Extension of Base-Criterion Method Based on Fuzzy Set Theory
Abstract
Due to the complexity as well as the uncertainty of the purpose and fuzziness of human thinking, human qualitative judgments generally hold the characteristics of obscurity and approximate. In order to extend the base-criterion method (BCM) to uncertain circumstances, fuzzy information recruiting may be a better way to address a lot of multi-criteria decision-making problems. In this paper, we have developed the BCM method based on the linguistic variables to the fuzzy environment. The base-comparisons for the base-criterion (selective or preferential) relative to the other criteria expressed by linguistic variables of decision-makers, which can be transformed into triangular fuzzy numbers to be utilized in the nonlinear optimization program. Afterward, the optimum fuzzy weights are determined according to the decision-maker preference. The optimum fuzzy weights of criteria can be transferred (if need) to crisp ranking scores by employing the GMIR (graded mean integration representation) method. The fuzzy BCM method can be used to tackle the problems with the characteristics of ambiguity and intangibility. This method uses linguistic terms such as “Extreme important”, “Very strong importance”, “Strong importance”, “Moderate importance”, and “Equally importance” to execute the base-comparisons. Using the linguistic variables causes executing the pairwise comparisons more accurately and easily and gets more trustworthy decision-making results. To show the applicability of fuzzy BCM, we analyzed two numerical examples (optimal transportation mode selection and car selection) for decision-making problems under a fuzzy environment. The results of this paper shows the fuzzy BCM results are fully consistent in terms of direction and strength.