Laura De Miguel

Interval-Valued Atanassov Intuitionistic OWA Aggregations Using Admissible Linear Orders and Their Application to Decision Making

Based on the definition of admissible order for interval-valued Atanassov intuitionistic fuzzy sets, we study ordered weighted averaging operators in these sets, distinguishing between the weights associated with the membership and those associated with the nonmembership degree, which may differ from the latter. We also study Choquet integrals for aggregating information, which is represented using interval-valued Atanassov intuitionistic fuzzy sets. We conclude with two algorithms to choose the best alternative in a decision-making problem when we use this kind of sets to represent information.

Unbalanced interval-valued OWA operators

In this work, we introduce a new class of functions defined on the interval-valued setting. These functions extend classical OWA operators but allow for different weighting vectors to handle the lower bounds and the upper bounds of the considered intervals. As a consequence, the resulting functions need not be an interval-valued aggregation function, so we study, in the case of the lexicographical order, when these operators give an interval as output and are monotone. We also discuss an illustrative example on a decision making problem in order to show the usefulness of our developments.

Application of two different methods for extending lattice-valued restricted equivalence functions used for constructing similarity measures on L-fuzzy sets

This work was partially supported by the Brazilian Funding Agency CNPq under the Process 307781/2016-0, the Research Services of Universidad Publica de Navarra and by the research project TIN2016-77356-P from MINECO, AEI/FEDER, UE.

Forest fire detection

Graphical abstractDisplay Omitted HighlightsWe propose a new inference algorithm using overlap functions and indices.The convex combination of overlap expressions maintains the overlap properties.We avoid the difficult selection of appropriate expressions for each problem.We use our new inference algorithm in a Fuzzy Logic System to detect forest fire. It is well known that a powerful method to tackle diverse problems with lack of knowledge and/or uncertainty are Fuzzy Logic Systems (FLSs). In the literature, there exist different fuzzy inference mechanisms based on fuzzy variables and fuzzy rules to obtain a solution. In this work we introduce a generalization of the inference algorithm proposed by Mamdani, by using overlap functions and overlap indices. A challenging issue is the selection of most suitable overlap expressions for each problem. For this aim, we propose to use the convex combination of several ones. In this way, the conclusions obtained by our FLSs avoid the bad results obtained by an inadequate overlap expression. We test our proposal on a real problem of forest fire detection using a wireless sensor network.

First Approach of Type-2 Fuzzy Sets via Fusion Operators

In this work we introduce the concept of a fusion operator for type-2 fuzzy sets as a mapping that takes m functions from [0,1] to [0,1] and brings back a new function of the same type. We study in depth the properties of pointwise fusion operators and representable fusion operators. Finally, we study the union and intersection of type-2 fuzzy sets and we analyze when these functions are pointwise and representable fusion operators.

Strengthened Ordered Directional and Other Generalizations of Monotonicity for Aggregation Functions.

A tendency in the theory of aggregation functions is the generalization of the monotonicity condition. In this work, we examine the latest developments in terms of different generalizations. In particular, we discuss strengthened ordered directional monotonicity, its relation to other types of monotonicity, such as directional and ordered directional monotonicity and the main properties of the class of functions that are strengthened ordered directionally monotone. We also study some construction methods for such functions and provide a characterization of usual monotonicity in terms of these notions of monotonicity.

Pseudo strong equality indices for interval-valued fuzzy sets with respect to admissible orders

The introduction of admissible orders for intervals, i.e. linear orders which refine the partial orders, has stirred up a novel interest in the redefinition of many theoretical concepts which require an order for their appropriate definition. In this study, we introduce pseudo strong equality indices for interval-valued fuzzy sets. We also present a construction method of these indices in terms of interval-valued implications, interval-valued negations and interval-valued aggregation functions. The main novelty of these concepts is that we only consider admissible orders in order to avoid the loss of information resulting from the incomparability of some elements in the usual partial order.

Image inpainting using colour and gradient features

In this work we propose a new inpainting algorithm for color images. It is a patch-based algorithm that replicates some small areas across the image into the unknown area, in order to obtain a complete image with no visual differences between the original part and the reconstructed one. In this proposal we use color and gradient features to calculate the similarity between small windows of the image. The results show that our algorithm is able to obtain final results with better textures than the ones that only take into account the color features.

About directionally monotone and pre-aggregation functions

In this contribution, we discuss the role and potential of pre-aggregation functions. This class of functions has the same boundary conditions as aggregation functions, but differs in the constraints related to function increase. Specifically, monotonicity is replaced by the so-called directional monotonicity. With this work, we attempt to shed light on the relationship between aggregation and pre-aggregation functions, as well as to discuss some construction methods of pre-aggregation functions.

Convolution on Bounded Lattices

The union and intersection of two membership degrees of type-2 fuzzy sets are defined using a generalization of the mathematical operation of convolution. In the literature, it has been deeply studied when these convolution operations constitute a bounded distributive lattice. In this paper, we generalize the union and intersection convolution operations by replacing the functions from [0, 1] to itself with functions from a bounded lattice \(\mathbb {L}_1\) to a frame \(\mathbb {L}_2\), a particular type of bounded lattice. Similarly to some previous studies in the literature, we analyze when these new convolution operations constitute a bounded distributive lattice.