Abstract
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.
Highlights
The theoretical foundations of Fuzzy Logic are based on Fuzzy Sets that deal with the information that is uncertain, generic, imprecise, or vague
Fuzzy Logic is a many-valued logic that is based on the theory of Fuzzy Sets and it facilitates the representation of approximate reasoning
We have presented the founding principles of Fuzzy theory and its subsequent advancements for which Prof
Summary
The theoretical foundations of Fuzzy Logic are based on Fuzzy Sets that deal with the information that is uncertain, generic, imprecise, or vague. The theory of Fuzzy Sets is associated with the idea of membership function by the course of human thinking and understanding. It gives an effective means for understanding better assessment options. Linguistic Variables are used for this purpose. A Linguistic Variable is a value which is given in the form of word or sentences rather than in a numeric form. Treating the incomplete information as a vague concept, the theory of Possibility provides an alternative to Probability theory by dealing with certain types of ambiguity
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