Geodesic
On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric
Kybernetika, Tome 50 (2014) no. 5, pp. 758-773
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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.
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.
DOI : 10.14736/kyb-2014-5-0758
Classification : 03E72, 46S40, 54A40, 54B20
Keywords: Hausdorff metric; hyperspace; triangular norms; stationary fuzzy metric 
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Qiu, Dong; Lu, Chongxia; Deng, Shuai; Wang, Liang. On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric. Kybernetika, Tome 50 (2014) no. 5, pp. 758-773. doi: 10.14736/kyb-2014-5-0758

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