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Saxena, B.; Pal, S. K.

Some new concepts in fuzzy arithmetic. (English) Zbl 1219.03057

J. Discrete Math. Sci. Cryptography 13, No. 3, 257-270 (2010).
Summary: The theory of classical fuzzy sets has found applications in diverse areas such as fuzzy control, fuzzy inferencing, fuzzy pattern recognition etc. However in its present form there are a number of drawbacks leading to limited applications for handling many real-world problems. In this paper, the concepts of fuzzy sets, fuzzy numbers and fuzzy arithmetic are critically examined and need for their improvement is explained. Based on Piegat’s work, modifications in the existing schemes are suggested and computer implementation is carried out for their realization.

MSC:

03E72 Theory of fuzzy sets, etc.

Keywords:

fuzzy sets; fuzzy numbers; fuzzy arithmetic; membership function; \(\alpha \)-cut; qualification probability
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References:

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