International Journal of Intelligent Systems and Applications(IJISA)
ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)
Published By: MECS Press
IJISA Vol.5, No.6, May. 2013
On Cardinality of Fuzzy Sets
Full Text (PDF, 263KB), PP.47-52
In this article, we would like to revisit and comment on the widely used definition of cardinality of fuzzy sets. For this purpose we have given a brief description of the history of development of fuzzy cardinality. In the process, we can find that the existing definition fails to give a proper cardinality while dealing with complementation of fuzzy sets. So there arises the need of defining the cardinality in a different manner. Here a new definition of cardinality is proposed which is rooted in the definition of complementation of fuzzy sets on the basis of reference function. This definition of cardinality will inevitably play an important role in any problem area that involves complementation. Further, some important results are proven with the help of the proposed definition and it is found that these properties are somewhat analogus to those obtained with the help of the existing definition.
Cite This Paper
Mamoni Dhar,"On Cardinality of Fuzzy Sets", International Journal of Intelligent Systems and Applications(IJISA), vol.5, no.6, pp.47-52, 2013.DOI: 10.5815/ijisa.2013.06.06
Zadeh L A, Inform. and Control, 1965,8: 338-353.
De Luca A, Rermini S, A definition of non probabilistic entropy in the settings of fuzzy set theory, Information and Control, 1972, 20:301-312.
Zazeh L A, A theory of approximate reasoning, Machine Intelligence, 1979, 9: 149-194.
Zazeh L A, A computational approach to fuzzy quantifiers in Natural Languages, Computation and Mathematics, 1983, 9: 149-184
Baruah H K, Fuzzy Membership with respect to a Reference Function, Journal of the Assam Science Society, 1999, 40(.3):65-73.
Baruah H K, Towards Forming A Field of Fuzzy Sets, International Journal of Energy Information and Communications, 2011, 2(1): 16 – 20.
Baruah H K, Theory of Fuzzy sets Beliefs and Realities, International Journal of Energy, Information and Communications, 2011, 2(2): 1-22.
Baruah H K, In Search of the Root of Fuzziness: The Measure Theoretic Meaning of Partial Presence, Annals of Fuzzy Mathematics and Informatics, 2011, 2(1): 57 – 68.
Dhar M, On Hwang and Yang’s definition of Entropy of Fuzzy sets, International Journal of Latest Trend Computing, 2011, 2(4): 496-497.
Dhar M, A Note on existing Definition of Fuzzy Entropy, International Journal of Energy Information and Communications, 2012, 3( 1): 17-21.
Dhar M, On Separation Index of Fuzzy Sets, International Journal of Mathematical Archives, 2012, .3(3): 932-934.
Dhar M, On Geometrical Representation of Fuzzy Numbers, International Journal of Energy Information and Communications, 2012, 3(2): 29-34.
Dhar M, On Fuzzy Measures of Symmetry Breaking of Conditions, Similarity and Comparisons: Non Statistical Information for the Single Patient., Accepted for publication in International Journal of Mathematical Archives, 2012.
Dhar M, A Note on Subsethood measure of fuzzy sets, accepted for publication in International Journal of Energy, Information and Communications, 2012.
Kosko B, Counting with fuzzy sets, Transaction Pattern analysis and Machine Intelligence, IEEE, 1986, 9(4): 556-557