Application of Fuzzy Numbers to the Assessment of CBR Systems

Michael Gr. Voskoglou

doi:10.6000/2371-1647.2016.02.05

Authors

Michael Gr. Voskoglou Department of Mathematical Sciences, School of Technological Applications, Graduate Technological Educational Institute (T. E. I.) of Western Greece, Meg. Alexandrou 1, 26334 Patras, Greece

DOI:

https://doi.org/10.6000/2371-1647.2016.02.05

Keywords:

Analogical Reasoning (AR), Case-Based Reasoning (CBR), Fuzzy Logic (FL), Centre of Gravity (COG) Defuzzification Technique, Triangular and Trapezoidal Fuzzy Numbers (TFNs and TpFNs), GPA index.

Abstract

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.

References

Holyoak KJ. The pragmatics of analogical transfer, in: Bower GH, Ed. The psychology of learning and motivation, Academic Press, New York, USA, 1985; Vol. 19: pp. 59-87. http://dx.doi.org/10.1016/s0079-7421(08)60524-1 DOI: https://doi.org/10.1016/S0079-7421(08)60524-1

Voskoglou MGr, Salem A-B. Analogy-Based and Case-Based Reasoning: Two Sides of the Same Coin. International Journal of Applications of Fuzzy Sets and Artificial Intelligence 2014; 4: 7-18.

Veloso MM, Carbonell J. Derivational analogy in PRODIGY. Machine Learning 1993; 10(3): 249-278. http://dx.doi.org/10.1023/A:1022686910523 DOI: https://doi.org/10.1023/A:1022686910523

Hall RP. Computational approaches to analogical reasoning: A comparative analysis. Artificial Intelligence 1989; 39(1): 39-120. http://dx.doi.org/10.1016/0004-3702(89)90003-9 DOI: https://doi.org/10.1016/0004-3702(89)90003-9

Kedar-Cabelli S. Analogy – from a unified perspective, in Helman DH, Ed. Analogical Reasoning, Kluwer Academic, 1988; pp. 65-103. DOI: https://doi.org/10.1007/978-94-015-7811-0_4

Silvana Q, Pedro B, Steen A. Proceedings of 8th Conference on Artificial Intelligence in Medicine in Europe (AIME), Springer, Cascais, Portugal, 2001.

Hinkle D, Toomey C. Applying Case-Based Reasoning to Manufacturing. AI Magazine 1995; 65-73.

Hans-Dieter, Salem AB, El Bagoury BM. Ideas of Case-Based Reasoning for Keyframe Technique, Proceedings of the 16th International Workshop on the Concurrency Specification and Programming, Logow, Warsa, Poland, 2007; pp. 100-106.

Rissland EL, Danials JJ. A Hybrid CBR-IR Approach to Legal Information Retrieval, Proceedings of the Fifth International Conference on Artificial Intelligence and Law (ICAIL-95), College Park, MD, 1995; pp. 52-61. http://dx.doi.org/10.1145/222092.222125 DOI: https://doi.org/10.1145/222092.222125

Salem A-BM, Baeshen N. Artificial Intelligence Methodologies for Developing Decision Aiding Systems, Proceedings of 5th International Conference, Integrating Technology and Human Decisions: Global Bridges into the 21st Century, Decision Sciences Institute, Athens, Greece, 1999; pp. 168-170.

Voskoglou MGr. Case-Based Reasoning: History, methodology and Development Trends, in Leeland, A. M. (Ed.), Case-Based Reasoning: Processes, Suitability and Applications, Nova Publishers, NY, 2011; Chapter 3: 59-76.

Voskoglou MGr. A stochastic model for Case-Based Reasoning, Journal of Mathematical Modelling and Application (Blumenau University, Brazil) 2010; 3: 33-59.

Voskoglou MGr. Fuzzy sets in Case-Based Reasoning, Fuzzy Systems and Knowledge Discovery, IEEE Computer Society, 2009; Vol. 6: pp. 252-256. DOI: https://doi.org/10.1109/FSKD.2009.667

Voskoglou MGr. Evaluating the Effectivness of a CBR System: A Fuzzy Logic Approach. American Journal of Computational and Applied Mathematics 2015; 5(2): 27-32.

Voskoglou MGr, Subbotin IYa. Fuzzy Models for Learning Assessment. Turkish Journal of Fuzzy Systems 2014; 5(2): 100-113. DOI: https://doi.org/10.13189/ujam.2014.020902

Zadeh LA. Fuzzy Sets. Information and Control 1965; 8: 338-353. http://dx.doi.org/10.1016/S0019-9958(65)90241-X DOI: https://doi.org/10.1016/S0019-9958(65)90241-X

Klir GJ, Folger TA. Fuzzy Sets, Uncertainty and Information, Prentice-Hall, London, 1988.

Kaufmann A, Gupta M. Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold Company, New York, 1991.

Sakawa M. Fuzzy Sets and Interactive Multiobjective Optimization, Plenum press, NY and London, 1993. http://dx.doi.org/10.1007/978-1-4899-1633-4 DOI: https://doi.org/10.1007/978-1-4899-1633-4

Theodorou J. Introduction to Fuzzy Logic, Tzolas Publications, Thessaloniki, Greece, 2010; (in Greek language).

Voskoglou M Gr. Use of the Triangular Fuzzy Numbers for Student Assessment (Revised), arXiv: 1507.03257, [cs.AI].

Wikipedia, Center of mass: A system of particles, retrieved on October 10, 2014 from: http://en.wikipedia.org/wiki/ Center_of_mass#A_system_of_particles

Swinburne.edu. Grade Point Average Assessment, retrieved on October 15, 2014 from: http://www.swinburne.edu.au/ studentadministration/assessment/gpa.html