Neutrosophic sets and numbers are extensions of classical set theory and real numbers, respectively, introduced by Florentin Smarandache in 1995 to address indeterminate, vague, or imprecise information. Neutrosophic numbers are defined by three components: truth-membership, indeterminacy-membership, and falsity-membership degrees, each ranging from 0 to 1. These components encapsulate the degrees of truth, indeterminacy, and falsity associated with a statement or quantity. Real neutrosophic numbers are a subset of neutrosophic numbers where the truth-membership degree is 1. This simplifies calculations and interpretations, making them closer to classical real numbers while still accounting for indeterminacy and falsity. The Gauss elimination method, when applied to neutrosophic linear equations, involves solving systems of linear equations where the coefficients and constants are represented as real neutrosophic numbers. Adapting traditional Gaussian elimination incorporates the uncertainties and indeterminacies inherent in neutrosophic data, ensuring more robust solutions in uncertain contexts. Overall, neutrosophic sets and numbers, along with their operations and applications such as solving neutrosophic linear equations offer a versatile framework for managing incomplete, imprecise, or contradictory information, making them highly valuable in decision-making and computational sciences.
Fuzzy system of equations, Neutrosophic numbers, Gauss-elimination method
