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The present article focuses on two directions. First, a new fuzzy method using TFNs or TpFNs as tools is developed for evaluating a group's mean performance, when qualitative grades instead of numerical scores are used for assessing its members' individual performance. Second, a new technique is applied for solving linear programming problems with fuzzy coefficients. Examples are presented on real life situations connected to hyper connectivity and computing problems. Such examples illustrate the applicability of our methods in the modern practice of the forthcoming era of a new industrial revolution that will be characterized by the development of an advanced Internet of Things and energy and by the cyber-physical systems controlled through it. A discussion follows for the perspectives of future research on the subject and the article closes with the general conclusions.

Controllers are devices regulating the operation of other devices or systems. Fuzzy controllers analyze the input data in terms of variables which take on continuous values in the interval [0, 1]. Since fuzzy logic has the advantage of expressing the solution of the problems in the natural language, the use of fuzzy instead of traditional controllers makes easier the mechanization of tasks that have been already successfully performed by humans. In the present paper a theoretical fuzzy control model is developed for the braking system of autonomous vehicles, which are included among the most characteristic examples of Cyber-Physical Systems. For this, a simple geometric approach is followed using triangular fuzzy numbers as the basic tools.

In this work a combination is applied of triangular fuzzy numbers (TFNs) and of the centre of gravity (COG) defuzzification technique as means for assessing student skills in solving mathematical problems by analogy. A classroom experiment is also presented performed with students of the Graduate Technological Educational Institute (T. E. I.) of Western Greece, which illustrates our results in practice. In order to check the validity of the fuzzy assessment method, its outcomes in this experiment are compared to the corresponding outcomes of two traditional assessment methods of the bi-valued logic, the calculation of the mean value of student scores and the grade point average (GPA) index. The usefulness of the fuzzy approach becomes evident when linguistic grades only and not numerical scores are used for student assessment.

Fuzzy logic, due to its nature of characterizing the ambiguous cases with multiple values, offers rich resources for dealing with assessment situations, a fact that gave us several times in past the impulse to apply its principles for such kind of situations. Fuzzy Numbers (FNs) play a fundamental role in fuzzy mathematics, analogous to the role played by the ordinary numbers in classical mathematics. In the present paper, the author utilizes a combination of the Triangular and Trapezoidal FNs with the Center of Gravity Defuzzification technique for assessing human skills. The results are illustrated by suitable examples (student and basketball players' assessment), while the author's method is compared with assessment methods of the bivalent and fuzzy logic that has been already used in earlier works.

They appear often situations in a system’s operation characterized by a degree of vagueness and/or uncertainty. In the present paper, the author uses principles of fuzzy logic to develop a general model representing such kind of situations. They also present three alternative methods for measuring a fuzzy system’s effectiveness, including the use of its total possibilistic uncertainty, the classical Shannon’s entropy properly modified for use in a fuzzy environment and the “centroid” method in which the coordinates of the center of mass of the graph of the membership function involved provide an alternative measure of the system’s performance The advantages and disadvantages of each of the above methods are discussed and a combined use of them is suggested in obtaining the ideal profile of the system’s performance according to the user’s personal criteria of goals. An application of their general model is also developed for the Mathematical Modelling process illustrating the use of the author’s fuzzy model in practice.

Case-based reasoning (CBR) is a recent approach to problem solving and learning for computers and humans. In this paper, we introduce a finite Markov chain on the main steps of the CBR process. Using this approach we succeed in calculating the probabilities for the CBR process to be at a certain step in a certain phase of the solution of a real-world problem and we obtain a measure of the effectiveness of a CBR system in solving similar new problems. Next, the steps of the CBR process are represented as fuzzy subsets of a set of linguistic labels characterising the success of the CBR process in each of the above steps. Thus, we build a fuzzy model for the representation of a CBR system and we use the total possibilistic uncertainty as a measure of its effectiveness in solving new related problems. Examples are also given to illustrate our results.

We apply Markov chain process and through this we obtain several possibilities about the 'behaviour' of a group of solvers during the process of the problem-solving strategy, which may be useful to the teacher of mathematics in organizing and planning lectures. As an example, we study the progress in mathematics of the second term students of our institution. Finally, we describe.