Abstract
Often in the scholastic context the efficiency of the teaching depends to a large extent on the system of relationships established within the classroom. In this paper we show how the relatively recent mathematical theories on fuzzy sets and algebraic hyperstructures can make a significant contribution to the understanding of the system of relationships within the class. Furthermore, it is possible to evaluate the impact of interventions aimed at improving the system of relationships and therefore to establish a serene participation of the students in the learning process.
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Ceccatelli, C., Di Battista, T., Fortuna, F., Maturo, F.: L’item response theory come strumento di valutazione delle eccellenze nella scuola. Sci. Philos. 1(1), 143–156 (2013)
Ceccatelli, C., Di Battista, T., Fortuna, F., Maturo, F.: Best Practices to Improve the Learning of Statistics: The Case of the National Olympics of Statistic in Italy. Procedia - Social and Behavioral Sciences, vol. 93, pp. 2194–2199 (2013b). https://doi.org/10.1016/j.sbspro.2013.186
de Finetti, B.: Teoria delle Probabilità, vol. I e II, Einaudi, Torino (1970)
Delli, R.L., Maturo, A.: Teaching mathematics to children: social aspects, psychological problems and decision-making models. In: Soitu, D., Gavriluta, C., Maturo, A. (eds.) Interdisciplinary Approaches in Social Sciences. Editura Universitatii A.I. Cuza, Iasi, Romania (2013)
Delli, R.L., Maturo, A.: Interdisciplinarity, logic of uncertainty and fuzzy logic in primary school. Sci. Philos. 3(2), 11–26 (2015)
Delli, R.L., Maturo, A.: Social problems and decision making for teaching approaches and relationship management in an elementary school. (2017). https://doi.org/10.1007/978-3-319-54819-7_7
Delli, R.L., Maturo, A.: Problems and Decision-Making Models in the First Cycle of Education, in press, to appear (2018)
Fadini, A.: Introduzione alla teoria degli insiemi sfocati. Liguori, Napoli (1979)
Fortuna, F., Maturo, F.: K-means clustering of item characteristic curves and item information curves via functional principal component analysis. Qual. Quant. (2018). https://doi.org/10.1007/s11135-018-0724-7
Gentilhomme, M.Y.: Les ensembles flous en linguistiques. Cahiers de linguistique theorique et appliquée, Bucarest 5(47), 47–65 (1968)
Hošková-Mayerová, Š.: Operational program“Education for competitive advantage”, preparation of study materials for teaching in English. Proc. – Soc. Behav. Sci. 15, 3800–3804 (2011). https://doi.org/10.1016/j.sbspro.2011.04.376
Hošková-Mayerová, Š.: The effect of language preparation on communication skills and growth of students’ self - confidence, Proc. – Soc. Behav. Sci. 114, 644–648 (2014). https://doi.org/10.1016/j.sbspro.2013.12.761
Hošková-Mayerová, Š.: Education and Training in Crisis Management. In: ICEEPSY 2016 - 7th International Conference on Education and Educational Conference, pp. 849–856. Future Academy (2016). ISSN 2357-1330
Hošková-Mayerová, Š.: Quasi-order hypergroups determinated by T-hypergroups. Ratio Math. 32(2017), 37–44 (2017). https://doi.org/10.23755/rm.v32i0.333
Hošková-Mayerová, Š., Maturo, A.: Hyperstructures in social sciences. In: AWER Procedia Information Technology and Computer Science, vol. 3, 547—552. Barcelona, Spain (2013)
Hošková-Mayerová, Š., Maturo, A.: An analysis of Social Relations and Social Group behaviors with fuzzy sets and hyperstructures. Int. J. Algebraic Hyperstruct. Appl. 2(1), 91–99 (2016). ISSN 2383-2851
Hošková-Mayerová, Š., Maturo, A.: Fuzzy sets and algebraic hyperoperations to model interpersonal relations. In: Recent Trends in Social Systems: Quantitative Theories and Quantitative Models. Studies in Systems, Studies in Systems, Decision and Control, 66 (2016). https://doi.org/10.1007/978-3-319-40583-8_19
