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Let Q be a left Module over a ring with identity ℝ. In this paper, we introduced the concept of T-small Quasi-Dedekind Modules as follows, An R-module Q is T-small quasi-Dedekind Module if, ∀ w ∈ E n d R ( Q ) , w ≠ 0 then Ker w ≪T Q. Also, we illustrate it by examples and give basic properties.

In this paper a new algorithm is used which depending on ranking function for conclusion an optimal solution when transportation cost, sources to destination are fuzzy and were represented by abnormal triangular fuzzy numbers. A numerical example is given to display the efficiency of this algorithm.

Let ℝ be a ring with identity and let T be a unitary left Module over ℝ. In this paper, we give some cases when a direct sum of hollow Modules is semihollow-lifting, Also; we give a condition under which a direct sum of two Modules is semihollow-lifting,