Generalized intuitionistic fuzzy aggregation operators based on confidence levels for group decision making
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ORIGINAL PAPER
Generalized intuitionistic fuzzy aggregation operators based on confidence levels for group decision making K. Rahman1 • S. Ayub2 • S. Abdullah3 Received: 5 June 2020 / Accepted: 18 August 2020 Ó Springer Nature Switzerland AG 2020
Abstract The focus of our this paper is to develop a series of Einstein hybrid aggregation operators using confidence level, such as confidence intuitionistic fuzzy Einstein hybrid averaging operator, confidence intuitionistic fuzzy Einstein hybrid geometric operator, generalized confidence intuitionistic fuzzy Einstein hybrid averaging operator and generalized confidence intuitionistic fuzzy Einstein hybrid geometric operator. The main advantage of the new operators is that these operators not only provide information to the experts of the problems, but these methods also consider the degrees of the experts of the problems that they are familiar with the selection option. The new approaches provide more general, more accurate and precise results as compared to the existing methods. Finally, the proposed operators have been applied to decision-making problems to show the validity, practicality and effectiveness of the new approach. Keywords CIFEHA operator CIFEHG operator GCIFEHA operator GCIFEHG operator MAGDM problem
1 Introduction Multi-attribute group decision making (MCDM) is one of the wanton developing study active problems recently for a last decision within a time. However, it is not always acceptable to give the preferences in a specific method due to many constraints and hence their corresponding results are not ideal in some environments. To handle this Zadeh (1965) presented the idea of fuzzy sets (FSs), which has only one element called membership function. After their prosperous and successful application, Atanassov (1986) generalized this concept and improve the notion of fuzzy & K. Rahman [email protected] S. Ayub [email protected] S. Abdullah [email protected] 1
Department of Mathematics, Hazara University, Mansehra, Pakistan
2
Department of Mathematics and Statistics, Riphah International University, Islamabad, Pakistan
3
Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
sets (FSs) to intuitionistic fuzzy sets (IFSs), in which each element can be written in the form of ordered pair. Under this situation, there are many scholars pay more attention on IFSs for aggregating the different options using different method and operators. Chen and Chen (2014), Chen and Niou (2011), Chen et al. (2009), Chen et al. (2012) developed several intuitionistic fuzzy aggregation operators and also applied them on group decision making. Yager (1988) presented OWA operator. Yager and Kacprzyk (1997) presented some basic and an important and role for fusion procedure. Chen and Chang (2016), Chen et al. (2016) developed many aggregation operators and their applications. Xu and Yager (2006) explored the idea of IFWG operator and IFOWG operator and also developed their application
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