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An algorithm for group decision making using n-dimensional fuzzy sets, admissible orders and OWA operators

We present the concept of admissible order for n-dimensional fuzzy sets.We give a construction method for those admissible orders using aggregation functions.We extent to the field of n-dimensional fuzzy sets the concept of OWA operators (which are always associated to a linear order).We design a decision making algorithm using n-dimensional fuzzy sets and n-tuple aggregation OWA operators.We justify our theoretical developments with an illustrative example applying the proposed algorithm. In this paper we propose an algorithm to solve group decision making problems using n-dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an increasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n-dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these conditions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples.

Edge Detection Based on Ordered Directionally Monotone Functions

We present an image edge detection algorithm that is based on the concept of ordered directionally monotone functions, which permit our proposal to consider the direction of the edges at each pixel and perform accordingly. The results of this method are presented to the EUSFLAT 2017 Competition on Edge Detection.

Consensus Image Feature Extraction with Ordered Directionally Monotone Functions

In this work we propose to use ordered directionally monotone functions to build an image feature extractor. Some theoretical aspects about directional monotonicity are studied to achieve our goal and a construction method for an image application is presented. Our proposal is compared to well-known methods in the literature as the gravitational method, the fuzzy morphology or the Canny method, and shows to be competitive. In order to improve the method presented, we propose a consensus feature extractor using combinations of the different methods. To this end we use ordered weighted averaging aggregation functions and obtain a new feature extractor that surpasses the results obtained by state-of-the-art methods.

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.

Strengthened ordered directionally monotone functions. Links between the different notions of monotonicity

Abstract In this work, we propose a new notion of monotonicity: strengthened ordered directional monotonicity. This generalization of monotonicity is based on directional monotonicity and ordered directional monotonicity, two recent weaker forms of monotonicity. We discuss the relation between those different notions of monotonicity from a theoretical point of view. Additionally, along with the introduction of two families of functions and a study of their connection to the considered monotonicity notions, we define an operation between functions that generalizes the Choquet integral and the Łukasiewicz implication.

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.

Some properties and construction methods for ordered directionally monotone functions

In this work we propose a new generalization of the notion of monotonicity, the so-called ordered directionally monotonicity. With this new notion, the direction of increasingness or decreasingness at a given point depends on that specific point, so that it is not the same for every value on the domain of the considered function.

A New Extension of Monotonicity: Ordered Directional Monotonicity.

In this work, we discuss a recent generalization of the classical notion of monotonicity, with a special focus on the idea of directional monotonicity. This idea leads to the concepts of pre-aggregation functions and of ordered directional monotonicity. For the former, the direction along which monotonicity is considered is the same for all the points of the domain and the same boundary conditions as for aggregation functions are imposed. For the latter, different directions of monotonicity may be considered at different points.

A Generalization of the Gravitational Search Algorithm

In this work we propose a generalization of the gravitational search algorithm where the product in the expression of the gravitational attraction force is replaced by more general functions. We study some conditions which ensure convergence of our proposal and we show that we recover a wide class of aggregation functions to replace the product.

Linking Mathematical Morphology and L-Fuzzy Concepts

Electronic version of an article published as International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 25, Suppl. 1 (December 2017) 73–98