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Maji et al. introduced in 2002 a method of parametric decision making using soft sets as tools and representing their tabular form as a binary matrix. In cases, however, where some or all of the parameters used for the characterization of the elements of the universal set are of fuzzy texture, their method does not give always the best decision making solution. In order to tackle this problem, we modified in earlier works the method of Maji et al. by replacing the binary elements in the tabular form of the corresponding soft set either by grey numbers or by triangular fuzzy numbers. In this work, in order to tackle more efficiently cases in which the decision maker has doubts about the correctness of the fuzzy/qualitative characterizations assigned to some or all of the elements of the universal set, we replace the binary elements of the tabular form by neutrosophic triplets. Our new, neutrosophic decision making method is illustrated by an application concerning the choice of a new player by a soccer club., Comment: 9 pages, 4 tables

The present paper comes across the main steps that laid from Zadeh's fuzziness ana Atanassov's intuitionistic fuzzy sets to Smarandache's indeterminacy and to Molodstov's soft sets. Two hybrid methods for assessment and decision making respectively under fuzzy conditions are also presented through suitable examples that use soft sets and real intervals as tools. The decision making method improves an earlier method of Maji et al. Further, it is described how the concept of topological space, the most general category of mathematical spaces, can be extended to fuzzy structures and how to generalize the fundamental mathematical concepts of limit, continuity compactness and Hausdorff space within such kind of structures. In particular, fuzzy and soft topological spaces are defined and examples are given to illustrate these generalizations., Comment: 15 pages, 2 figures, 3 Tables, 30n references

A new fuzzy method is developed using triangular/trapezoidal fuzzy numbers for evaluating a group's mean performance, when qualitative grades instead of numerical scores are used for assessing its members' individual performance. Also, a new technique is developed for solving Linear Programming problems with fuzzy coefficients and everyday life applications are presented to illustrate our results., Comment: 19 pages, 3 figures

Fuzzy relation equations (FRE)are associated with the composition of binary fuzzy relations. In the present work FRE are used as a tool for studying the process of learning a new subject matter by a student class. A classroom application and other csuitable examples connected to the student learning of the derivative are also presented illustrating our results and useful conclusions are obtained., Comment: 8 pages, 1 Table

The theory of grey systems plays an important role in science,engineering and in the everyday life in general for handling approximate data. In the present paper grey numbers are used as a tool for assessing with linguistic expressions the mean performance of a group of objects participating in a certain activity. Two applications to student and football player assessment are also presented illustrating our results.

The Center of Gravity (COG) method is one of the most popular defuzzification techniques of fuzzy mathematics. In earlier works the COG technique was properly adapted to be used as an assessment model (RFAM)and several variations of it (GRFAM, TFAM and TpFAM)were also constructed for the same purpose. In this paper the outcomes of all these models are compared to the corresponding outcomes of a traditional assessment method of the bi-valued logic, the Grade Point Average (GPA) Index. Examples are also presented illustrating our results., Comment: 11 pages, 5 figures, 2 tables

The authors apply the Generalized Rectangular Model to assessing critical thinking skills and its relations with their language competency.

Markov Chains offer ideal conditions for the study and mathematical modelling of a certain kind of situations depending on random variables. The basic concepts of the corresponding theory were introduced by Markov in 1907 on coding literary texts. Since then, the Markov Chain theory was developerd by a number of leading mathematicians, such as Kolmogorov, Feller etc. However, only from the 1960's the importance of this theory to the Natural, Social and most of the other Applied Sciences has been recognized. In this review paper we present applications of finite Markov Chains to management problems, which can be solved, as most of the problems concerning applications of Markov chains in general do, by distinguishing between two types of Chains, the Ergodic and the Absorbing ones., Comment: 10 pages, 1 figure, 18 references

In an earlier work we have used the Triangular Fuzzy Numbers (TFNs)as an assessment tool of student skills.This approach led to an approximate linguistic characterization of the students' overall performance, but it was not proved to be sufficient in all cases for comparing the performance of two different student groups, since tywo TFNs are not always comparable. In the present paper we complete the above fuzzy assessment approach by presenting a defuzzification method of TFNS based on the Center of Gravity (COG) technique, which enables the required comparison. In addition we extend our results by using the Trapezoidal Fuzzy Numbers (TpFNs) too, which are a generalization of the TFNs, for student assessment and we present suitable examples illustrating our new results in practice., Comment: 9 pages, 2 figures

