Displaying similar documents to “On some properties of α -planes of type-2 fuzzy sets”

On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric

Dong Qiu, Chongxia Lu, Shuai Deng, Liang Wang (2014)

Kybernetika

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In this paper, we generalize the classical Hausdorff metric with t-norms and obtain its basic properties. Furthermore, for a given stationary fuzzy metric space with a t-norm without zero divisors, we propose a method for constructing a generalized Hausdorff fuzzy metric on the set of the nonempty bounded closed subsets. Finally we discuss several important properties as completeness, completion and precompactness.

On a functional equation connected to the distributivity of fuzzy implications over triangular norms and conorms

Michał Baczyński, Tomasz Szostok, Wanda Niemyska (2014)

Kybernetika

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Distributivity of fuzzy implications over different fuzzy logic connectives have a very important role to play in efficient inferencing in approximate reasoning, especially in fuzzy control systems (see [9, 15] and [4]). Recently in some considerations connected with these distributivity laws, the following functional equation appeared (see [5]) f ( min ( x + y , a ) ) = min ( f ( x ) + f ( y ) , b ) , where a , b > 0 and f : [ 0 , a ] → [ 0 , b ] is an unknown function. In this paper we consider in detail a generalized version of this equation, namely the equation f ( m 1 ( x + y ) ) = m 2 ( f ( x ) + f ( y ) ) , where...

Hypotheses testing with the two-parameter Pareto distribution on the basis of records in fuzzy environment

Ali Reza Saeidi, Mohammad Ghasem Akbari, Mahdi Doostparast (2014)

Kybernetika

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In problems of testing statistical hypotheses, we may be confronted with fuzzy concepts. There are also situations in which the available data are record statistics such as weather and sports. In this paper, we consider the problem of testing fuzzy hypotheses on the basis of records. Pareto distribution is investigated in more details since it is used in applications including economic and life testing analysis. For illustrative proposes, a real data set on annual wage is analyzed using...