The present research work deals with a logistic membership function (MF), within non-linear MFs, in finding out fuzziness patterns in disparate level of satisfaction for Multiple Criteria Decision-Making (MCDM) problem. This MF is a modified form of general set of S-curve MF. Flexibility of this MF in applying to real world problem has also been validated through a detailed analysis. An example illustrating an MCDM model applied in an industrial engineering problem has been considered to demonstrate the veracity of the proposed technique. 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 paper is to guide decision makers in finding out the best candidate-alternative with higher degree of satisfaction with lesser degree of vagueness under tripartite fuzzy environment.