Grey relational analysis method for SVTrNN based multi-attribute decision making with partially known or completely unkn
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ORIGINAL PAPER
Grey relational analysis method for SVTrNN based multi-attribute decision making with partially known or completely unknown weight information Bibhas C. Giri1 • Mahatab Uddin Molla1 • Pranab Biswas1 Received: 13 March 2019 / Accepted: 8 May 2019 Springer Nature Switzerland AG 2019
Abstract Single-valued trapezoidal neutrosophic number (SVTrNN), an extension of single-valued neutrosophic set, effectively deals with indeterminate and incomplete information in multi-attribute decision making (MADM) problem. In this paper, we extend the grey relational analysis (GRA) method for solving SVTrNN based MADM problem, where the weight information of attributes is partially known or completely unknown. Following the classical GRA method, we define grey relational co-efficient using a new distance measure. We develop two optimization models to determine the weights of the attributes. We calculate grey positive and negative relational degrees and define the relative closeness co-efficient of each alternative to determine the best alternative. We take a numerical example to validate the proposed approach and compare the proposed method with other exiting methods. It is observed from the numerical study that the proposed GRA method has an advantage over the existing methods for solving SVTrNN based MADM problem with partially known or completely unknown attribute weight information. Keywords Multi-attribute decision making Single-valued trapezoidal neutrosophic number Grey relational analysis Unknown weight information
1 Introduction Grey relational analysis (GRA) is an important part of grey system theory, which is used to conduct relational analysis of uncertainty of the system. There are many applications of this method in different multi-attribute decision making (MADM) problems (Zhang et al. 2005; Wei 2011; Wei et al. 2011). However, in practice, decision makers face difficulties to collect accurate information of preference values of alternatives in MADM due to imprecise and incomplete data (Xu 2015).
& Bibhas C. Giri [email protected] Mahatab Uddin Molla [email protected] Pranab Biswas [email protected] 1
Department of Mathematics, Jadavpur University, Kolkata 700032, India
During the past several years, fuzzy sets (Zadeh 1965), intuitionistic fuzzy sets (Atanasso 1986), and neutrosophic sets (Smarandache 1999) have gained much attention from the researchers to deal with uncertain information in decision making problems. Fuzzy sets is used in various optimization techniques (Chen and Wang 1995; Chen and Tanuwijaya 2011; Chen and Chang 2011; Cheng et al. 2016; Lee and Chen 2008; Chen and Huang 2003. Intuitionistic fuzzy set is useful to handle various MCDM problems (Chen and Chang 2015; Chen et al. 2016a, b, Liu and Chen 2018a; Liu et al. 2017). Recently, MADM method is being developed under hesitant fuzzy sets and type-2 fuzzy sets (Mishra et al. 2018; Qin 2017). GRA method is one of the accepted MADM methods among TOPSIS (Hwang
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