New approach of triangular neutrosophic cubic linguistic hesitant fuzzy aggregation operators
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ORIGINAL PAPER
New approach of triangular neutrosophic cubic linguistic hesitant fuzzy aggregation operators Aliya Fahmi1 • Muhammad Aslam2 • Muhammad Riaz3 Received: 25 November 2018 / Accepted: 17 May 2019 Ó Springer Nature Switzerland AG 2019
Abstract In this paper, we define the new concepts of a triangular neutrosophic cubic linguistic hesitant fuzzy number (TNCLHFN), the basic operational relations of TNCHLFNs, and the score function of TNCLHFNs. Then, we develop a triangular neutrosophic cubic linguistic hesitant fuzzy weighted arithmetic averaging (TNCLHFWAA) operator and a triangular neutrosophic cubic linguistic hesitant fuzzy weighted geometric averaging (TNCLHFWGA) operator to aggregate TNCLHFN information and investigate their properties. Furthermore, a multiple attribute decision-making method based on the TNCLHFWAA and TNCLHFWGA operators, and the score function of TNCLHFN is established under a TNCLHFN environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach. Triangular neutrosophic cubic linguistic hesitant fuzzy number with a wider scope of applications, and hence, the motivation for investigating into its applicability in different diseases in medical patients. Keywords Triangular neutrosophic cubic linguistic hesitant fuzzy number Score function TNCLHFWAA operator TNCLHFWGA operator Multiple attribute decision-making
1 Introduction Chen et al. (2015) presented a new similarity measure between Atanassov’s intuitionistic fuzzy values. Chen et al. (2016a) proposed method uses the evidential reasoning methodology to aggregate each decision-maker’s decision matrix and the weights of the attributes to get the aggregated decision matrix of each decision-maker. Liu et al. (2017) proposed the intuitionistic fuzzy Archimedean & Aliya Fahmi [email protected] Muhammad Aslam [email protected] Muhammad Riaz [email protected] 1
Department of Mathematics, Hazara University Mansehra, Dhodial, Pakistan
2
Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi Arabia
3
Department of Mathematics, University of the Punjab, Lahore, Pakistan
Heronian aggregation (IFAHA) operator. Liu et al. (2017) defined some properties and some special cases of these proposed operators. Liu and Chen (2018) proposed a new MAGDM method with the I2LI based on the proposed I2LGA operator. Chen et al. (2016b) calculated the weighted positive score and the weighted negative score of each alternative. Wang and Chen (2018) proposed a new MADM method using the linear programming (LP) methodology and the new score function. Since the influences of subjective and objective factors, it is not easy for decision-makers to give the accurate evaluation on complex things in practical decision problems. There usually exist some hesitations for decisionmakers to assess the fuzzy and uncertain quantities. Intuitionistic fuzzy set (IFS) is one of the generaliz
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