Use of Grey Numbers and Soft Sets as Assessment Tools

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Published: 2022-04-14

Page: 306-312

Michael Gr. Voskoglou *

Department of Mathematical Sciences, Graduate Technological Educational Institute of Western Greece, Patras, Greece.

*Author to whom correspondence should be addressed.


The traditional assessment methods are not suitable for use when assessment is performed under vague conditions, e.g. by using linguistic grades or expressions. Among a series of methods for assessment under fuzzy conditions, developed by the present author in earlier works, the most suitable for use seems to be the method utilizing grey numbers as tools. Recently, however, we also developed a method using soft sets for assessment in a parametric manner. These two methods are compared in this paper, listing their differences, advantages and disadvantages.

Keywords: Fuzzy set (FS), soft set, grey number (GN), fuzzy assessment methods, case-based reasoning (CBR)

How to Cite

Gr. Voskoglou, M. (2022). Use of Grey Numbers and Soft Sets as Assessment Tools. Asian Journal of Pure and Applied Mathematics, 4(1), 306–312. Retrieved from


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Voskoglou, M. Gr. Finite Markov chain and fuzzy logic assessment models: Emerging Research and Opportunities, – Amazon, Columbia, SC; 2017.

Voskoglou, M. Gr. Use of Grey Numbers for Evaluating a System’s Performance Under Fuzzy Conditions, in M. Khosrow-Pour (Ed.), Encyclopaedia of Information Science and Technology, Fifth Edition. IGI-Global, Hersey, PA, USA. 2020;315-331.

Voskoglou, M. Gr. A study of the problem solving process using fuzzy relation equations. NAUN Int. Journal of Mathematical Models and Methods in Applied Sciences. 2017;11:303-307.

Voskoglou, M. Gr. Assessing human-machine performance under fuzzy conditions. Mathematics. 2019;7, article 230.

Voskoglou, M. Gr. Application of soft sets to assessment processes. American Journal of Applied Mathematics and Statistics. 2022;10(1):1-3.

Zadeh LA. Fuzzy sets. Information and Control. 1965;8:338-353.

Zadeh LA. Outline of a new approach to the analysis of complex systems and decision processes, IEEE Transactions on Systems Man and Cybernetics. 1973;3:28-44.

Kosko B. Fuzzy thinking: The new science of fuzzy logic. NY, Hyperion; 1993.

Voskoglou, M. Gr. Fuzzy systems, extensions and relative theories, WSEAS Transactions on Advances in Engineering Education. 2019;16:63-69.

Deng J. Control problems of grey systems, Systems and Control Letters. 1982;288-294.

Deng J. Introduction to grey system theory. The Journal of Grey System. 1989;1:1-24.

Liu SF, Lin Y (Eds.). Advances in grey system research. Springer, Berlin – Heidelberg; 2010.

Moore RA, Kearfort RB, Clood MJ. Introduction to interval analysis. 2nd Printing, SIAM, Philadelphia; 1995.

Molodtsov D. Soft set theory-first results. Computers and Mathematics with Applications. 1999; 37(4-5):19-31.

Maji PK, Biswas R, Ray AR. Soft set theory. Computers and Mathematics with Applications. 2003;45:555-562.

Tripathy BK, Arun KR. Soft sets and its applications, in J.S. Jacob (Ed.), Handbook of Research on Generalized and Hybrid Set Structures and Applications for Soft Computing, IGI Global, Hersey, PA. 2016;65-85.

Kharal A, Ahmad B. Mappings on soft classes. New Mathematics and Natural Computation. 2011;7(3):471-481.

Voskoglou, M. Gr., Salem ABM. Analogy Based and Case Based Reasoning: Two Sides of the Same Coin, International Journal of Applications of Fuzzy Sets and Artificial Intelligence. 2014;4:5-51.