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People use granulation to represent original data as a set of entities that are better suited for managing resulting subtasks. Concept that are introduced in this paper are based on two features of granulation: the revelance of all the points in a granule and relative number of points in every granule. Based on these features several concepts are introduced that include granular relevance, defined as sum of relevancies of all the points in the granule and granular entropy, that is similar to information entropy and reflects the dispersion of relevant points across granules. Using these concepts granulation process is represented as solution of optimization problem where objective function is granular entropy. To this end the theorem, that shows how the change in relevance of points in a granule affects granular entropy, was proved. The last two sections of the paper show how leverage over the granulation process can be achieved by using t-norm and uni-norm operators.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
457--467
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
- Jerusalem College of Technology, 21 HaVaad Haleumi st., Jerusalem, Israel, alxndr_r@yahoo.com.
Bibliografia
- [1] J.C. Fodor, R.R. Yager and A. Rybalov: Structure of uni-norms. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 5 (1997), 411-427.
- [2] C.J. Harris, C.G. Moore and M. Brown: Intelligent Control - Aspects of Fuzzy Logic and Neural Nets. World Scientific, Singapore, 1993.
- [3] W. Pedrycz: Computational Intelligence: An Introduction. CRC Press, Boca Baton, 1997.
- [4] A. Rybalov and R.R. Yager: Control Clustering, Uni-Norm Operators and OWA operators. IFSA/NAFIPS Conf., Vancouver, (2001).
- [5] R.R. Yager: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. on Systems, Man and Cybernetics, 18 (1998), 183-190.
- [6] R.R. Yager: Intelligent control of the hierarchical agglomerative granulation process. IEEE Trans. on Systems, Man and Cybernetics: Part B, 30 (2000), 835-845.
- [7] R.R. Yager and J. Kacprzyk: The Ordered Weighted Averaging Operators: Theory and Applications. Kluwer: Norwell, 1997.
- [8] R.R. Yager and A. Rybalov: Full reinforcement operators in aggregation techniques. IEEE Trans. on Systems, Man and Cybernetics, 28 (1998), 757-769.
- [9] R.R. Yager and A. Rybalov: Uninorm aggregation operators. Fuzzy Sets and Systems, 80 (1996), 111-120.
- [10] L.A. Zadeh: Fuzzy sets and information granularity. In M.M. Gupta, R.K. Ragade, R.R. Yager (Eds), Advances in Fuzzy Set Theory and Applications, North Holland, Amsterdam, 1979.
- [11] L.A. Zadeh: Fuzzy logic = Computing with words. IEEE Trans. on Fuzzy Systems, 4(2) (1996), 103-111.
- [12] L.A. Zadeh: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems, 90 (1997), 111-117.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0003-0006