Um estudo sobre operações aritméticas com números fuzzy

Abstract

This dissertation is based on a research work carried out in the classroom with high school students of a public school, and aims to show that the introduction of initial elements of Fuzzy Logic in the first grades of high school is possible and can contribute to the development of mathematical thinking of such students. It would be a way to assist in the understanding, analysis and treatment of difficult-to-deal problems, subjective issues with varying degrees of uncertainty. This new tool, currently compartmentalized, only in the stages of Higher Education - or later - can prove to be a field of interest for many students who are unaware of this theory, and its reach in current technology. To this end, it began with the study of the basic concepts of Fuzzy Set Theory with emphasis on fuzzy number and fuzzy arithmetic, generating the proposition of a didactic sequence acceptable to students at the beginning of high school, through tests specially elaborated with the theme 'intervals' and 'interval operations' – object of this study – and classes taught by the researcher. Subsequently, the results obtained were tabulated and analyzed showing that, although the students presented some difficulty in relation to the research in the work with intervals, the content is easily incorporated those already studied by them in their school career, and that the benefits can be significant in the long term, bringing to their reality the possibility and instrumentation necessary for the elaboration of mathematical models for situations of our daily lives.