Gaussian single-valued neutrosophic numbers and its application in multi-attribute decision making

Abstract

The fuzzy set and intuitionistic fuzzy set are two useful mathematical tool for dealing with impression
and uncertainty. However sometimes these theories may not suffice to model indeterminate and inconsistent information encountered in real world. To overcome this insufficiency, neutrosophic set theory and single-valued neutrosophic
set (SVNS) theory which is useful in practical applications, were proposed. Many researchers have studied on singlevalued triangular neutrosophic numbers and single-valued trapezoidal neutrosophic numbers. In this paper, concepts
of Gaussian single-valued neutrosophic number (GSVNN), α-cut of a GSVNN and parametric form of a GSVNN
are defined, and based on α-cuts of GSVNNs, arithmetic operations for GSVNNs are defined. Also, some results
are obtained related to arithmetic operations of GSVNNs. Furthermore, a decision making algorithm is developed by
using GSVNNs operations, and its an application in medical diagnosis is given.