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## Rock mechanics applications of fuzzy sets theory - OnePetro

Skip to main content. Title An application of fuzzy logic to prospect theory. Abstract This paper is a Master's thesis paper in Applied Mathematics. Included in Applied Mathematics Commons. The representation of the stimulus input is relied upon the individual's ability to use content of his memory in order to find information that will facilitate a solution development.

Learning consists of developing an appropriate number of interpretations of the various input information and generalizing the respective interpretations to a variety of situations. When knowledge becomes substantial, much of the process involves categorization, i. Thus the individual becomes able to relate new information to his knowledge structures. Obviously, from the point of view of the teacher, there exists an uncertainity about the degree of acquisition of each state of the process as it has been described in the previous paragraph from his students, a fact which gave us the hint to introduce the fuzzy sets theory in order to achieve a mathematical representation of the process of learning in the classroom.

At this point notice that a fuzzy relationship, like the classical ones, can be considered as a fuzzy set of tuples each one of which posseses a degree of membership included between 0 and 1. The fuzzy relation R represents all the possible profiles overall states of the behaviour of a student during the learning process. In the next, and in order to simplify our notation, we shall write ms instead of mR s.

The possibility of s t measures the degree of evidence of combined results, i.

### 2. MTL: A fundamental fuzzy logic

An application of the fuzzy sets theory to the process of learning mathematics: A classroom experiment. The following experiment took place at the Technological Educational Institute T. During my 3 hour lecture I used the method of rediscovery keeping in mind what Polya [5] says about active learning: "For an effective learning the learner discovers alone the biggest possible, under the circumstances, part of the new information".

Thus, in my short introduction, I presented the concept of the definite integral through the need of calculating an area under a curve, but I gave the fundamental theorem of integral calculus connectlng the definite with the indefinite integral of a continuous function in the interval [a, b] without proof.

Then I left my students to work alone on their papers and 1 was inspecting their works and reactions, giving to them from time to time suitable hints or instructions. My aim was to help them to understand the basic methods of calculating the definite integrals, with respect to what they already knew about the indefinite integrals state A1. Please review our Terms and Conditions of Use and check box below to share full-text version of article.

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## Applications of Fuzzy Sets Theory

View Preview. Learn more Check out. Abstract Fuzziness is quite a different notion from probability. Citing Literature.

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