Student assessment is a very important process in education, because it helps the instructor to determine student mistakes and to improve their performance by reforming his/her teaching plans. A hybrid assessment method using qualitative grades for evaluating student mathematical skills is presented in this work. The paper starts with the mathematical background which is necessary for the understanding of its contents. This includes basic information about fuzzy, neutrosophic and soft sets, and about grey numbers. It also includes a description of the use of the center of gravity (COG) defuzzification technique for assessing a student group’s quality performance. The COG technique is compared with the classical method of calculating the GP A index. The hybrid assessment method, which is based on all the previous concepts and processes, is developed next and the article closes with the final conclusion and some recommendations for future research. Manuscript profile

Learning, a universal process that all individuals experience, is a fundamental component of human cognition. It combines cognitive, emotional and environmental influences for acquiring or enhancing ones knowledge and skills. Volumes of research have been written about learning and many theories have been developed for the description of its mechanisms. The goal was to understand objectively how people learn and then develop teaching approaches accordingly. In this paper soft sets, a generalization of fuzzy sets introduced in 1999 by D. Molodstov as a new mathematical tool for dealing with the uncertainty in a parametric manner, are used for assessing student learning skills with the help of the Blooms taxonomy. Blooms taxonomy has been applied and is still applied by generations of teachers as a teaching tool to help balance assessment by ensuring that all orders of thinking are exercised in student learning. The innovative assessment method introduced in this paper is very useful when the assessment has qualitative rather than quantitative characteristics. A classroom application is also presented illustrating its applicability under real conditions. Manuscript profile

The present paper reviews and compares the main theories reported in the literature for managing the existing real life uncertainty by listing their advantages and disadvantages. Starting with a comparison of the bivalent logic (including probability) and fuzzy logic, proceeds to a brief description of the primary generalizations of fuzzy sets (FSs) including interval valued FSs, type-2 FSs, intuitionistic FSs, neutrosophic sets, etc. Alternative theories related to fuzziness are also examined including grey system theory, rough sets and soft sets. The conclusion obtained at the end of this discussion is that there is no ideal model for managing the uncertainty; it all depends upon the form, the available data and the existing knowledge about the problem under solution. The combination of all the existing models, however, provides a sufficient framework for efficiently tackling several types of uncertainty appearing in real life. Manuscript profile

Zadeh extended in 1965 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. Manuscript profile