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Convergence of sequences of fuzzy numbers and fixed point theorems for increasing fuzzy mappings and application. (English) Zbl 1031.26025

Fuzzy mappings (i.e., mappings assigning to an input fuzzy number an output fuzzy number) are discussed from fixed-point existence view. Based on some convergence results for sequences of fuzzy numbers, three types of fixed-point theorems (under different requirements) are shown. Obtained results are applied in fish production domain, discussing the balance problem between the quantity of catched fish and the reproduction and growth of the remaining fish. Another example concerns the solvability of an integral equation for fuzzy mappings (integral in Kaleva sense, i.e., a level-wise extension of the Aumann integral) is taken into account.

MSC:

26E50 Fuzzy real analysis
54A40 Fuzzy topology
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
03E72 Theory of fuzzy sets, etc.
92D40 Ecology
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References:

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