Clustering Algorithm of Triple Refined Indeterminate Neutrosophic Set for Personality Grouping

Triple Refined Indeterminate Neutrosophic Set (TRINS) which is a case of the refined neutrosophic set was introduced in [27]. It provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world. More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into three, based on membership; as indeterminacy leaning towards truth membership (IT ), indeterminacy membership (I) and indeterminacy leaning towards false membership (IF ). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS). TRINS is better equipped at dealing indeterminate and inconsistent information, with more accuracy than SVNS and Double Refined Indeterminate Neutrosophic Set (DRINS), which fuzzy sets and Intuitionistic Fuzzy Sets (IFS) are incapable of. TRINS can be used in any place where the Likert scale is used, which is an advantage. Personality test usually make use of the Likert scale. Using the Open Extended Jung Type Scale test and TRINS, an indeterminacy based personality test was introduced and personality classification was done [27]. A generalized distance measure between TRINS and related distance matrix is defined, based on which a clustering algorithm is constructed. This article proposes a Triple Refined Indeterminate Neutrosophic Minimum Spanning Tree (TRIN-MST) clustering algorithm, to cluster the data represented by Triple Refined Indeterminate Neutrosophic information. Illustrative examples using the indeterminacy based personality test are given to exhibit the applications and effectiveness of the TRIN-MST clustering algorithm. Keywords—Personality test; Personality grouping, Neutrosophic Set, Triple Refined Neutrosophic Set (TRINS), TRIN-MST clustering algorithm