Analogy-Based (or Analogical) and Case-Based Reasoning (ABR and CBR) are two similar problem solving processes based on the adaptation of the solution of past problems for use with a new analogous problem. In this paper we review these two processes and we give some real world examples with emphasis to the field of Medicine, where one can find some of the most common and useful CBR applications. We also underline the differences between CBR and the classical rule-induction algorithms, we discuss the criticism for CBR methods and we focus on the future trends of research in the area of CBR., Comment: 47 pages, 2 figures, 1 table, 124 references

Contract bridge occupies nowadays a position of great prestige being, together with chess, the only mind games officially recognized by the International Olympic Committee. In the present paper an innovative method for assessing the total performance of bridge- players' belonging to groups of special interest(e.g. different bridge clubs during a tournament, men and women, new and old players, etc) is introduced, which is based on principles of fuzzy logic. For this, the cohorts under assessment are represented as fuzzy subsets of a set of linguistic labels characterizing their performance and the centroid defuzzification method is used to convert the fuzzy data collected from the game to a crisp number. This new method of assessment could be used informally as a complement of the official bridge-scoring methods for statistical and other obvious reasons. Two real applications related to simultaneous tournaments with pre-dealt boards, organized by the Hellenic Bridge Federation, are also presented, illustrating the importance of our results in practice., Comment: 6 pages, 2 figures, 2 tables

Case-Bsed Reasoning (CBR) is a recent theory for problem-solving and learning in computers and people.Broadly construed it is the process of solving new problems based on the solution of similar past problems. In the present paper we introduce an absorbing Markov chain on the main steps of the CBR process.In this way we succeed in obtaining the probabilities for the above process to be in a certain step at a certain phase of the solution of the corresponding problem, and a measure for the efficiency of a CBR system. Examples are given to illustrate our results., Comment: 7 pages, 2 figures

Reasoning, the most important human brain operation, is charactrized by a degree fuzziness. In the present paper we construct a fuzzy model for the reasoning process giving through the calculation of the possibilities of all possible individuals' profiles a quantitative/qualitative view of their behaviour during the above process and we use the centroid defuzzification technique for measuring the reasoning skills. We also present a number of classroom experiments illustrating our results in practice., Comment: 16 pages, 3 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:1212.2614

We use princiles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy. Further, we introduce three altenative measures of a fuzzy system's effectiveness connected to the above model. An applcation is also developed for the Mathematical Modelling process illustrating our results., Comment: 9 pages, 3 figures, 1 table

Computational thinking is a new problem soling method named for its extensive use of computer science techniques. It synthesizes critical thinking and existing knowledge and applies them in solving complex technological problems. The term was coined by J. Wing, but the relationship between computational and critical thinking, the two modes of thiking in solving problems, has not been yet learly established. This paper aims at shedding some light into this relationship. We also present two classroom experiments performed recently at the Graduate Technological Educational Institute of Patras in Greece. The results of these experiments give a strong indication that the use of computers as a tool for problem solving enchances the students' abilities in solving real world problems involving mathematical modelling. This is also crossed by earlier findings of other researchers for the problem solving process in general (not only for mathematical problems)., Comment: 19 pages, 2 figures

Two are the objectives of the present paper. First we study properties of a differentially simple commutative ring R with respect to a set D of derivations of R. Among the others we investigate the relation between the D-simplicity of R and that of the local ring RP with respect to a prime ideal P of R and we prove a criterion about the D- simplicity of R in case where R is a 1-dimensional (Krull dimension) finitely generated algebra over a field of characteristic zero and D is a singleton set. The above criterion was quoted without proof in an earlier paper of the author. Second we construct a special class of iterated skew polynomial rings defined with respect to finite sets of derivations of a ring R (not necessarily commutative) commuting to each other. The important thing in this class is that, if R is a commutative ring, then its differential simplicity is the necessary and sufficient condition for the simplicity of the corresponding skew polynomial ring. Key-Words- Derivations, Differentially simple rings, Finitely-generated algebras, Iterated skew polynomial rings, Simple rings., Comment: 9 pages

In this paper we develop a fuzzy model for the description of the process of Analogical Reasoning by representing its main steps as fuzzy subsets of a set of linguistic labels characterizing the individuals' performance in each step and we use the Shannon- Wiener diversity index as a measure of the individuals' abilities in analogical problem solving. This model is compared with a stochastic model presented in author's earlier papers by introducing a finite Markov chain on the steps of the process of Analogical Reasoning. A classroom experiment is also presented to illustrate the use of our results in practice., Comment: 10 pages, 1 Table

The article discusses some applications of fuzzy logic ideas to formalizing of the Case-Based Reasoning (CBR) process and to measuring the effectiveness of CBR systems