Hošková-Mayerová, Š., Maturo, A.: On some applications of algebraic hyperstructures for the management of teaching and relationships in schools (2018, submitted)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River (1995)
Maturo, A.: Struttura algebrica degli eventi generalizzati. Periodico di Matematiche 4(1993), 18–26 (1993)
Maturo, A., Porreca, A.: Algebraic hyperstructures and fuzzy logic in the treatment of uncertainty. Sci. Philos. 4(1), 31–42 (2016)
Maturo, A., Sciarra, E., Tofan, I.: A formalization of some aspects of the social organization by means of the fuzzy set theory. Ratio Sociol. 1(2008), 5–20 (2008)
Maturo., F.: Dealing with randomness and vagueness in business and management sciences: the fuzzy-probabilistic approach as a tool for the study of statistical relationships between imprecise variables. Ratio Math. 30(1), 45–58 (2016). doi:http://dx.doi.org/10.23755/rm.v30i1.8
Maturo, F., Fortuna, F.: Bell-shaped fuzzy numbers associated with the normal curve. In: Topics on Methodological and Applied Statistical Inference, pp. 131–144 (2016). https://doi.org/10.1007/978-3-319-44093-4_13
Maturo, F., Fortuna, F., Di Battista, T.: Testing equality of functions across multiple experimental conditions for different ability levels in the IRT context: the case of the IPRASE TLT 2016 Survey. Soc. Indic. Res. (2018). https://doi.org/10.1007/s11205-018-1893-4
Maturo, F., Hošková-Mayerová, Š.: Fuzzy regression models and alternative operations for economic and social sciences. In: Recent Trends in Social Systems: Quantitative Theories and Quantitative Models. Series Studies in Systems, Decision and Control 66, 235–247 (2017). https://doi.org/10.1007/978-3-319-40585-8_21
Maturo, F., Ventre, V.: Consensus in multiperson decision making using fuzzy coalitions. Stud. Fuzziness Soft Comp. 357, 451–464 (2017). https://doi.org/10.1007/978-3-319-60207-3_26
Moreno, J.L.: Who Shall Survive? Beacon Press, New York (1953)
Moreno, J.L.: Sociometry. Experimental Methods and the Science of Society. Beacon Press, New York (1951)
Ragin, C.C.: Fuzzy-Set Social Science. University Chicago Press, Chicago (2000)
Reichenbach, H.: Philosophic Foundations of Quantum Mechanics. University of California Press, Berkeley (1944)
Ross, T.J.: Fuzzy logic with engineering applications. McGraw-Hill, New York (1995)
Rosická, Z., Hošková-Mayerová, Š., Motivation to study and work with talented students, Proc. – Soc. Behav. Sci. 114, 234–238 (2014). https://doi.org/10.1016/j.sbspro.2013.12.691
Sciarra, E.: Paradigmi e metodi di ricerca sulla socializzazione autorganizzante. Sigraf Edizioni Scientifiche, Pescara (2007)
Svatoňová, H., Hošková-Mayerová, Š.: Social aspects of teaching: Subjective preconditions and objective evaluation of interpretation of image data. (2017). https://doi.org/10.1007/978-3-319-54819-7_13
Vougiouklis, T.: Hyperstructures as models in social sciences. Ratio Math. 21(2011), 27–42 (2011)
Vougiouklis, T., Vougiouklis, S.: Helix-hopes on finite hyperfields. Ratio Math. 31(2016), 65–78 (2016)
Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–358 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. (1975);8 Part I:199–-249, Part II 301–-357, Part III. Inf Sci 1975;9: 43–-80
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Hošková-Mayerová, Š., Maturo, A. (2019). On Some Applications of Fuzzy Sets for the Management of Teaching and Relationships in Schools. In: Flaut, C., Hošková-Mayerová, Š., Flaut, D. (eds) Models and Theories in Social Systems. Studies in Systems, Decision and Control, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-030-00084-4_19
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