Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives

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 reference

A Stochastic Model for the Process of Learning

A Markov chain is introduced to the major steps of the process of learning a subject matter by a group of students in the classroom, in order to obtain a mathematical representation of the above process. A classroom experiment for learning mathematics is also presented illustrating the applicability of our results in practice

Application of Fuzzy Numbers to the Assessment of CBR Systems

Case-Based Reasoning (CBR) is the process of solving problems by properly adapting the solutions of similar (analogous) problems solved in the past. As an Artificial Intelligence's method CBR has become recently very popular to information managers increasing the effectiveness and reducing the cost of various human activities by substantially automated processes, such as diagnosis, scheduling, design, etc. In this paper a combination is utilized of the Centre of Gravity defuzzification technique and of the Fuzzy Numbers for assessing the effectiveness of CBR systems. Our new fuzzy assessment approach is validated by comparing its outcomes in our applications with the corresponding outcomes of two traditional assessment methods, the calculation of the mean values and the GPA index