It is hard to sense the degree of vagueness while using a Multiple Criteria Decision-Making (MCDM) model in industrial engineering problems. Selection of best candidate-alternative is an important issue when the attributes of the candidate-alternatives are conflicting in nature and they have incommensurable units. An MCDM model makes it possible to select the candidate-alternative that suits best for the investor. An example illustrating an MCDM model applied in plant-site selection problem has been considered in this article to demonstrate the veracity of the proposed methodology. The degree of vagueness hidden in the proposed approach has been investigated using a flexible modified logistic membership function (MF). The approach presented here provides feedback to the decision maker, implementer and analyst and gives a clear indication about the appropriate application and usefulness of the MCDM model. The key objective of this article is to guide decision makers in finding out the best candidate-alternative with higher degree of satisfaction and lesser degree of vagueness.