Using fuzzy numbers and OWA operators in the weighted average and its application in decision making

Se presenta un nuevo método para tratar situaciones de incertidumbre en los que se utiliza el operador OWAWA (media ponderada – media ponderada ordenada). A este operador se le denomina operador OWAWA borroso (FOWAWA). Su principal ventaja se encuentra en la posibilidad de representar la información incierta del problema mediante el uso de números borrosos los cuales permiten una mejor representación de la información ya que consideran el mínimo y el máximo resultado posible y la posibilidad de ocurrencia de los valores internos. Se estudian diferentes propiedades y casos particulares de este nuevo modelo. También se analiza la aplicabilidad de este operador y se desarrolla un ejemplo numérico sobre toma de decisiones en la selección de políticas fiscalesWe present a new approach for dealing with an uncertain environment when using the ordered weighted averaging – weighted averaging (OWAWA) operator. We call it the fuzzy OWAWA (FOWAWA) operator. The main advantage of this new aggregation operator is that it is able to represent the uncertain information with fuzzy numbers. Thus, we are able to give more complete information because we can consider the maximum and the minimum of the problem and the internal information between these two results. We study different properties and different particular cases of this approach. We also analyze the applicability of the new model and we develop a numerical example in a decision making problem about selection of fiscal policies

Searching for a consensus similarity function for generalized trapezoidal fuzzy numbers

There is controversy regarding the use of the similarity functions proposed in the literature to compare generalized trapezoidal fuzzy numbers since conflicting similarity values are sometimes output for the same pair of fuzzy numbers. In this paper we propose a similarity function aimed at establishing a consensus. It accounts for the different approaches of all the similarity functions. It also has better properties and can easily incorporate new parameters for future improvements. The analysis is carried out on the basis of a large and representative set of pairs of trapezoidal fuzzy numbers

A new similarity function for generalized trapezoidal fuzzy numbers

Numerous authors have proposed functions to quantify the degree of similarity between two fuzzy numbers using various descriptive parameters, such as the geometric distance, the distance between the centers of gravity or the perimeter. However, these similarity functions have drawback for specific situations. We propose a new similarity measure for generalized trapezoidal fuzzy numbers aimed at overcoming such drawbacks. This new measure accounts for the distance between the centers of gravity and the geometric distance but also incorporates a new term based on the shared area between the fuzzy numbers. The proposed measure is compared against other measures in the literature

An improvised similarity measure for generalized fuzzy numbers

Similarity measure between two fuzzy sets is an important tool for comparing various characteristics of the fuzzy sets. It is a preferred approach as compared to distance methods as the defuzzification process in obtaining the distance between fuzzy sets will incur loss of information. Many similarity measures have been introduced but most of them are not capable to discriminate certain type of fuzzy numbers. In this paper, an improvised similarity measure for generalized fuzzy numbers that incorporate several essential features is proposed. The features under consideration are geometric mean averaging, Hausdorff distance, distance between elements, distance between center of gravity and the Jaccard index. The new similarity measure is validated using some benchmark sample sets. The proposed similarity measure is found to be consistent with other existing methods with an advantage of able to solve some discriminant problems that other methods cannot. Analysis of the advantages of the improvised similarity measure is presented and discussed. The proposed similarity measure can be incorporated in decision making procedure with fuzzy environment for ranking purposes