Antonio Francisco Roldán López de Hierro

Estimation of a Fuzzy Regression Model Using Fuzzy Distances

Regression analysis is a powerful statistical tool that has many applications in different areas. The problem of regression analysis under a fuzzy environment has been treated in the literature from different points of view and considering a variety of input/output data (crisp or fuzzy). However, we realize that, in general, most research papers have a conflict between the solution of the fuzzy regression problem using crisp distances (minimizing a real error function) and the interpretation of fuzzy data as possibility distributions. The main aim of this paper is to develop a methodology to solve this problem introducing a fuzzy partial order and a family of fuzzy distance measures on the whole set of fuzzy numbers. The new approach allows us to obtain linear and nonlinear models that reach the lowest fuzzy error; the estimation process, in general, can be considered easier to apply in practice, and it is not limited to triangular fuzzy numbers. Numerical examples are provided to illustrate the usefulness and applicability of these results, and comparisons with existing methodologies show that the performance of the proposed solution is very satisfactory.

Fixed point theory in metric type spaces

Introduction with a Brief Historical Survey.- Preliminaries.- G-Metric Spaces.- Basic Fixed Point Results in the Setting of G-Metric Spaces.- Fixed Point Theorems in Partially Ordered G-Metric Spaces.- Further Fixed Point Results on G-Metric Spaces.- Fixed Point Theorems via Admissible Mappings.- New Approaches to Fixed Point Results on G-Metric Spaces.- Expansive Mappings.- Reconstruction of G-Metrics: G*-Metrics.- Multidimensional Fixed Point Theorems on G-Metric Spaces.- Recent Motivating Fixed Point Theory.

A fuzzy regression approach using Bernstein polynomials for the spreads

An important research topic in applied statistics consists of determining the relationship between several variables through a regression function. Recently, fuzzy regression analysis has become important to deal with fuzzy data and vague information captured from the real world. When we are modeling relationships between an imprecise response and several real exploratory variables, one of the main difficulties is to guarantee the condition of non-negativity of the spreads. In this paper, due to their ease of implementation, continuous differentiability, and theoretical properties, Bernstein polynomials are used to develop a fuzzy regression procedure which guarantees this condition. We demonstrate the applicability and effectiveness of our method through the analysis of real data and comparisons with existing methodologies.

Some fixed point theorems in Menger probabilistic metric-like spaces

In this manuscript we extend very recent fixed point theorems in the setting of Menger spaces in three senses: on the one hand, we introduce the notion of Menger probabilistic metric-like space by avoiding a non-necessary constraint (at least, for our purposes) in the properties that define a Menger space; on the other hand, we consider a more general class of auxiliary functions in the contractivity condition; finally, we show that the function t→1/t−1

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

t\rightarrow1/t-1

New fixed point theorem under R-contractions

(which appears in many fixed point theorems in the fuzzy context) can be replaced by more appropriate and general functions. We illustrate our main statements with an example in which previous results cannot be applied.

Fixed point theorems in new generalized metric spaces

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.