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“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

Neutrosophic set has the ability to handle uncertain, incomplete, inconsistent, indeterminate information in a more accurate way. In this paper, we proposed a neutrosophic recommender system to predict the diseases based on neutrosophic set which includes single-criterion neutrosophic recommender system (SC-NRS) and multi-criterion neutrosophic recommender system (MC-NRS). Further, we investigated some algebraic operations of neutrosophic recommender system such as union, complement, intersection, probabilistic sum, bold sum, bold intersection, bounded difference, symmetric difference, convex linear sum of min and max operators, Cartesian product, associativity, commutativity and distributive. Based on these operations, we studied the algebraic structures such as lattices, Kleen algebra, de Morgan algebra, Brouwerian algebra, BCK algebra, Stone algebra and MV algebra. In addition, we introduced several types of similarity measures based on these algebraic operations and studied some of their theoretic properties. Moreover, we accomplished a prediction formula using the proposed algebraic similarity measure. We also proposed a new algorithm for medical diagnosis based on neutrosophic recommender system. Finally to check the validity of the proposed methodology, we made experiments on the datasets Heart, RHC, Breast cancer, Diabetes and DMD. At the end, we presented the MSE and computational time by comparing the proposed algorithm with the relevant ones such as ICSM, DSM, CARE, CFMD, as well as other variants namely Variant 67, Variant 69, and Varian 71 both in tabular and graphical form to analyze the efficiency and accuracy. Finally we analyzed the strength of all 8 algorithms by ANOVA statistical tool., Comment: Keywords: Medical diagnosis, neutrosophic set, neutrosophic recommender system, non-linear regression model

Neutrosophic set is a generalization of classical set, fuzzy set, and intuitionistic fuzzy set by employing a degree of truth (T), a degree of indeterminacy (I), and a degree of falsehood (F) associated with an element of the dataset. One of the most essential problems is studying set-theoretic operators in order to be applied to practical applications. Developing Matlab toolboxes for computing the operational matrices in neutrosophic environments is essential to gain more widely-used of neutrosophic algorithms. In this paper, we propose some computing procedures in Matlab for neutrosophic operational matrices, especially i) computing the single-valued neutrosophic matrix; ii) determining complement of a single-valued neutrosophic matrix; iii) computing max-min-min and min-max-max of two single-valued neutrosophic matrices; v) computing power of a single-valued neutrosophic matrix; vi) computing additional operation and subtraction of two single-valued neutrosophic matrices; and ix) computing transpose of a single-valued neutrosophic matrix. Numerical examples are given to illustrate their applicability.