Predictions with Intuitionistic Fuzzy Soft Sets
This paper is applying methods from soft sets theory for timely identification of students who are in danger to fail their exam in a particular subject. The work exploits the advantages of soft sets compare to fuzzy logics and statistical methods. While m
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Predictions with Intuitionistic Fuzzy Soft Sets Sylvia Encheva
Abstract This paper is applying methods from soft sets theory for timely identification of students who are in danger to fail their exam in a particular subject. The work exploits the advantages of soft sets compare to fuzzy logics and statistical methods. While most statistical methods require large data sets and perform well in stochastically stable environments, the ones we have been addressing in this paper can give results within a very small data sets and can accommodate additional information derived from later experiments. Keywords Soft sets
Uncertainties Decision making
372.1 Introduction Molodtsov introduced the theory of soft sets [8], which can be seen as a new mathematical approach to vagueness, [1]. Soft set theory is very useful in the presence of uncertainties since it does not require special functions like in fuzzy set theory. The choice of convenient parametrization strategies such as real numbers, functions, and mappings makes soft-set theory very convenient and practicable for decision making applications, [9]. Correlations between midterm tests outcomes and exam results derived from available data can be summarized and applied on new cases. As pointed in [11] similar inductions can be found in statistical reasoning and are more or less unavoidable if a model is to be applied in real life situations. Therefore, all conclusions derived from sample data are true only with respect to that set of data,
S. Encheva (&) Stord/Haugesund University College, Bjørnsong. 45 5528 Haugesund, Norway e-mail: [email protected]
S. Li et al. (eds.), Frontier and Future Development of Information Technology 2935 in Medicine and Education, Lecture Notes in Electrical Engineering 269, DOI: 10.1007/978-94-007-7618-0_372, Springer Science+Business Media Dordrecht 2014
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S. Encheva
and, they should be treated as uncertain hypotheses about properties of a large universe, [11]. In our case preliminary data on students taking intermediate tests and final exams is extracted from already completed courses. New students who experience problems with these topics (i.e. failed on the corresponding intermediate tests) are to receive special attention. They are offered extra tutorials in digital form or face to face tutoring when ever needed. Contents providers can use tests outcomes for further adjustment of the related teaching materials.
372.2 Preliminaries In the soft set theory, the initial description of the object has an approximate nature, [9]. Notions regarding soft sets follow [1]. Let U be an initial universe set and EU be the set of all possible parameters under consideration with respect to U. The power set of U (i.e., the set of all subsets of U) is denoted by PðU Þ and A E. Intuitionistic fuzzy sets were introduced in [3] and further developed by many authors, see f. ex. [2, 5, 6, 10]. A pair ðF; AÞ is called a soft set over U, where F is a mapping given by F : A ! PðU Þ. A soft set over U is a parametrized family of subsets of the univers
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