Abstract
The Logarithm Methodology of Additive Weights (LMAW) method is a very young method and in its basic form is defined for crisp values. In this paper, the LMAW method was improved by being modified with triangular fuzzy numbers. The modification significantly improved the capacity of the LMAW method to consider uncertainty in decision making. The special importance of the method is reflected in a relatively simple mathematical apparatus due to which it is possible to define, with high quality, weight coefficients of criteria and rank alternative solutions in uncertain environments. The method was tested in solving the problem of the location selection for a landing operations point (LOP) in combat operations of the army. The validation of the obtained results was performed: (1) by means of comparison with the Fuzzy Simple Additive Weighting (FSAW) Method, the Fuzzy Multi-Attributive Border Approximation area Comparison (FMABAC), the fuzzy Višekriterijumsko KOmpromisno Rangiranje (FVIKOR), the fuzzy COmpressed PRoportional ASsessment (FCOPRAS), and the fuzzy Multi Attributive Ideal-Real Comparative Analysis (FMAIRCA); (2) by means of sensitivity analysis by changing the weight coefficients of criteria; and (3) using simulation software. In comparison with other methods, the quality of the ranking of alternative solutions was confirmed, which highlighted the special importance of the fuzzy LMAW method relative to that of certain standard methods, respectively, the ones that are often used and confirmed in practice. On the other hand, the sensitivity analysis, including the changing of the weight coefficients of criteria, showed that the model could tolerate smaller errors in defining the weight coefficients of criteria, and it provided stable results. Finally, the validation of results achieved with the use of simulation software confirmed the obtained output results. The output results confirmed the quality of the modified method.
Highlights
Decision making is an important aspect of human life
In addition to solving a specific problem, the aim of the paper is to present in detail the fuzzy LMAW (FLMAW) methods, in order to test this method with other issues
Basic settings related to fuzzy numbers were explained and the FLMAW method was described step by step, respectively, with the equities defining the presented methods
Summary
Decision making is an important aspect of human life. It is present in everyday human activities, from making daily and individual decisions, to decisions that are important to a group of people or even to the wider community. The importance of decision making has conditioned the development of a large number of techniques—methods that support the decision-making process, such as by helping decision makers to perceive a problem more comprehensively and make a rational decision. The new methods of multicriteria decision making have appeared in contemporary literature. Some methods are developed for the complete process, for defining weights of criteria and ranking alternatives, and when using some of them, weights of criteria can be defined or the alternatives can be ranked
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