• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.253-266
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• 2011

We would like to generalize about trapezoidal fuzzy set and to calculate four operations based on the Zadeh's extension principle for two generalized trapezoidal fuzzy sets. And we roll up triangular fuzzy numbers and generalized triangular fuzzy sets into it. Since triangular fuzzy numbers and generalized triangular fuzzy sets are generalized trapezoidal fuzzy sets, we need no more the separate painstaking calculations of addition, subtraction, multiplication and division for two such kinds once the operations are done for generalized trapezoidal fuzzy sets.

• East Asian mathematical journal
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• v.29 no.3
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• pp.269-278
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• 2013

A fuzzy set A defined on a probability space (${\Omega}$, $\mathfrak{F}$, P) is called a fuzzy event. Zadeh defines the probability of the fuzzy event A using the probability P. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. We calculate the normal fuzzy probability for generalized trapezoidal fuzzy sets and give some examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.2
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• pp.212-217
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• 2012

A fuzzy set $A$ defined on a probability space ${\Omega}$, $\mathfrak{F}$, $P$ is called a fuzzy event. Zadeh defines the probability of the fuzzy event $A$ using the probability $P$. We define the generalized triangular fuzzy set and apply the extended algebraic operations to these fuzzy sets. A generalized triangular fuzzy set is symmetric and may not have value 1. For two generalized triangular fuzzy sets $A$ and $B$, $A(+)B$ and $A(-)B$ become generalized trapezoidal fuzzy sets, but $A({\cdot})B$ and $A(/)B$ need not to be a generalized triangular fuzzy set or a generalized trapezoidal fuzzy set. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized triangular fuzzy sets.