arXiv subjects
Publications and source records attributed to Benjamín Bedregal.
In this paper, we propose a method of extending quasi-overlap and grouping functions defined on a sublattice $ M $ of a bounded lattice $ L $ to this lattice considering a more general version of sublattice definition, introduced by Palmeira and Bedregral.
Admissible orders on fuzzy numbers are total orders which refine a basic and well-known partial order on fuzzy numbers. In this work, we define an admissible order on triangular fuzzy numbers (i.e. TFN's) and study some fundamental properties with its arithmetic and their relation with this admissible order. In addition, we also introduce the concepts of average function on TFN$'s and studies a generalized structure of the vector spaces. In particular we consider the case of TFN's.
Moore and Yang defined an integral notion, based on an extension of Riemann sums, for inclusion monotonic continuous interval functions, where the integrations limits are real numbers. This integral notion extend the usual integration of real functions based on Riemann sums. In this paper, we extend this approach by considering intervals as integration limits instead of real numbers and we abolish the inclusion monotonicity restriction of the interval functions and this notion is used to determine interval probability density functions.
In this paper we introduce a new class of fuzzy implications called ($S$,$N$,$T$)-implications inspired in the logical equivalence $p\rightarrow q \equiv \neg(p\wedge\neg q)\vee\neg p$ and present a brief study of some of the main properties that characterize this class. We present methods of obtaining $t$-norms and $t$-conorms from an ($S$,$N$,$T$)-implication and a fuzzy negation.
Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have been usually applied when there is uncertainty regarding the assignment of membership degrees. The choice of a total order for intervals can be significant, which motivated the recent developments on interval-valued aggregation functions and interval-valued overlap functions that are increasing to a given admissible order, that is, a total order that refines the usual partial order for intervals. Also, width preservation has been considered on these recent works, in an intent to avoid the uncertainty increase and guarantee the information quality, but no deeper study was made regarding the relation between the widths of the input intervals and the output interval, when applying interval-valued functions, or how one can control such uncertainty propagation based on this relation. Thus, in this paper we: (i) introduce and develop the concepts of width-limited interval-valued functions and width limiting functions, presenting a theoretical approach to analyze the relation between the widths of the input and output intervals of bivariate interval-valued functions, with special attention to interval-valued aggregation functions; (ii) introduce the concept of $(a,b)$-ultramodular aggregation functions, a less restrictive extension of one-dimension convexity for bivariate aggregation functions, which have an important predictable behaviour with respect to the width when extended to the interval-valued context; (iii) define width-limited interval-valued overlap functions, taking into account a function that controls the width of the output interval; (iv) present and compare three construction methods for these width-limited interval-valued overlap functions.
$n$-Dimensional fuzzy sets are a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0,1] increasingly ordered, called n-dimensional intervals. The set of n-dimensional intervals is denoted by $L_n([0,1])$. This paper aims to investigate semi-vector spaces over a weak semifield and aggregation functions concerning an admissible order on the set of $n$-dimensional intervals and the construction of aggregation functions on $L_n([0,1])$ based on the operations of the semi-vector spaces. In particular, extensions of the family of OWA and weighted average aggregation functions are investigated. Finally, we develop a multi-criteria group decision-making method based on n-dimensional aggregation functions with respect to an admissible order and give an illustrative example.
In this paper, we introduce the concept of residuated implications derived from quasi-overlap functions on lattices and prove some related properties. In addition, we formalized the residuation principle for the case of quasi-overlap functions on lattices and their respective induced implications, as well as revealing that the class of quasi-overlap functions that fulfill the residuation principle is the same class of continuous functions according to topology of Scott. Also, Scott's continuity and the notion of densely ordered posets are used to generalize a classification theorem for residuated quasi-overlap functions. Finally, the concept of automorphisms are extended to the context of quasi-overlap functions over lattices, taking these lattices into account as topological spaces, with a view to obtaining quasi-overlap functions conjugated by the action of automorphisms.
In the context of fuzzy logic, ordinal sums provide a method for constructing new functions from existing functions, which can be triangular norms, triangular conorms, fuzzy negations, copulas, overlaps, uninorms, fuzzy implications, among others. As our main contribution, we establish conditions for the ordinal sum of a family of fuzzy negations to be a fuzzy negation of a specific class, such as strong, strict, continuous, invertible and frontier. Also, we relate the natural negation of the ordinal sum on families of t-norms, t-conorms and fuzzy implications with the ordinal sum of the natural negations of the respective families of t-norms, t- conorms and fuzzy implications. This motivated us to introduces a new kind of ordinal sum for families of fuzzy implications.
