Abstract
An important research topic related to the theory and application of the interval-valued intuitionistic fuzzy weighted aggregation operators is how to determine their associated weights. In this paper, we propose a precise weight-determined (PWD) method of the monotonicity and scale-invariance, just based on the new score and accuracy functions of interval-valued intuitionistic fuzzy number (IIFN). Since the monotonicity and scale-invariance, the PWD method may be a precise and objective approach to calculate the weights of IIFN and interval-valued intuitionistic fuzzy aggregation operator, and a more suitable approach to distinguish different decision makers (DMs) and experts in group decision making. Based on the PWD method, we develop two new interval-valued intuitionistic fuzzy aggregation operators, i.e. interval-valued intuitionistic fuzzy ordered precise weighted averaging (IIFOPWA) operator and interval-valued intuitionistic fuzzy ordered precise weighted geometric (IIFOPWG) operator, and study their desirable properties in detail. Finally, we provide an illustrative example.
Highlights
Atanassov (1986) introduced the concept of intuitionistic fuzzy set (IFS), which is an extended and generalized definition of fuzzy set (FS) by Zadeh (1965), and is a powerful tool to deal with vagueness and uncertainty
We propose a precise weight-determined (PWD) method to obtain interval-valued intuitionistic fuzzy aggregation operator weights, based on the new score and accuracy functions of intuitionistic fuzzy number (IIFN)
Since the monotonicity and scale-invariance, the PWD method may be a precise and objective approach to calculate the weights of IIFN and interval-valued intuitionistic fuzzy aggregation operator, and a more suitable approach to distinguish different decision makers (DMs) and experts in group decision making
Summary
Kharal 2009; Ye 2010; Xu 2011; Zavadskas, Turskis 2011). decision making often occurs under the situation where there are time pressure and lack of data, and experts may not be able to express their preference between decisions with precise reasons. The weighted object of these approaches is the intuitionistic fuzzy value or the fuzzy value which is different from the interval-valued intuitionistic fuzzy number It seems that there is no investigation on the monotonous and scale-invariant properties of the weight-determined method, which is decisive for aggregation and calculation of interval-valued intuitionistic fuzzy values in group decision making. We propose a precise weight-determined (PWD) method to obtain interval-valued intuitionistic fuzzy aggregation operator weights, based on the new score and accuracy functions of IIFN. Since the monotonicity and scale-invariance, the PWD method may be a precise and objective approach to calculate the weights of IIFN and interval-valued intuitionistic fuzzy aggregation operator, and a more suitable approach to distinguish different DMs and experts in group decision making.
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