## Fuzzy inventory with backorder for fuzzy total demand based on interval-valued fuzzy set.(English)Zbl 0978.90009

Summary: It is difficult to determine the fixed total demand $$r_0$$ in an inventory problem with backorder in a whole plan period. We will fuzzify it as $$R=\lceil\text{near} r_0\rceil$$. In this article, we will classify $$R$$ into three kinds: (1) fuzzy total demand with triangular fuzzy number (Section 2), (2) fuzzy total demand with interval-valued fuzzy set based on two triangular fuzzy numbers (Section 3), (3) fuzzy total demand with interval-valued fuzzy set based on two trapezoidal fuzzy numbers (Section 4). We will find the corresponding order quantities and the shortage inventories, respectively.

### MSC:

 90B05 Inventory, storage, reservoirs 03E72 Theory of fuzzy sets, etc.
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### References:

 [1] Chang, S.-C.; Yao, J.-S.; Lee, H.-M., Economic reorder point for fuzzy backorder quantity, Europan journal operational research, 109, 183-202, (1998) · Zbl 0951.90003 [2] Gorzalczany, M.B., A method of inference in approximate resoning,based on interval-valued fuzzy sets, Fuzzy sets and systems, 21, 1-17, (1987) · Zbl 0635.68103 [3] H. Lee, J.-S. Yao, Economic order quantity in fuzzy sense for inventory without backorder model. Fuzzy Sets and Systems (to appear) · Zbl 0947.90005 [4] Lee, H.-M.; Yao, J.-S., Economic production quantity for fuzzy demand quantity and fuzzy production quantity, European journal operational research, 109, 203-211, (1998) · Zbl 0951.90019 [5] Yao, J.-S.; Lee, H.-M., Fuzzy inventory with backorder for fuzzy order quantity, Information science, 93, 283-319, (1996) · Zbl 0884.90077
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