fuzzy relations, possibility theory, measures of uncertainty, mathematical modeling.
Authors
abstract
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.
similar resources
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...
full textFuzzy 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.
full textUncertainty 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...
full textFuzzy 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...
full textR-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...
full textMeasures 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...
full textMy Resources
Save resource for easier access later
Journal title:
iranian journal of fuzzy systemsPublisher: university of sistan and baluchestan
ISSN 1735-0654
volume 8
issue 3 2011
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023