Fuzzy inventory without backorder for fuzzy order quantity and fuzzy total demand quantity

In this paper, we consider the inventory problem without backorder such that both order and the total demand quantities are triangular fuzzy numbers &Qtilde; = (q1, q0, q2), and &Rtilde; = (r1, r0, r2), respectively, where q1 = q0 − Δ1, q2 = q0 + Δ2, r1 = r0 − Δ3, r2 = r0 + Δ4 such that 0 < Δ1 < q0, 0 < Δ2, 0 < Δ3 < r0, 0 < Δ4, and r0 is a known positive number. Under conditions 0 ⩽ q1 < q0 < q2 < r1 < r0 < r2 we find the membership function μG(&Qtilde;,&Rtilde;)(z) of the total fuzzy cost function G(&Qtilde;, &Rtilde;) and their centroid, then obtain order quantity q** in the fuzzy sense and the estimate of the total demand quantity.