  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.
