• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.217-225
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• 2012

A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh defines the probability of the fuzzy event using the probability. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.4
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• pp.592-595
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• 2010

The extended algebraic operations are defined by applying the extension principle to normal algebraic operations. And these operations are calculated for some kinds of fuzzy numbers. In this paper, we get exact membership function as a results of calculation of these operations for generalized quadratic fuzzy sets.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.4
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• pp.379-386
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• 2018

We generalized the quadratic fuzzy numbers on ${\mathbb{R}}$ to ${\mathbb{R}}_2$. By defining parametric operations between two regions valued ${\alpha}-cuts$, we got the parametric operations for two triangular fuzzy numbers defined on ${\mathbb{R}}_2$. The results for the parametric operations are the generalization of Zadeh's extended algebraic operations. We generalize the 2-dimensional quadratic fuzzy numbers on ${\mathbb{R}}_2$ that may have maximum value h < 1. We calculate the algebraic operations for two generalized 2-dimensional quadratic fuzzy sets.