Interval Rough Neutrosophic TOPSIS Strategy for Multi-Attribute Decision Making

1. Introduction

Broumi et al. (2014) introduced rough neutrosophic set by combining the concept of rough set (Pawlak et al., 1982) and neutrosophic set (Smarandache et al., 1998). Neutrosophic sets have been widely applied in decision making problems (Biswas et la, 2014). So there is enormous chance of success of rough neutrosophic set in decision making. Several studies of rough neutrosophic sets have been reported in the literature. Mondal and Pramanik (2015) applied the concept of rough neutrosophic set in multi-attribute decision making (MADM) based on grey relational analysis. Pramanik and Mondal (2015) presented cosine similarity measure of rough neutrosophic sets and its application in medical diagnosis. Pramanik and Mondal (2015) also proposed some rough neutrosophic similarity measures namely Dice and Jaccard similarity measures of rough neutrosophic environment. Mondal and Pramanik (2015) proposed rough neutrosophic MADM based on rough score accuracy function. Pramanik and Mondal (2015) presented cotangent similarity measure of rough neutrosophic sets and its application to medical diagnosis. Pramanik and Mondal (2015) presented trigonometric Hamming similarity measure of rough neutrosophic sets. Mondal et al. (2019) presented rough neutrosophic aggregation operators for MADM.

Broumi and Smarandache defined interval rough neutrosophic set (IRNS) (Broumi et al., 2015) by combining the concept of rough set and interval neutrosophic set (Broumi et al., 2015). Pramanik et al. (2018) presented an MADM based on projection and bidirectional projection measures under IRNS environment. Pramanik et al. (2018) proposed an MADM based on trigonometric Hamming similarity measures in IRNS environment.

Hwang and Yoon (1981) introduced a technique for order preference by similarity to ideal solution(TOPSIS). Biswas et al. (2015) proposed TOPSIS strategy for MAGDM for under single valued neutrosophic environment. Chai and Liu (2013) developed TOPSIS strategy for MADM with interval neutrosophic set. Broumi et al. (Broumi et al., 2015) presented extended TOPSIS strategy for multiple attribute decision making based on interval neutrosophic uncertain linguistic variables. Pramanik et al. (2015) presented TOPSIS for singled valued soft expert set based MADM problems. Dey et al. (2015) presented TOPSIS for generalized neutrosophic soft MADM. Dey et al. (2016) proposed TOPSIS for solving MADM problems under bi-polar neutrosophic environment. Sahin et al.(2016) proposed another approach of TOPSIS strategy for supplier selection in neutrosophic environment. Elhassouny and Smarandache (Elhassouny e tal, 2016) briefly provided a survey on neutrosophic TOPSIS applications and its methodologies. Mondal et al. (2016) studied TOPSIS in rough neutrosophic environment. Interval rough TOPSIS is yet to appear in the literature. To fill the research gap, we extend the TOPSIS strategy in IRNS environment.

• Research gap:

MADM strategy using TOPSIS strategy in IRNS environment. The objectives of the paper are

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  To define Hamming distance measure and Euclidean distance measure between interval rough neutrosophic sets.

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  To develop a new MADM strategy based on the TOPSIS in IRNS environment.

  • Contributions:

• •

  In this paper, we propose Hamming distance measure and Euclidean distance measure under IRNS environment.

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  In this paper, we develop a new MADM strategy based on the TOPSIS method under IRNS environment.

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  We also present a numerical example to show the effectiveness and applicability of the proposed strategy.