Extended GRA-Based MADM Strategy With Single-Valued Trapezoidal Neutrosophic Numbers

Extended GRA-Based MADM Strategy With Single-Valued Trapezoidal Neutrosophic Numbers

Surapati Pramanik (Umeschandra College, India) and Rama Mallick (Umeschandra College, India)
Copyright: © 2020 |Pages: 30
DOI: 10.4018/978-1-7998-2555-5.ch008

Abstract

Multi-attribute decision-making(MADM) strategy has been proposed to handle uncertain decision-making problems. The most extensively used models of grey system theory is grey relational analysis (GRA). This strategy was flourished by Chinese Professor J. Deng. This strategy also known as Deng's grey incidence analysis model. GRA uses a generic concept of intelligence. It describes any circumstance as no information as black and perfect information as white. Nevertheless, these idealized situations appear in real-world problems. In this chapter, the authors extend GRA strategy for multi-attribute decision making in trapezoidal neutrosophic number (TrNN) environment. To develop a GRA strategy in trapezoidal neutrosophic number (TrNN) environment, the authors use score function and accuracy function. Then Hamming distance for two trapezoidal neutrosophic number (TrNN) are also described. The authors solve a numerical problem to explain the pertinence of the proposed strategy. Lastly, they provide a comparison between VIKOR strategy with existing strategy.
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1. Introduction

In 1998, Smarandache (Smarandache, 1998) consecrated the notion of neutrosophic set by incorporating the philosophy of neutrosophy (Smarandache, 1998) in mathematical arena. Thereafter, Wang et al. (Wang et al., 2010) defined single valued neutrosophic set. Neutrosophic set and its various extensions and neutrosophic hybrid sets have been widely employed in decision making problems such as single valued neutrosophic set environment (Biswas, Pramanik, & Giri, 2014, Biswas, Pramanik, & Giri, 2015, Mondal, & Pramanik, 2015, Pramanik, Dalapati, & Roy, 2016, Smarandache, & Pramanik, 2016, Biswas, Pramanik, & Giri, 2017, Pramanik, Mallick, & Dasgupta, 2018, Mondal, Pramanik, & Giri, 2018, Mondal, Pramanik, & Giri, 2018, Biswas, Pramanik, & Giri, 2018, Biswas, Pramanik, & Giri 2019, Abdel-Basset, Manogaran, Gamal, & Smarandache, 2018, Abdel-Basset, Mohamed, Zhou, Hezam, 2017, Abdel-Basset, Gunasekaran, Mohamed, Chilamkurti, 2018, Abdel-Basset, Mohamed, & Smarandache, 2018a, Abdel-Basset, Mohamed, & Smarandache, 2018b, Abdel-Basset, Zhou, Mohamed, Chang, 2018, Abdel-Basset, & Mohamed, 2018, Abdel-Basset, Mohamed, Sangaiah, & Jain, 2018, Abdel-Baset, Chang, Gamal, & Smarandache, 2019, Abdel-Baset, Chang, & Gamal, 2019, Abdel-Basset, Manogaran, Gamal, & Smarandache, 2019, Abdel-Basset, Gamal, Manogaran, Son, & Long, 2019, Biswas, Pramanik, & Giri, 2019), interval neutrosophic set environment (Pramanik, Dey, & Giri, 2015, Dey, Pramanik, & Giri, 2016, Dalapati, Pramanik, Alam, Smarandache, & Roy, 2017, Mondal, Pramanik, & Giri, 2018), neutrosophic single valued soft expert set environment (Pramanik, Dey, & Giri, 2015, Pramanik, Dey, & Giri, 2016a, Pramanik, Dey, & Giri 2016b, Pramanik, & Dalapati, 2016), rough neutrosophic set environment (Mondal, & Pramanik, 2015, Mondal, & Pramanik, 2015, Mondal, & Pramanik, 2015, Mondal, Pramanik, & Smarandache 2016a, Mondal, Pramanik, & Smarandache 2016b, Mondal, Pramanik, & Smarandache 2016c, Pramanik, Roy, Roy, & Smarandache, 2017, Pramanik, Roy, & Roy, 2018, Mondal, Pramanik, & Giri, 2018, Mondal, Pramanik, 2015, Pramanik, Roy, Roy, & Smarandache, 2018, Pramanik, Roy, Roy, & Smarandache, 2018), neutrosophic refined set environment (Mondal, & Pramanik, 2015, Mondal, & Pramanik, 2015, Mondal, Pramanik, & Giri, 2018), neutrosophic hesitant fuzzy set environment (Biswas, Pramanik, & Giri, 2016a, Biswas, Pramanik, & Giri, 2016b, Biswas, Pramanik, & Giri, 2019), bipolar neutrosophic set environment (Dey, Pramanik, & Giri, 2016, Dey, Pramanik, & Giri, Smarandache, 2017, Pramanik, Dalapati, Alam, & Roy, 2018, Pramanik, Dalapati, Alam, & Roy, 2018, Pramanik, Dey, Smarandache, & Ye, 2018, Pramanik, Dey, & Smarandache, 2018, Pramanik, Dalapati, Alam, & Roy, 2018), neutrosophic cubic set environment (Pramanik, Dalapati, Alam, & Roy, 2017, Pramanik, Dalapati, Alam, Roy, & Smarandache, 2017, Pramanik, Dey, & Smarandache, 2017, Pramanik, Dalapati, Alam, & Roy, 2018, Dalapati, & Pramanik, 2018), triangular and trapezoidal neutrosophic set environment (Biswas, Pramanik, & Giri, 2016, Giri, Molla, & Biswas, 2018, Abdel-Basset, Mohamed, Hussien, Sangaiah, 2018, Biswas, Pramanik, & Giri, 2015, Biswas, Pramanik, & Giri, 2018), neutrosophic number environment (Pramanik, Roy, & Roy, 2016, Pramanik, & Dey, 2018, Mondal, Pramanik, & Smarandache, 2018, Pramanik, & Banerjee, 2018), conflict resolution (Pramanik, & Roy, 2014), image processing (Xu, Wang, Yang, & Jiang, 2018), medical diagnosis (Mondal, & Pramanik, 2015), social science (Pramanik, & Chackrabarti, 2013) etc.

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