Triple Refined Indeterminate Neutrosophic Sets for personality classification

Personality tests are most commonly objective type, where the users rate their behaviour. Instead of providing a single forced choice, they can be provided with more options. A person may not be in general capable to judge his/her behaviour very precisely and categorize it into a single category. Since it is self rating there is a lot of uncertain and indeterminate feelings involved. The results of the test depend a lot on the circumstances under which the test is taken, the amount of time that is spent, the past experience of the person, the emotion the person is feeling and the person's self image at that time and so on. In this paper Triple Refined Indeterminate Neutrosophic Set (TRINS) which is a type of the refined neutrosophic set is introduced. It provides the additional possibility to represent with sensitivity and accuracy the imprecise, uncertain, inconsistent and incomplete 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 (I T ), indeterminacy membership (I) and indeterminacy leaning towards false membership (I F ). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS), but it is a particular category of the refined neutrosophic set (where each T, I, F can be refined into T 1 , T 2 , … ; I 1 , I 2 , … ; F 1 , F 2 , … ). 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. Personality test usually make use of the Likert scale. In this paper a indeterminacy based personality test is introduced for the first time. Here personality classification is made based on the Open Extended Jung Type Scale test and TRINS.