Pub. online:29 Mar 2024Type:Research ArticleOpen Access
Journal:Informatica
Volume 35, Issue 2 (2024), pp. 311–339
Abstract
The extensions of ordinary fuzzy sets are problematic because they require decimal numbers for membership, non-membership and indecision degrees of an element from the experts, which cannot be easily determined. This will be more difficult when three or more digits’ membership degrees have to be assigned. Instead, proportional relations between the degrees of parameters of a fuzzy set extension will make it easier to determine the membership, non-membership, and indecision degrees. The objective of this paper is to present a simple but effective technique for determining these degrees with several decimal digits and to enable the expert to assign more stable values when asked at different time points. Some proportion-based models for the fuzzy sets extensions, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets are proposed, including their arithmetic operations and aggregation operators. Proportional fuzzy sets require only the proportional relations between the parameters of the extensions of fuzzy sets. Their contribution is that these models will ease the use of fuzzy set extensions with the data better representing expert judgments. The imprecise definition of proportions is also incorporated into the given models. The application and comparative analyses result in that proportional fuzzy sets are easily applied to any problem and produce valid outcomes. Furthermore, proportional fuzzy sets clearly showed the role of the degree of indecision in the ranking of alternatives in binomial and trinomial fuzzy sets. In the considered car selection problem, it has been observed that there are minor changes in the ordering of intuitionistic and spherical fuzzy sets.
Pub. online:1 Jan 2018Type:Research ArticleOpen Access
Journal:Informatica
Volume 29, Issue 2 (2018), pp. 303–320
Abstract
The probabilistic linguistic terms set (PLTS) can reflect different importance degrees or weights of all possible linguistic terms (LTs) given by the experts for a specific object. The PROMETHEE II method is an important ranking method which can comprise preferences as well as indifferences, and it has a unique characteristic that can provide different types of preference functions. Based on the advantages of the PLTS and the PROMETHEE II method, in this paper, we extend the PROMETHEE II method to process the probabilistic linguistic information (PLI), and propose the PL-PROMETHEE II method with an improved possibility degree formula which can avoid the weaknesses from the original formula. Then concerning the multi-attribute decision making (MADM) problems with totally unknown weight information, the maximum deviation method is used to get the objective weight vector of the attributes, and net flows of the alternatives from the PROMETHEE II method are used to rank the alternatives. Finally, a numerical example is given to illustrate the feasibility of the proposed method.
Journal:Informatica
Volume 25, Issue 2 (2014), pp. 185–208
Abstract
In this study, we evaluated the effects of the normalization procedures on decision outcomes of a given MADM method. For this aim, using the weights of a number of attributes calculated from FAHP method, we applied TOPSIS method to evaluate the financial performances of 13 Turkish deposit banks. In doing this, we used the most popular four normalization procedures. Our study revealed that vector normalization procedure, which is mostly used in the TOPSIS method by default, generated the most consistent results. Among the linear normalization procedures, max-min and max methods appeared as the possible alternatives to the vector normalization procedure.