Approach for weighting criterias in engineering decision making problems in fuzzy environment

A general working methodology for solving engineering design problems must be involved the following activities: (a) Defined the goals; (b) Clarify the boundary conditions; (c) Dispel prejudice to ensure the most wide-ranging possible search for solutions; (d) Search for variants; (e) Evaluate and; (f) Make decision.; In decision making, in general, and engineering decision making, in particular, it is essential to determine the set of criteria, which represent the point of view taken into account in the decision problem.; The points of view are generally in conflict and have different importance for the decision-maker. Most of multiple attribute decision making methods require a quantification of importance of criterias as input data, but only some of them treat how to determinate of weights. Classical methods proposed require exact values for x_ij (rating of criteria i with respect to criteria j). But, at times, it is common that the x_ij value cannot be assessed precisely due to partial ignorance of the problem, unquantifiable criteria or nonobtainable information. So, classical methods cannot be effectively handle problems with imprecise information.; To resolve this difficulty, a few new methods for determining the weight of criteria, based on Fuzzy Set Theory, have been proposed. For fuzzy methods, the x_ij value are “imprecise quantities”, that is, the decision-maker can express his preference judgements among the criteria in form of fuzzy terms such as “close to 10”, “about 7”, “approximately 4” or linguistic terms such as “very important”, “not very important”, “medium”. These fuzzy data have to be transformed into fuzzy numbers to operate with them.; But, most real world problems contain a mixture of fuzzy and crisp data. When precise information cannot be obtained or is too costly to assess, the imperfect information must be noted in fuzzy format; however, when information is easily measurable or accessible, the information must be coded in crisp notation.; After analised all methods for obtaining the weight of decision criteria, this thesis presents a new method based on using fuzzy/crisp pairwise comparison. The most important characteristics of this new method are: (a) The rating of importance between two criterias can be expressed in linguistic terms, fuzzy terms or crisp number; (b) The weight of criterias can be crisp or fuzzy; (c) There can be multiple decision-makers, and; (d) The solutions are unique and easy to obtaining. Finally, this method has been applied to a real case and the results have been excellent.