Application of Grey Numbers and Neutrosophic Sets to Assessment Processes

Zadeh extended in ۱۹۶۵ crisp sets to the concept of fuzzy set (FS) on the purpose of tackling mathematically the partial truths and the definitions with no clear boundaries. In a later stage FSs were extensively used for tackling the existing in the real world uncertainty. Neutrosophic sets (NSs) are extensions of FSs in which each element of the universal set is characterized, apart from Zadeh’s membership degree, by the degrees of non-membership and indeterminacy. Grey numbers (GNs) are real numbers with known range, represented by a closed real interval, but with unknown exact value. GNs and NSs are used in this paper as tools for assessment processes under fuzzy conditions. The use of GNs enables the evaluation of the mean performance of a group of objects when qualitative grades (linguistic expressions) are used for the individual assessment of its members. The use of NSs, on the other hand, is useful for assessing the overall performance of a group, when one, due to incomplete assessment data, is not sure about the exactness of the grades assigned to its members. It is concluded that the suitable combination of two or more theories related to FSs give better assessment outcomes in general. Examples are also presented on student assessment illustrating our results.

Keywords:

fuzzy set , Neutrosophic set , Grey system , Grey Number , Assessment under Fuzzy Conditions