In this paper we introduce a class of operators on complete lattices called Dynamic Ordered Weighted Averaging (DYOWA) functions. These functions provide a generalized form of an important class of aggregation functions: The Ordered Weighted Averaging (OWA) functions, whose applications can be found in several areas like: Image Processing and Decision Making. The wide range of applications of OWAs motivated many researchers to study their variations. One of them was proposed by Lizassoaim and Moreno in 2013, which extends those functions to complete lattices. Here, we propose a new generalization of OWAs that also generalizes the operators proposed by Lizassoaim and Moreno.
In literature, it is common to find problems which require a way to encode a finite set of information into a single data; usually means are used for that. An important generalization of means are the so called Aggregation Functions, with a noteworthy subclass called OWA functions. There are, however, further functions which are able to provide such codification which do not satisfy the definition of aggregation functions; this is the case of pre-aggregation and mixture functions. In this paper we investigate two special types of functions: Generalized Mixture and Bounded Generalized Mixture functions. They generalize both: OWA and Mixture functions. Both Generalized and Bounded Generalized Mixture functions are developed in such way that the weight vectors are variables depending on the input vector. A special generalized mixture operator, H, is provided and applied in a simple toy example.
Classifier ensembles are pattern recognition structures composed of a set of classification algorithms (members), organized in a parallel way, and a combination method with the aim of increasing the classification accuracy of a classification system. In this study, we investigate the application of a generalized mixture (GM) functions as a new approach for providing an efficient combination procedure for these systems through the use of dynamic weights in the combination process. Therefore, we present three GM functions to be applied as a combination method. The main advantage of these functions is that they can define dynamic weights at the member outputs, making the combination process more efficient. In order to evaluate the feasibility of the proposed approach, an empirical analysis is conducted, applying classifier ensembles to 25 different classification data sets. In this analysis, we compare the use of the proposed approaches to ensembles using traditional combination methods as well as the state-of-the-art ensemble methods. Our findings indicated gains in terms of performance when comparing the proposed approaches to the traditional ones as well as comparable results with the state-of-the-art methods.
n-Dimensional fuzzy sets is a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0,1] orderly increased, called n-dimensional intervals. The set of n-dimensional intervals is denoted by Ln([0,1]). This paper aims to investigate a special extension from [0,1] - n-representable fuzzy negations on Ln([0,1]), summarizing the class of such functions which are continuous and monotone by part. The main properties of (strong) fuzzy negations on [0,1] are preserved by representable (strong) fuzzy negation on Ln([0,1]), mainly related to the analysis of degenerate elements and equilibrium points. The conjugate obtained by action of an n-dimensional automorphism on an $n$-dimensional fuzzy negation provides a method to obtain other n-dimensional fuzzy negation, in which properties such as representability, continuity and monotonicity on Ln([0,1]) are preserved.
In this paper we consider the class of lambda-nondeterministic linear automata as a model of the class of linear languages. As usual in other automata models, lambda-moves do not increase the acceptance power. The main contribution of this paper is to introduce the deterministic linear automata and even linear automata, i.e. the natural restriction of nondeterministic linear automata for the deterministic and even linear language classes, respectively. In particular, there are different, but not equivalents, proposals for the class of "deterministic" linear languages. We proved here that the class of languages accepted by the deterministic linear automata are not contained in any of the these classes and in fact they properly contain these classes. Another, contribution is the generation of an infinite hierarchy of formal languages, going from the class of languages accepted by deterministic linear automata and achieved, in the limit, the class of linear languages.
In this paper we propose a special type of aggregation function which generalizes the notion of Ordered Weighted Averaging Function - OWA. The resulting functions are called Dynamic Ordered Weighted Averaging Functions --- DYOWAs. This generalization will be developed in such way that the weight vectors are variables depending on the input vector. Particularly, this operators generalize the aggregation functions: Minimum, Maximum, Arithmetic Mean, Median, etc, which are extensively used in image processing. In this field of research two problems are considered: The determination of methods to reduce images and the construction of techniques which provide noise reduction. The operators described here are able to be used in both cases. In terms of image reduction we apply the methodology provided by Patermain et al. We use the noise reduction operators obtained here to treat the images obtained in the first part of the paper, thus obtaining images with better quality.