A Bag Theoretic Approach towards the Count of an Intuitionistic Fuzzy Set

Full Text (PDF, 454KB), PP.16-23

Views: 0 Downloads: 0


B.K. Tripathy 1,* S.Khandelwal 1 M.K.Satapathy 2

1. School of Computing Science and Engineering, VIT University, Vellore -632014, Tamil Nadu, India

2. Department of Mathematics, R.G. College, Padmapur, Odisha, India

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2015.05.03

Received: 10 Sep. 2014 / Revised: 17 Nov. 2014 / Accepted: 21 Jan. 2015 / Published: 8 Apr. 2015

Index Terms

Fuzzy Set, Intuitionistic Fuzzy Set, IFGCount, IFLCount, IFECount, Bags


The cardinality of fuzzy sets was introduced by DeLuca and termini, Zadeh and Tripathy et al, where the first one is a basic one, the second one is based on fuzzy numbers and the final one introduces a bag theoretic approach. The only approach to find the cardinality of an intuitionistic fuzzy set is due to Tripathy et al. In this paper, we introduce a bag theoretic approach to find the cardinality of intuitionistic fuzzy set, which extends the corresponding definition of fuzzy sets introduced by Tripathy et al. In fact three types of intuitionistic fuzzy counts are introduced and we also establish several properties of these count functions.

Cite This Paper

B.K.Tripathy, S.Khandelwal, M.K.Satapathy, "A Bag Theoretic Approach towards the Count of an Intuitionistic Fuzzy Set", International Journal of Intelligent Systems and Applications(IJISA), vol.7, no.5, pp.16-23, 2015. DOI:10.5815/ijisa.2015.05.03


[1]Zadeh, L. A.: Fuzzy Sets, Information and Control, vol.8, (1965), pp.338-353
[2]Klir, G. J. and Yuan, B.: Fuzzy Sets and Fuzzy Logic, Theory and Applications, Prentice Hall of India pvt. Ltd., New Delhi, (1997).
[3]DeLuca, A. and Termini, S.: A definition of a non-probabilistic entropy in the setting of Fuzzy Set Theory, Information and Control, Vol.20, (1972), pp.301-302.
[4]Zadeh, L. A.: Probability measures of fuzzy events, Journal of Mathematical Analysis and Applications, vol.23, (1968), pp.421-427.
[5]Zadeh, L.A.: test-score semantics for Natural Languages and meaning representation via PRUF, in: Rieger, B. (ed.), Empirical Semantics, Brockmeyer, Bochum, Germany, (1982), pp. 281-349.
[6]Mizumoto, M. and Tanaka, K.: Some Properties of fuzzy numbers, in: Advances in Fuzzy Set Theory and Applications, eds.M.M.Gupta, R.K.Ragade and R.R.Yager, North Holland, Amsterdam, (1979), pp.153-164.
[7]Atanassov, K.T.: intuitionistic fuzzy sets, Fuzzy Sets and Systems, vol.20, (1986), pp.87-96.
[8]Tripathy, B.K., Jena, S.P. and Ghosh, S.K.: An Intuitionistic fuzzy count and cardinality of Intuitionistic fuzzy sets, Malaya Journal of Matematik, 4(1), (2013), pp. 123–133.
[9]Cerf, V., Fernandez, E., Gostalow, K. and Volausky, S.: Formal control and low properties of a model of computation, report ENG, 7178, Computer Science Dept. of California, Los-Angeles, California, Dec (1971), pages -81.
[10]Jena, S.P., Ghosh, S.K. and Tripathy, B. K.: On the theory of bags and lists, Information Science, vol.132, (2001), pp.241-254.
[11]Peterson, J.: Computation sequence spaces, Journal of Computer and System Sciences, vol.13, no.1, Aug. (1976), pp.1-24.
[12]Yager, R.R.: On the theory of bags, International Journal of General Systems, 13, (1986), pp.23-37
[13]Tripathy, B.K., Jena, S.P. and Ghosh, S.K.: A Bag Theoretic Fuzzy Count and Cardinality of Fuzzy Sets, 2013 IEEE ICCIC, Madurai, Dec.26-28, (2013), pp.379 – 384.
[14]Chakraborty, K., Biswas, R, and Nanda, S.: On Yager’s theory of bags and fuzzy bags, Computer and Artificial Intelligencs, 18, (1999), pp. 1-17.