Fuzzy relations, Possibility theory, Measures of uncertainty, Mathematical modeling.
نویسنده
چکیده مقاله:
A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzzy sets in a set of linguistic labels indicating the degree of a student's success in each of these stages. We use the total possibilistic uncertainty on the ordered possibility distribution of all student profiles as a measure of the students' modeling capacities and illustrate our results by application to a classroom experiment.
منابع مشابه
fuzzy relations, possibility theory, measures of uncertainty, mathematical modeling.
a central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. in this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. the main stages of the modeling process are represented as fuzz...
متن کاملFuzzy Matrix Theory and Infertility Management – Measures Follicle Fertilization Possibility
In this paper, we are exploring fuzzy logic in medical diagnosis of infertility where our aim is to predict the possibility of total fertility using fuzzy matrix theory by measuring the follicle fertilization possibility based on follicle size. Also developed a computer program to calculate fuzzy matrix based on MaxMin rule using JavaScript.
متن کاملUncertainty measures for fuzzy relations and their applications
Relations and relation matrices are important concepts in set theory and intelligent computation. Some general uncertainty measures for fuzzy relations are proposed by generalizing Shannon’s information entropy. Then, the proposed measures are used to calculate the diversity quantity of multiple classifier systems and the granularity of granulated problem spaces, respectively. As a diversity me...
متن کاملFuzzy Measures on Finite Scales as Families of Possibility Measures
We show that any capacity or fuzzy measure ranging on a qualitative scale can be viewed both as the lower bound of a set of possibility measures, and the upper bound of a set of necessity measures. An algorithm is provided to compute the minimal set of possibility measures dominating a given capacity. This algorithm relies on the representation of the capacity by means of its qualitative Moebiu...
متن کاملR-bounded Fuzzy Measures Are Equivalent to Ε-possibility Measures
Traditional probabilistic description of uncertainty is based on additive probability measures. To describe nonprobabilistic uncertainty, it is therefore reasonable to consider non-additive measures. An important class of non-additive measures are possibility measures, for which μ(A ∪ B) = max(μ(A), μ(B)). In this paper, we show that possibility measures are, in some sense, universal approximat...
متن کاملMeasures of uncertainty mathematical programming and physics
The first section gives the measure of uncertainty given by Shannon (1948) and the generalizations thereof by Schvitzenberger (1954), Kullback (1959), Renyi (1961,1965), Kapur (1967, 1968), and Rathie (1970). It gives some postulates characterizing Shannon's entropy, Renyi's entropy of order a and our entropy of order a and type P. It also gives some properties of this most general type of entr...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 8 شماره 3
صفحات 23- 33
تاریخ انتشار 2011-10-17
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023