Issue:An experimental analysis of some measures of information and knowledge for intuitionistic fuzzy sets

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Title of paper: An experimental analysis of some measures of information and knowledge for intuitionistic fuzzy sets Author(s): Eulalia Szmidt Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447 Warsaw, Poland szmidt@ibspan.waw.pl Janusz Kacprzyk Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447 Warsaw, Poland kacprzyk@ibspan.waw.pl Paweł Bujnowski Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447 Warsaw, Poland Presented at: 16th ICIFS, Sofia, 9-10 September 2012 Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 18 (2012) Number 3, pages 39—48 Download:  PDF (198  Kb, File info) Abstract: The evaluation of information and knowledge conveyed by an Atanassov’s intuitionistic fuzzy set (A-IFS, for short) is discussed. We pay particular attention to the relationship between positive and negative knowledge (expressed by the entropy which may be seen as a dual measure to information), and also take into account the reliability of information expressed by the hesitation margin. Keywords: Intuitionistic fuzzy sets, amount of information, amount of knowledge, entropy, hesitation margin. AMS Classification: 03E72 References: Atanassov, K. Intuitionistic Fuzzy Sets. VII ITKR Session. Sofia, 1983 (Deposed in Centr. Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 20, 1986, 87–96. Atanassov, K. Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag, 1999. Atanassov, K., V. Tasseva, E. Szmidt, J. Kacprzyk. On the geometrical interpretations of the intuitionistic fuzzy sets. In: Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics. (Eds. Atanassov, K., J. Kacprzyk, M. Krawczak, E. Szmidt), EXIT, Warsaw, 2005. Bustince, H., V. Mohedano, E. Barrenechea, M. Pagola. An algorithm for calculating the threshold of an image representing uncertainty through A-IFSs. Proceedings of IPMU’2006, 2383–2390. Bustince, H., V. Mohedano, E. Barrenechea, M. Pagola. Image thresholding using intuitionistic fuzzy sets. In: Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics. (Eds. Atanassov, K., J. Kacprzyk, M. Krawczak, E. Szmidt), EXIT, Warsaw 2005. De Luca, A., S. Termini. A definition of a non-probabilistic entropy in the setting of fuzzy sets theory. Inform. and Control, Vol. 20, 1972, 301–312. Narukawa, Y., V. Torra. Non-monotonic fuzzy measure and intuitionistic fuzzy set. LNCS Vol. 3885, 2006, 150–160. Quinlan, J. R. Induction of decision trees. Machine Learning, Vol. 1, 1986, 81–106. Stewart, T. Wealth of Knowledge. Doubleday, New York, 2001. Szmidt, E., J. Baldwin. New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes on Intuitionistic Fuzzy Sets, Vol. 9, 2003, No. 3, 60–76. Szmidt, E., J. Baldwin. Entropy for intuitionistic fuzzy set theory and mass assignment theory. Notes on Intuitionistic Fuzzy Sets, Vol. 10, 2004, No. 3, 15–28. Szmidt, E., J. Baldwin. Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms. Proc. of 2006 IEEE World Congress on Computational Intelligence, 2006, 237–243. Szmidt, E., J. Kacprzyk. On measuring distances between intuitionistic fuzzy sets,Notes on Intuitionistic Fuzzy Sets, Vol. 3, 1997, No. 4, 1–13. Szmidt, E., J. Kacprzyk. Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 114, 2000, No. 3, 505–518. Szmidt, E., J. Kacprzyk. Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 118, 2001, No. 3, 467–477. Szmidt, E., J. Kacprzyk. Similarity of intuitionistic fuzzy sets and the Jaccard coefficient. Proc. of IPMU’2004, 2004, 1405–1412. Szmidt, E., J. Kacprzyk. Distances between intuitionistic fuzzy sets: straightforward approaches may not work. Proc. of 3rd International IEEE Conference Intelligent Systems IS06, London, 2006, 716–721. Szmidt, E., J. Kacprzyk. Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. Applications of Fuzzy Sets Theory. Lecture Notes on Artificial Intelligence, Springer-Verlag, Vol. 4578, 2007, 291–297. Szmidt, E., J. Kacprzyk. A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. Proc. of 2007 IEEE Conf. on Fuzzy Systems, 2007, 481–486. Szmidt, E., J. Kacprzyk. Dealing with typical values via Atanassov’s intuitionistic fuzzy sets. Int. J. of General Systems, Vol. 39, 2010, No. 5, 489–506. Szmidt, E., J. Kacprzyk, P. Bujnowski. On some measures of information and knowledge for intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, Vol. 16, 2010, No. 2, 1–11. Szmidt, E., M. Kukier. Classification of imbalanced and overlapping classes using intuitionistic fuzzy sets. Proc. of 3rd International IEEE Conference Intelligent Systems IS06, London, 2006, 722–727. Szmidt, E., M. Kukier. A new approach to classification of imbalanced classes via Atanassov’s intuitionistic fuzzy sets. In: Hsiao-Fan Wang (Ed.): Intelligent Data Analysis: Developing New Methodologies Through Pattern Discovery and Recovery. Idea Group, 2008, 65–102. Szmidt, E., M. Kukier. Atanassov’s intuitionistic fuzzy sets in classification of imbalanced and overlapping classes. In: Intelligent Techniques and Tools for Novel System Architectures. (Eds. Chountas, P., I. Petrounias, J. Kacprzyk), Series: Studies in Computational Intelligence. Springer, Berlin-Heidelberg, 2008, 455–471. Zadeh, L. A. Fuzzy sets. Information and Control, Vol. 8, 1965, 338–353. Zadeh, L. A. A computational approach to fuzzy quantifiers in natural languages. Comp. Math. Appl., Vol. 9, 1983, No. 1, 149–184. http://archive.ics.uci.edu/ml/datasets/Connectionist+Bench+(Sonar,+Mines+vs.+Rocks) http://archive.ics.uci.edu/ml/datasets/Ionosphere http://archive.ics.uci.edu/ml/datasets/Pima+Indians+Diabetes Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.