The solution techniques for linear and quadratic equations with coefficients as Cauchy neutrosphic numbers

Abstract

Finding the roots of equations is an ancient art of mathematics. To deal with the physical phenomena with vague information, the relations and equalities have to be expressed in terms of uncertain coefficients. In this context, the theory of fuzzy equations attained huge attentions to model the phenomena under uncertainty. However, a Neutrosophic set (or numbers) has the capabilities to carry more structured sense about the imprecise data in the domain of uncertainty analysis. In this present paper, the solutions of the polynomial equations of one and two degree are bothered in a Neutrosophic arena. The whole study is organized on the basis of two distinct pockets of theoretical enrichment. The establishment of the mathematical frame of generalized bell-shaped Neutrosophic number (more specifically, Cauchy Neutrosophic number) and exploration of the arithmetic properties of the defined number are the initial objectives. Subsequently, the main goal of the paper is executed through the illustration of the proposed number as a domain of interpretation for the detailed manifestation of different solution approaches of linear and quadratic equations. In this paper, several possible solution techniques of linear and quadratic equations are theoretically addressed assuming the association of Neutrosphic data as the coefficients of the equations. The theoretical advancements are crystallized through the numerical simulation and graphical visualizations in the every pocket of discussions. A problem of investment firm is viewed in the light of Neutrosophic philosophy and is solved as an aptly fitted physical scenario of the proposed theory.