Hesitant Bipolar-Valued Neutrosophic Set: Formulation, Theory and Application

Azzah Awang,Mumtaz Ali,Lazim Abdullah

doi:10.1109/access.2019.2946985

Azzah Awang, Mumtaz Ali + Show 1 more

Open Access

https://doi.org/10.1109/access.2019.2946985

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Journal: IEEE Access	Publication Date: Jan 1, 2019
Citations: 10	License type: CC BY 4.0

Affiliation: Deakin University, Universiti Malaysia Terengganu

Abstract

This paper proposes a hesitant bipolar-valued neutrosophic set (HBVNS) based on the combination of bipolar neutrosophic sets and hesitant fuzzy sets. The proposed set generalizes the notions of fuzzy set, intuitionistic fuzzy set, hesitant fuzzy set, single-valued neutrosophic set, single-valued neutrosophic hesitant fuzzy set, bipolar fuzzy set and bipolar neutrosophic set. Further, we define the basic operational laws, union, intersection and complement for hesitant bipolar-valued neutrosophic elements (HBVNEs) and study its associated properties. Some relevant examples are also given to provide a better understanding of the proposed concept. Two aggregation operators are developed based on HBVNS which are the hesitant bipolar-valued neutrosophic weighted averaging (HBVNWA) and the hesitant bipolar-valued neutrosophic weighted geometric (HBVNWG). A decision making method is developed based on new sets and the proposed HBVNWA and HBVNWG operators. Finally, an illustrative example is given to show the applicability of the proposed decision making method. A comparative analysis with the existing methods is also provided.

Highlights

The neutrosophic set (NS) [1] is a set that is characterized by three independent functions which are the truthfulness, indeterminacy and falsity functions
NUMERICAL EXAMPLE we present an example adopted from Ye [31] where multi-attribute decision-making (MADM) problem under hesitant bipolar-valued neutrosophic environment is involved
By adopting the characteristics of the hesitant fuzzy sets, the proposed set provides a lenient way of judgmental process instead of apprehensive typical concrete judgments

Summary

INTRODUCTION

The neutrosophic set (NS) [1] is a set that is characterized by three independent functions which are the truthfulness, indeterminacy and falsity functions. The neutrosophic set which was first introduced based on the philosophical point of view has been extended to more approachable sets and theories that are applicable in the real multi-criteria decision-making problems [6]–[8]. Malik and Shabir [23] employed the bipolar information in its set development and introduced the rough fuzzy bipolar soft set with its application to the decision-making problem. Bipolarity and hesitancy are two different but complementary concepts that are created to model an easygoing but accurate judgments when dealing with the imprecision and uncertainty in bipolar neutrosophic information For this purpose, this paper attempts in developing a new set combining the bipolar neutrosophic set (BNS) and hesitant fuzzy set (HFS).

PRELIMINARIES

PROPOSED METHOD

NUMERICAL EXAMPLE

THE HBVNS DECISION MAKING PROCEDURE

CONCLUSION