 10.3934/math.2021221

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Research article

Some notes on possibilistic variances of generalized trapezoidal intuitionistic fuzzy numbers

Qiansheng Zhang ^{1
,
,},
Dongfang Sun ²

1.
School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China
2.
School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China

Received: 24 October 2020 Accepted: 08 January 2021 Published: 26 January 2021
MSC : 03E72

Intuitionistic fuzzy number as the generalization of fuzzy number has better capability to model uncertain data in management decision science and mathematical engineering problem. In this paper, we present a new definition of possibilistic mean and variance for generalized trapezoidal intuitionistic fuzzy number (GTIFN), and show that some properties of crisp mean and variance in probability theory are preserved by possibilistic mean and variance of generalized trapezoidal intuitionistic fuzzy numbers. We also discuss some notes on possibilistic variance of GTIFNs and get the important relationships between the proposed two possibilistic variances of generalized trapezoidal intuitionistic fuzzy number.
- generalized trapezoidal intuitionistic fuzzy number,
- possibilistic mean,
- possibilistic variance,
- possibilistic covariance
Citation: Qiansheng Zhang, Dongfang Sun. Some notes on possibilistic variances of generalized trapezoidal intuitionistic fuzzy numbers[J]. AIMS Mathematics, 2021, 6(4): 3720-3740. doi: 10.3934/math.2021221

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Abstract

Intuitionistic fuzzy number as the generalization of fuzzy number has better capability to model uncertain data in management decision science and mathematical engineering problem. In this paper, we present a new definition of possibilistic mean and variance for generalized trapezoidal intuitionistic fuzzy number (GTIFN), and show that some properties of crisp mean and variance in probability theory are preserved by possibilistic mean and variance of generalized trapezoidal intuitionistic fuzzy numbers. We also discuss some notes on possibilistic variance of GTIFNs and get the important relationships between the proposed two possibilistic variances of generalized trapezoidal intuitionistic fuzzy number.

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