On Some Applications of Fuzzy Sets for the Management of Teaching and Relationships in Schools

  • Šárka Hošková-MayerováEmail author
  • Antonio Maturo
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 179)


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.


Relations and directed graph Fuzzy relations Algebraic hyperstructures Strategies for teaching and managing relationships 


  1. 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)Google Scholar
  2. 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).
  3. de Finetti, B.: Teoria delle Probabilità, vol. I e II, Einaudi, Torino (1970)Google Scholar
  4. 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)Google Scholar
  5. Delli, R.L., Maturo, A.: Interdisciplinarity, logic of uncertainty and fuzzy logic in primary school. Sci. Philos. 3(2), 11–26 (2015)Google Scholar
  6. Delli, R.L., Maturo, A.: Social problems and decision making for teaching approaches and relationship management in an elementary school. (2017). Scholar
  7. Delli, R.L., Maturo, A.: Problems and Decision-Making Models in the First Cycle of Education, in press, to appear (2018)Google Scholar
  8. Fadini, A.: Introduzione alla teoria degli insiemi sfocati. Liguori, Napoli (1979)Google Scholar
  9. Fortuna, F., Maturo, F.: K-means clustering of item characteristic curves and item information curves via functional principal component analysis. Qual. Quant. (2018). Scholar
  10. Gentilhomme, M.Y.: Les ensembles flous en linguistiques. Cahiers de linguistique theorique et appliquée, Bucarest 5(47), 47–65 (1968)Google Scholar
  11. 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). Scholar
  12. 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). Scholar
  13. 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 2357-1330Google Scholar
  14. Hošková-Mayerová, Š.: Quasi-order hypergroups determinated by T-hypergroups. Ratio Math. 32(2017), 37–44 (2017). Scholar
  15. Hošková-Mayerová, Š., Maturo, A.: Hyperstructures in social sciences. In: AWER Procedia Information Technology and Computer Science, vol. 3, 547—552. Barcelona, Spain (2013)Google Scholar
  16. 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 2383-2851Google Scholar
  17. 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).
  18. Hošková-Mayerová, Š., Maturo, A.: On some applications of algebraic hyperstructures for the management of teaching and relationships in schools (2018, submitted)Google Scholar
  19. Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, Upper Saddle River (1995)zbMATHGoogle Scholar
  20. Maturo, A.: Struttura algebrica degli eventi generalizzati. Periodico di Matematiche 4(1993), 18–26 (1993)Google Scholar
  21. Maturo, A., Porreca, A.: Algebraic hyperstructures and fuzzy logic in the treatment of uncertainty. Sci. Philos. 4(1), 31–42 (2016)Google Scholar
  22. 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)Google Scholar
  23. 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:
  24. 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). Scholar
  25. 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). Scholar
  26. 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). Scholar
  27. Maturo, F., Ventre, V.: Consensus in multiperson decision making using fuzzy coalitions. Stud. Fuzziness Soft Comp. 357, 451–464 (2017). Scholar
  28. Moreno, J.L.: Who Shall Survive? Beacon Press, New York (1953)Google Scholar
  29. Moreno, J.L.: Sociometry. Experimental Methods and the Science of Society. Beacon Press, New York (1951)Google Scholar
  30. Ragin, C.C.: Fuzzy-Set Social Science. University Chicago Press, Chicago (2000)Google Scholar
  31. Reichenbach, H.: Philosophic Foundations of Quantum Mechanics. University of California Press, Berkeley (1944)Google Scholar
  32. Ross, T.J.: Fuzzy logic with engineering applications. McGraw-Hill, New York (1995)zbMATHGoogle Scholar
  33. Rosická, Z., Hošková-Mayerová, Š., Motivation to study and work with talented students, Proc. – Soc. Behav. Sci. 114, 234–238 (2014). Scholar
  34. Sciarra, E.: Paradigmi e metodi di ricerca sulla socializzazione autorganizzante. Sigraf Edizioni Scientifiche, Pescara (2007)Google Scholar
  35. Svatoňová, H., Hošková-Mayerová, Š.: Social aspects of teaching: Subjective preconditions and objective evaluation of interpretation of image data. (2017). Scholar
  36. Vougiouklis, T.: Hyperstructures as models in social sciences. Ratio Math. 21(2011), 27–42 (2011)Google Scholar
  37. Vougiouklis, T., Vougiouklis, S.: Helix-hopes on finite hyperfields. Ratio Math. 31(2016), 65–78 (2016)Google Scholar
  38. Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–358 (1965)CrossRefGoogle Scholar
  39. 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–-80Google Scholar

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Authors and Affiliations

  1. 1.Department of Mathematics and PhysicsUniversity of Defence BrnoBrnoCzech Republic
  2. 2.Department of ArchitectureUniversity “G. d’Annunzio’’ of Chieti-PescaraPescaraItaly

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