| This paper mainly proves the following three conclusions:Let (c|)j,(a|)ij and (b|)i, be fuzzy numbers for all i∈M and j∈N . α, β∈(0,1) ,α + β = 1 .Let (X|) bea feasible region of FLP problem (P) with fuzzy relation (P|), (Y|)be a feasible region of FLP problem (D) with fuzzy relation (Q|).(P|) is dual to (Q|). Theorem 2.21 (First Weak Duality Theorem)If a vector x=(x1,…xn)≥0, x∈[(X|)]α and y = (y1,…ym)≥0, y∈[(Y|)]β.(1) If (2) If Theorem2. 25 (Second Weak Duality Theorem) If for some x∈[(X|)]α, x=(x1,…xn)≥0, y∈[(Y|)]β, y = (y1,…ym)≥0 .If then x is (α,α)-maximal solution of FLP problem (P) and y is (β,β) -minimalsolution of FLP problem (D)Theorem2. 28 (Strong Duality Theorem)If for some α,β ∈ (0,1), [(X|)]α and [(Y|)]β are nonempty, α + β = 1 .then:(1) If , then there exists x* - an (α,α) -maximalsolution of FLP problem and there exists y*-an (β,β) -minimal solution of FLP problem(D) such that:(2) If , then there exists x*-an(α,α) -maximalsolution of FLP problem(P) and there exists y*-an (β,β) -minimal solution of FLP problem(D) such that:...
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