Concepción Roldán

Multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces

In recent times, coupled, tripled and quadruple fixed point theorems have been intensively studied by many authors in the context of partially ordered complete metric spaces using different contractivity conditions. Roldan et al. showed a unified version of these results for nonlinear mappings in any number of variables (which were not necessarily permuted or ordered) introducing the notion of multidimensional coincidence point. Very recently, Choudhury et al. proved coupled coincidence point results in the context of fuzzy metric spaces in the sense of George and Veeramani. In this paper, using the idea of coincidence point for nonlinear mappings in any number of variables, we study a fuzzy contractivity condition to ensure the existence of coincidence points in the framework of fuzzy metric spaces provided with Hadzic type t-norms. Then, we present an illustrative example in which our methodology leads to the existence of coincidence points but previous theorems cannot be applied.

F-closed sets and coupled fixed point theorems without the mixed monotone property

In this paper we present the notion of F-closed set (which is weaker than the concept of F-invariant set introduced in Samet and Vetro (Ann. Funct. Anal. 1:46-56, 2010), and we prove some coupled fixed point theorems without the condition of mixed monotone property. Furthermore, we interpret the transitive property as a partial preorder and, then, some results in that paper and in Sintunavarat et al. (Fixed Point Theory Appl. 2012:170, 2012) can be reduced to the unidimensional case.MSC:46T99, 47H10, 47H09, 54H25.

Multidimensional fixed point theorems under ( ψ , Φ ) -contractive conditions in partially ordered complete metric spaces

In this paper, we study the existence and uniqueness of coincidence points for nonlinear mappings of any number of arguments under a weak ( ? , ? ) -contractive condition. Our results generalize, extend and unify several classical and very recent related results in the literature (see Aydi et?al. (2011), Berinde (2010), Gnana-Bhaskar and Lakshmikantham (2006), Berzig and Samet (2012), Borcut and Berinde (2012), Choudhury et?al. (2011), Karapinar and Luong (2012), Lakshmikantham and ?iric (2009), Luong and Thuan (2011), Roldan (2012)).

Some applications of the study of the image of a fuzzy number

In this paper, we present a characterization of the image of a fuzzy number in terms of the extremes of its level sets. Then we deduce some consequences: we show some relationships between the image of two fuzzy numbers and the images of their usual operations and it is proved that the continuity of some fuzzy numbers is preserved under the usual operations. As applications, we introduce a fuzzy regression model involving a parametric family of fuzzy semidistances between fuzzy numbers with finite image and an ordering process of fuzzy numbers with compact support that satisfies specificity-type properties.

A fuzzy regression model based on finite fuzzy numbers and its application to real-world financial data

Different sources of imprecision and uncertainty are encountered in practical problems and, thus, many elements may need to be imprecisely observed, defined or treated. In this setting, one of the most successfully applied techniques to describe possible relationships between fuzzy variables is the regression methodology. In this paper, we introduce a fuzzy regression procedure involving a class a fuzzy numbers defined by some level sets called finite fuzzy numbers. We give a characterization of the image of a finite fuzzy number in terms of the extremes of its level sets and we present a parametric family of fuzzy semidistances between them that let us to consider a total fuzzy error of estimation (described as a fuzzy sum of squares of residuals in particular cases). The estimation process consists in finding a regression model that minimizes, in a fuzzy sense, such fuzzy error. Although spreads of finite fuzzy numbers can take some values very close to zero, which complicate the task of finding nonnegative models, the presented algorithm is able to guarantee that the predicted response is a fuzzy variable. Finally a numerical example based on fuzzy economic data of China is given to illustrate the use of the proposed method.

Coupled coincidence point theorems in (intuitionistic) fuzzy normed spaces

In this paper, we prove some coupled coincidence point theorems in fuzzy normed spaces. Our results improve and restate the proof lines of the main results given in the papers (Eshaghi Gordji et al. in Math. Comput. Model. 54:1897-1906, 2011) and (Sintunavarat et al. in Fixed Point Theory Appl. 2011:81, 2011).MSC:47H10, 54H25, 34B15.

On a new methodology for ranking fuzzy numbers and its application to real economic data

Abstract Ranking fuzzy numbers plays an important role in the decision process. Several strategies can be found in the abundant literature existing on this topic, which can be basically classified into two main groups: approaches based on the so-called ranking indices and based on fuzzy binary relations. Ranking indices are functions from fuzzy numbers to real values. These defuzzification methods are critiqued by its implicit information loss which leads to results that might not be consistent with human intuition in certain cases. In a fuzzy context, approaches based on binary relations can be considered more suitable solutions. Following this strategy, this paper introduces a new technique for ranking fuzzy numbers which is applicable to the whole set of fuzzy numbers. It is proved that many desired properties (in particular, we give several new properties) are satisfied and numerical examples show reasonable results. The developed technique is very easy to compute and interpret in practice, and it overcomes certain shortcomings that appear when applying other more complex algorithms. In the case of triangular or trapezoidal fuzzy numbers, the procedure is particularly simple and intuitive. Finally, a real-life example involving data of Chinese Economy is also carried out.

Two novel methodologies for considering aggregation functions by implicit equations and minimization problems

Abstract In this work, we consider the problem of defining aggregation functions by means of two distinct methodologies. In the first one, we obtain an aggregation function in an implicit way, from a function which fulfills appropriate conditions. The second methodology, related to the idea of penalty function, is based on the minimization of a distance or error and can be seen as a generalization of the idea of correlation in statistics. We analyze the aggregation functions obtained with both methodologies and we present an illustrative decision-making example to show their different behaviors.