Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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A note on T-sum of bell-shaped fuzzy intervals

  • Published : 2007.12.25
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Abstract

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

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References

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  2. D. H. Hong, T-sum of bell-shaped fuzzy intervals, Fuzzy Sets and Systems 158(2007) 739-746 https://doi.org/10.1016/j.fss.2006.10.021
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