Saniya Tasleem Zafar, Nafisur Rahman, Safdar Tanweer


The term ‘Fuzzy’ means vague, unclear, or imprecise. Fuzzy Logic is a many-valued logic that is based on the theory of Fuzzy Sets and it facilitates the representation of approximate reasoning. It finds its use in various areas where binary representations do not suffice. In this paper, we have confined our discussions on the theoretical foundations and advancements of modern Fuzzy Logic. We start with a brief account of Fuzzy Sets followed by the operations they support. Then we discuss how the Linguistic Variables allow more realistic reasoning as opposed to traditional binary reasoning. Then we introduce the theoretical aspects of the calculus of Fuzzy Restrictions. Finally, we discuss the theory of possibility as an alternative to the theory of probability. For the sake of simplicity and intelligibility, we have tried to avoid incommodious mathematical equations throughout this paper.


Fuzzy Sets; Approximate reasoning; Linguistic Variables; Fuzzy Restriction; Possibility theory

Full Text:



Zadeh, L.A. “Fuzzy sets”. Information and control, vol. 8, no. 3, pp. 338-353, 1965.

Bellman R., Kalaba R., and Zadeh L.A. “Abstraction and pattern classification”. Journal of Mathematical Analysis and Applications, vol. 13, no. 1, pp. 1-7, 1966.

Halmos, P.R. Naive Set Theory. New York: Van Nostrand, 1960.

Zadeh, L.A. “The concept of a linguistic variable and its application to approximate reasoning—I”. Information sciences, vol. 8, no. 3, pp. 199-249, 1975.

Zadeh, L.A. “The concept of a linguistic variable and its application to approximate reasoning—II”. Information sciences, vol. 8, no. 4, pp. 301-357, 1975.

Zadeh L.A. “Calculus of Fuzzy Restrictions,” in Proc. US-Japan Seminar on Fuzzy Sets and their Applications, 1975, pp. 1-39.

R. E. Bellman and L. A. Zadeh. “Local and fuzzy logics” in Modern Uses of Multiple-Valued Logics, edited by J. M. Dunn and G. Epstein, D. Reidel, Dordrecht-Holland, 1977, pp. 103 – 165.

Zadeh, L.A. “Fuzzy sets as a basis for a theory of possibility”. Fuzzy Sets and Systems, vol. 1, no. 1, pp. 3-28, 1978.

DOI: https://doi.org/10.26483/ijarcs.v9i2.5719


  • There are currently no refbacks.

Copyright (c) 2018 International Journal of Advanced Research in Computer Science