Decision-making model under complex picture fuzzy Hamacher aggregation operators
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Decision-making model under complex picture fuzzy Hamacher aggregation operators Muhammad Akram1 · Ayesha Bashir1 · Harish Garg2 Received: 22 February 2020 / Revised: 15 June 2020 / Accepted: 5 July 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract The paper aims are to propose a new concept called as complex picture fuzzy set (CPFS), as an extension of complex intuitionistic fuzzy set (CIFS). The addition of a neutral membership degree to the definition of CIFS makes CPFS a generalized form of CIFS. The uniqueness of this new theory lies in the capability to attain the wider range with the help of degree of neutral membership, non-membership, and membership. The range of values of membership degrees is broaden to the unit disk in a complex plane. We define elementary operations and properties of CPFSs and explore the MCDM issues with the help of CPFSs, based on Hamacher operations and some aggregation methods. Then, we introduce some operators to aggregate the CPF data, namely complex picture fuzzy Hamacher weighted averaging, ordered weighted averaging, hybrid averaging and complex picture fuzzy Hamacher weighted geometric, ordered weighted geometric and hybrid geometric operators, benefited from the basic Hamacher operations, and averaging, geometric aggregation techniques. We also construct MCDM problem using these operators and perform a calculation for the selection of best ERP system, to demonstrate the authenticity and efficiency of this manuscript. Moreover, we study a comparison to validate the consistency and superiority of our techniques. Keywords Complex picture fuzzy set · Hamacher operations · Averaging operators · Geometric operators Mathematics Subject Classification 03E72 · 47S40
1 Introduction Multiple criteria decision-making (MCDM) (Figueira et al. 2016) is a technique of evaluating the most relevant alternative on the basis of expert(s) decision in accordance with given
Communicated by Marcos Eduardo Valle.
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Harish Garg [email protected]; [email protected] http://sites.google.com/site/harishg58iitr/
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Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
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School of Mathematics, Thapar Institute of Engineering and Technology, Deemed University, Patiala, Punjab 147004, India 0123456789().: V,-vol
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criteria, to organize and solve the planning and judgemental issues. This process of decisionmaking has a significant importance and becomes the center of attraction of researchers (Pasi and Yager 2006). Generally, the experts or decision-makers solve the MCDM issues to evaluate the data with the vague information (Chen and Tan 1994). For example, many researcher had done a significant work in the field of fuzzy set (FS) (Zadeh 1965), intuitionistic fuzzy set (IFS) (Atanassov 1986), cubic intuitionistic fuzzy set (Garg and Kaur 2019), linguistic interval-valued IFS Garg and Kumar (2019), and the other generalized sets (Akram et al. 2019a, b; Kaur and Garg 2019; Shahza
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