Abstract
Diversity of opinion is an empirical fact often appearing in social networks. In the paper known statistical methods of evaluation is substituted by fuzzy concepts, namely Step Ordered Fuzzy Numbers (SOFN). SOFN are extentions of Ordered Fuzzy Numbers (OFN) introduced by Kosiński, Prokopowicz and Ślęzak in 2002. In 2011 Kacprzak and Kosiński observed that SOFN may be equipped with a lattice structure. In consequence, Boolean operations like conjunction, disjunction and, what is more important, diverse types of implications can be defined on SOFN. In this paper we show how SOFN can be applied for modelling diversity of beliefs even in fuzzy expressions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baczyński, M., Jayaram, B.: Fuzzy Implications. STUDFUZZ, vol. 231. Springer, Heidelberg (2008)
Baczyński, M.: S-implications in Atanassov’s intuitionistic and interval-valued fuzzy set theory revisited. In: Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topicss, vol. 1, pp. 33–42. IBS PAN - SRI PAS, Warsaw (2009)
Bruijn, B., Martin, J.: Getting to the (c)ore of knowledge: mining biomedical literature. Int. Journal Medical Informatics 67, 7–18 (2002)
Budzynska, K., Kacprzak, M., Rembelski, P.: Perseus. Software for analyzing persuasion process. Fundamenta Informaticae 93(1-3), 65–79 (2009)
Guanrong, C., Pham, T.T.: Introduction to Fuzzy Sets, Fuzzy Logic and Fuzzy Control Systems. CRC Press LLC, New York (2001)
Czogała, E., Pedrycz, W.: Elements and Methods of Fuzzy Set Theory. PWN, Warsaw (1985) (in Polish)
Dubois, D., Prade, H.: Operations on fuzzy numbers. International Journal of Systems Science 9(6), 613–626 (1978)
Fodor, J.C., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)
Goetschel Jr., R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets and Systems 18(1), 31–43 (1986)
Gruszczyńska, A., Krajewska, I.: Fuzzy calculator on step ordered fuzzy numbers. UKW, Bydgoszcz (2008) (in Polish)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)
Halpern, J.Y.: Reasoning about Uncertainty. MIT Press, Cambridge (2005)
Kacprzak, M., Kosiński, W.: On lattice structure and implications on ordered fuzzy numbers. In: Proc. of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), pp. 267–274 (2011)
Klir, G.J.: Fuzzy arithmetic with requisite constraints. Fuzzy Sets and Systems 91, 165–175 (1997)
Kosiński, W.: On fuzzy number calculus. International Journal of Applied Mathematics and Computer Science 16(1), 51–57 (2006)
Kosiński, W., Prokopowicz, P., Ślęzak, D.: Fuzzy numbers with algebraic operations: algorithmic approach. In: Klopotek, M., Wierzchoń, S.T., Michalewicz, M. (eds.) Proc. Intelligent Information Systems, IIS 2002, Sopot, Poland, June 3-6, pp. 311–320. Physica Verlag, Heidelberg (2002)
Kosiński, W., Prokopowicz, P., Ślęzak, D.: Drawback of fuzzy arithmetics - new intutions and propositions. In: Burczyński, T., Cholewa, W., Moczulski, W. (eds.) Proc. Methods of Aritificial Intelligence, pp. 231–237. PACM, Gliwice (2002)
Kosiński, W., Prokopowicz, P., Ślęzak, D.: On algebraic operations on fuzzy numbers. In: Klopotek, M., Wierzchoń, S.T., Trojanowski, K. (eds.) Intelligent Information Processing and Web Mining, Proc. of the International IIS: IIPWM 2003 Conference held in Zakopane, Poland, June 2-5, pp. 353–362. Physica Verlag, Heidelberg (2003)
Kosiński, W., Prokopowicz, P., Ślęzak, D.: Ordered fuzzy numbers. Bulletin of the Polish Academy of Sciences, Sér. Sci. Math. 51(3), 327–338 (2003)
Kosiński, W., Prokopowicz, P.: Algebra of fuzzy numbers. Applied Mathematics. Mathematics for Society 5(46), 37–63 (2004) (in Polish)
Kościeński, K.: A module of step ordered fuzzy numbers in control movement material point. PJIIT, Warsaw (2010) (in Polish)
Lukasiewicz, J.: Elements of the Mathematical Logic. PWN, Warsaw (1958) (in Polish)
Malinowski, G.: Many-valued logics. In: Goble, L. (ed.) The Blackwell Guide to Philosophical Logic, pp. 309–335. Blackwell Publishers, Oxford (2001)
Nguyen, H.T.: A note on the extension principle for fuzzy sets. Journal of Math. Anal. Appl. 64, 369–380 (1978)
Prokopowicz, P.: Algorithmization of Operations on Fuzzy Numbers and its Applications. Ph. D. Thesis, IPPT PAN (2005) (in Polish)
Spasic, I., Ananiadu, S., McNaught, J., Kumar, A.: Text mining and ontologies in biomedicine: making sense of raw text. Brief Bioinform. 6(3), 239–251 (2005)
Swanson, D.R.: Medical literature as a potential source of new knowledge. Bull. Med. Libr. Assoc. 78(1), 29–37 (1990)
Starosta, B., Kosiński, W.: Meta sets – another approach to fuzziness. In: Seising, R. (ed.) Views on Fuzzy Sets and Systems. STUDFUZZ, vol. 243, pp. 509–532. Springer, Heidelberg (2009)
Zadeh, L.A.: The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems 11(3), 199–227 (1983)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kacprzak, M., Kosiński, W., Węgrzyn-Wolska, K. (2013). Diversity of Opinion Evaluated by Ordered Fuzzy Numbers. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2013. Lecture Notes in Computer Science(), vol 7894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38658-9_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-38658-9_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38657-2
Online ISBN: 978-3-642-38658-9
eBook Packages: Computer ScienceComputer Science (R0)