Fuzzy Methods for Assessment and Decision Making presents the assessment of learning and problem-solving skills with qualitative grades. These methods are outcomes of the author’s research work on the subject for more than 20 years. In particular, a hybrid assessment model uses the Center of Gravity (COG) defuzzification technique, closed real intervals (grey numbers), neutrosophic sets, and soft sets as tools. The book starts with the basic mathematical background that is needed for an understanding of its contents. The Rectangular Fuzzy Assessment Model (RFAM) of Subbotin and Voskoglou is presented next, the outcomes of which are compared to those of the GPA index.
The book presents innovative fuzzy assessment methods, enabling readers to assess the mean and quality performance of learning or problem-solving skills of a group of students when qualitative (linguistic) grades are used for this purpose. In the case of using linguistic grades for the assessment of a group’s skills, the classical method of calculating the mean value of the (numerical) grades cannot be applied. Also, no safe conclusions can be obtained on comparing the quality performance of two groups when the values of their GPA index are equal.
1. 1. An introduction to assessment decision-making and to control systems - p. 1 2. 2. Probability, fuzzy sets, and soft computing - p. 15 3. 3. Models for the assessment of a system's effectiveness - p. 45 4. 4. Applications of fuzzy numbers to assessment control and linear programming - p. 63 5. 5. Using gray numbers as tools for assessment and linear programming - p. 91 6. 6. Intuitionistic fuzzy, neutrosophic, and soft assessment processes - p. 107 7. 7. Use of fuzzy relation equations as assessment tools - p. 127 8. 8. Fermatean neutrosophic cognitive maps to explore challenges in digital teaching of Mathematics - p. 141 9. 9. Decision making in fuzzy environments - p. 155 10. 10. Enforcing BHARAT-v2 in tree soft modelling for appraising E-mobility hurdles - p. 165 11. 11. Applications of finite markov chains to assessment and decision making - p. 181 12. List of symbols and abbreviations - p. 181 13. 1 Finite Markov Chains - p. 181 14. 2 The basic model - p. 182 15. 3 Ergodic Markov Chains - p. 184 16. 4 Absorbing Markov Chains - p. 186 17. 5 Applications of Markov Chains to assessment processes - p. 190 18. 6 An absorbing Markov chain model for decision making - p. 199 19. 7 Final conclusions - p. 201 20. 8 Appendix - p. 202 21. Index - p. 205
Fuzzy Methods for Assessment and Decision Making presents the assessment of learning and problem-solving skills with qualitative grades. These methods are outcomes of the author’s research work on the subject for more than 20 years. In particular, a hybrid assessment model uses the Center of Gravity (COG) defuzzification technique, closed real intervals (grey numbers), neutrosophic sets, and soft sets as tools. The book starts with the basic mathematical background that is needed for an understanding of its contents. The Rectangular Fuzzy Assessment Model (RFAM) of Subbotin and Voskoglou is presented next, the outcomes of which are compared to those of the GPA index.
The book presents innovative fuzzy assessment methods, enabling readers to assess the mean and quality performance of learning or problem-solving skills of a group of students when qualitative (linguistic) grades are used for this purpose. In the case of using linguistic grades for the assessment of a group’s skills, the classical method of calculating the mean value of the (numerical) grades cannot be applied. Also, no safe conclusions can be obtained on comparing the quality performance of two groups when the values of their GPA index are equal.
1. 1. An introduction to assessment decision-making and to control systems - p. 1 2. 2. Probability, fuzzy sets, and soft computing - p. 15 3. 3. Models for the assessment of a system's effectiveness - p. 45 4. 4. Applications of fuzzy numbers to assessment control and linear programming - p. 63 5. 5. Using gray numbers as tools for assessment and linear programming - p. 91 6. 6. Intuitionistic fuzzy, neutrosophic, and soft assessment processes - p. 107 7. 7. Use of fuzzy relation equations as assessment tools - p. 127 8. 8. Fermatean neutrosophic cognitive maps to explore challenges in digital teaching of Mathematics - p. 141 9. 9. Decision making in fuzzy environments - p. 155 10. 10. Enforcing BHARAT-v2 in tree soft modelling for appraising E-mobility hurdles - p. 165 11. 11. Applications of finite markov chains to assessment and decision making - p. 181 12. List of symbols and abbreviations - p. 181 13. 1 Finite Markov Chains - p. 181 14. 2 The basic model - p. 182 15. 3 Ergodic Markov Chains - p. 184 16. 4 Absorbing Markov Chains - p. 186 17. 5 Applications of Markov Chains to assessment processes - p. 190 18. 6 An absorbing Markov chain model for decision making - p. 199 19. 7 Final conclusions - p. 201 20. 8 Appendix - p. 202 21. Index - p. 205
