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Homogeneous properties of the triangular fuzzy number space. (Chinese. English summary) Zbl 0894.54010

A special fuzzy number, its graph like a triangle, is called triangular fuzzy number. Using the Hausdorff distance and the levels of fuzzy numbers, the author defines a metric \(d\) on the triangular fuzzy number space \(T\), and shows that (1) the space \(T\) is connected and locally connected; and (2) the space \(T\) is the union of \(T_i\) \((i=1,2,3,4)\), and for each \(T_i\) and points \(x,y\in T_i\), \(x\neq y\), there are neighbourhoods \(A\), \(B\) of \(x\) and \(y\) respectively, such that \(A\cap B=\emptyset\) and \(A\) and \(B\) are equispaced (i.e. there is a bijection \(\varphi:A\to B\) such that \(d(a_1,a_2)=d(\varphi(a_1),\varphi(a_2))\). The last property is called ‘homogeneous’ by the author.

MSC:

54A40 Fuzzy topology
26E50 Fuzzy real analysis
54D05 Connected and locally connected spaces (general aspects)
54E35 Metric spaces, metrizability
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