This survey is focussed on distance learning studies, where there can be met a lot of technical obstacles, which creates complications in decision making. To get an ideal solution for these kinds of problems, the Fuzzy TOPSIS (Technique for Order Preference by Similarities to Ideal Solution) is one of the best solutions. Therefore, this paper presents the distance learning quality assessment surveys when the Fuzzy AHP (Analytic Hierarchy Process) and TOPSIS methods are used. Research results describe the application of the Fuzzy AHP—TOPSIS hybrid method. MCDM (Multi-Criteria Decision Making) programs with MATLAB (R2020b) mathematical package were written to calculate the evaluation results for three distance learning courses. In the practical implementation of the proposed distance learning module evaluation methodology, the experts’ evaluation method was applied. Thirty-four judges were chosen with specific knowledge and skills and with very different competencies to assess three alternatives by fourteen criteria. Following the experts’ evaluation, a statistical analysis method was used to process the data. After applying the complex evaluation, the comparative analysis method was used to summarize the obtained results. This work further provides useful guidelines for the development of an easily understandable hierarchy of criteria model that reflects the main goal of study quality assessment.

A Krasner hyperring (for short, a hyperring) is a generalization of a ring such that the addition is multivalued and the multiplication is as usual single valued and satisfies the usual ring properties. One of the important subjects in the theory of hyperrings is the study of polynomials over a hyperring. Recently, polynomials over hyperrings have been studied by Davvaz and Musavi, and they proved that polynomials over a hyperring constitute an additive-multiplicative hyperring that is a hyperstructure in which both addition and multiplication are multivalued and multiplication is distributive with respect to the addition. In this paper, we first show that the polynomials over a hyperring is not an additive-multiplicative hyperring, since the multiplication is not distributive with respect to addition; then, we study hyperideals of polynomials, such as prime and maximal hyperideals and prove that every principal hyperideal generated by an irreducible polynomial is maximal and Hilbert’s basis theorem holds for polynomials over a hyperring.

In this paper we will introduce the notion of coprime hyperideals in multiplicative hyperrings and we will show some properties of them. Then we introduce the notion of hyperring of fractions generated by a multiplicative hyperring and then we will show some properties of them.