**Similarity Measures of Quadripartitioned Single Valued Bipolar Neutrosophic Sets and Its Application in Multi-Criteria Decision Making Problems**

#### **Subhadip Roy <sup>1</sup> , Jeong-Gon Lee 2,\*, Anita Pal <sup>1</sup> and Syamal Kumar Samanta <sup>3</sup>**


Received: 9 May 2020; Accepted: 11 June 2020; Published: 16 June 2020

**Abstract:** In this paper, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.

**Keywords:** neutrosophic sets; quadripartitioned bipolar neutrosophic sets; similarity measure; decision making
