Soft n-Valued Neutrosophic Algebraic Structures

Soft n-Valued Neutrosophic Algebraic Structures

We can generalize the soft neutrosophic algebraic structures to soft n-valued neutrosophic algebraic structures. Let's consider a universe of discourse U and let P(U) be the set of all n-valued neutrosophic sets included in U. Let's A be a set of attributes. The collection (f, A), where f: A→ P (U) is a soft n-valued neutrosophic set. For example, let U = {x, y, z, w} a set of houses, and A = {quality, price} a set of attributes. One has: f(quality)= <x; (T1, T2, T3; I1; F1, F2)>, where T1 = very high quality, T2 = high quality, T3 = medium quality; I1 = indeterminate quality; and F1 = low quality, F2 = very low quality. With T1 + T2 + T3 + I1 + F1 + F2 ∊[0, 6], since 3 + 1 + 2 = 6. Similarly for price: f(price)= <x; (T1, T2, T3; I1; F1, F2)>, where T1 = very high price, T2 = high price, T3 = medium price; I1 = indeterminate price; and F1 = low price, F2 = very low price. As numerical example, we may consider: f(quality) = {<x; (0.4, 0.5, 0.6; 0.1; 0.9, 0.3)>, <y; (0.0, 0.1, 0.9; 0.5; 0.8, 0.2)>, <z; (0.6, 0.0, 0.9; 0.7; 0.5, 0.5)>, <w; (0.1, 0.3, 0.6; 0.8; 0.3, 0.1)>} and f(price) = {<x; (0.3, 0.1, 0.5; 0.4; 0.2, 0.5)>, <y; (0.6, 0.6, 0.1; 0.5; 0.1, 0.9)>, <z; (0.3, 0.8, 0.2; 0.2; 0.5, 0.4)>, <w; (0.7, 0.2, 0.1; 0.2; 0.5, 0.9)>}.