Fuzzy-MACBETH Hybrid Method: Mathematical Treatment of a Qualitative Scale Using the Fuzzy Theory

Abstract This paper describes the research procedures adopted in developing a triangular fuzzy number scale based on semantic of MACBETH (Measuring Attractiveness by Categorical Based Evaluation Technique). The objective was to mathematically treat uncertainty and subjectivity linguistic variables used assess decision problem. A matrix initially obtained maker’s assessment given context analysis. then fuzzified Fuzzy numbers scale. Next, inference process performed using F-LP-MACBETH linear programming problem proposed here, resulting defuzzified centroid method, from which crisp basic emerged, cardinalized. results show that method here can overcome classical method’s cardinal inconsistency problem, facilitates its application complex contexts. Hence, Hybrid generated numerical values makers’ semantically consistent assessments matrix, presents inconsistency. Therefore, advantage consists possibility obtaining aligned preferences without need reassess context.