Computing the Greatest X-eigenvector of Fuzzy Neutrosophic Soft Matrix

Abstract

A Fuzzy Neutrosophic Soft Vector(FNSV) x is said to be a Fuzzy Neutrosophic Soft Eigenvector(FNSEv) of a square max-min Fuzzy Neutrosophic Soft Matrix (FNSM) A if $A\otimes x=x$. A FNSEv x of A is called the greatest X-FNSEv of A if $x \in X=\{x:\underline{x}\leq x\leq \overline{x}\}$ and $y\leq x$ for each FNSEv $y\in X$. A max-min FNSM A is called strongly X-robust if the orbit $x,A \otimes x,A^{2}\otimes x,...$ reaches the greatest X-FNSEv with any starting FNSV of X. We suggest an $O(n^{3})$ algorithm for computing the greatest X-FNSEv of A and study the strong X-robustness. The necessary and sufficient condition for strong X-robustness are introduced and an efficient algarithm for verifying these conditions is described.