O. Valero

O. Valero
University of the Balearic Islands | UIB · Department of Mathematic and Computer Sciences and IdISBa

PhD
Mathematical Models applied to Computer Science, Artificial Intelligence, Engineering, Economics and Medicine.

About

152
Publications
12,988
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Introduction
Oscar Valero currently works at the Department of Mathematics and Computer Science , University of the Balearic Islands. Oscar does research in Information Fusion, Aggregation Functions, Decision Making Methods, Generalized Metric Structures, Similarity Measures, Fixed Point Theory and their Applications to Engineering, Economics and Medicine.
Additional affiliations
October 2013 - present
University of the Balearic Islands
Position
  • Professor (Associate)
October 2003 - present
University of the Balearic Islands
Position
  • Professor (Associate)
October 2003 - present
University of the Balearic Islands
Position
  • Professor (Associate)

Publications

Publications (152)
Article
Full-text available
Fixed points results for rational type contractions in metric spaces have been widely studied in the literature. In the last years, many of these results are obtained in the context of partially ordered metric spaces. In this paper, we introduce a fixed point principle for a class of mappings between partially ordered metric spaces that we call orb...
Article
Full-text available
Information orders play a central role in the mathematical foundations of Computer Science. Concretely, they are a suitable tool to describe processes in which the information increases successively in each step of the computation. In order to provide numerical quantifications of the amount of information in the aforementioned processes, S.G. Matth...
Article
In the last years fuzzy (quasi-)metrics and indistinguishability operators have been used as a mathematical tool in order to develop appropriate models useful in applied sciences as, for instance, image processing, clustering analysis and multi-criteria decision making. The both aforesaid similarities allow us to fuzzify the crisp notion of equival...
Chapter
Robust model estimation is a recurring problem in application areas such as robotics and computer vision. Taking inspiration from a notion of distance that arises in a natural way in fuzzy logic, this paper modifies the well-known robust estimator RANSAC making use of a Fuzzy Metric (FM) within the estimator main loop to encode the compatibility of...
Chapter
Application domains, such as robotics and computer vision (actually, any sensor data processing field), often require from robust model estimation techniques because of the imprecise nature of sensor data. In this regard, this paper describes a robust model estimator which is actually a modified version of RANSAC that takes inspiration from the not...
Article
In 1994, S.G. Matthews introduced the notions of partial metric and weighted quasi-metric and, in addition, he showed that both are dual. In fact, he developed a method for generating weightable quasi-metrics from partial metrics and conversely. Recently, J.J. Miñana and O. Valero introduced a general method with the aim of inducing quasi-metrics f...
Article
Full-text available
Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguisha...
Article
In many fields of applied sciences, the aggregation of numerical values, in order to get a final one which allows to make a decision, plays a central role. Many times these numerical values represent dissimilarities and the merged value can be interpreted as a global dissimilarity. Inspired, on the one hand, by the interest that causes the dissimil...
Book
Full-text available
The book presents recent theoretical and practical information about the field of automation and control. It includes fifteen chapters that promote automation and control in practical applications in the following thematic areas: control theory, autonomous vehicles, mechatronics, digital image processing, electrical grids, artificial intelligence,...
Chapter
In this paper we prove an existence of fixed point theorem in partially ordered quasi-metric spaces which extends a celebrated result of Nieto and Rodríguez-López. Moreover, we derive from our main result a fixed point theorem for self-mappings in partially ordered metric spaces which improves the Nieto and Rodríguez-López one. Furthermore, we show...
Article
Full-text available
In this paper, we propose a family of indistinguishability operators, that we have called Yager Possibilitic Response Functions (YPRFs for short), as an appropriate tool for allocating tasks to a collective of agents. In order to select the best agent to carry out each task, we have used the so-called response threshold method, where each agent dec...
Article
Full-text available
A subset B of a space X is said to be bounded (in X ) if the restriction to B of every real-valued continuous function on X is bounded. A real-valued function on X is called b f -continuous if its restriction to each bounded subset of X has a continuous extension to the whole space X . b f -spaces are spaces such that b f -continuous functions are...
Article
In this paper, we consider the problem of aggregating a collection of transitive fuzzy binary relations in such a way that the aggregation process preserves transitivity. Specifically, we focus our efforts on the characterization of those functions that aggre-gate a collection of fuzzy binary relations which are transitive with respect to a collect...
Article
In this paper, we consider the problem of aggregating a collection of transitive fuzzy binary relations in such a way that the aggregation process preserves transitivity. Specifically, we focus our efforts on the characterization of those functions that aggregate a collection of fuzzy binary relations which are transitive with respect to a collecti...
Article
Full-text available
We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with “classic” fuzzy (pseudo)metrics. A method for construction CB-fuzzy...
Article
Full-text available
Since the notion of T-equivalence, where T is a t-norm, was introduced as a fuzzy generalization of the notion of crisp equivalence relation, many researchers have worked in the study of the metric behavior of such fuzzy relations. Concretely, a few techniques to induce metrics from T-equivalences, and vice versa, have been developed. In several fi...
Article
Full-text available
Borsík and Doboš studied the problem of how to merge a family of metric spaces into a single one through a function. They called such functions metric preserving and provided a characterization of them in terms of the so-called triangle triplets. Since then, different papers have extended their study to the case of generalized metric spaces. Concre...
Article
Full-text available
In 1981, J. Bors?k and J. Dob?s characterized those functions that allow to transform a metric into another one in such a way that the topology of the metric to be transformed is preserved. Later on, in 1994, S.G. Matthews introduced a new generalized metric notion known as partial metric. In this paper, motivated in part by the applications of par...
Conference Paper
Aggregation functions have been deeply studied in the literature and many applications to real life problems have been obtained. A specific aggregation function, known as OWA operator, has shown to be specially useful in decision making problems. In this paper we show that OWAs operators acting on a collection of distances can be considered as an a...
Conference Paper
In many real situations a practitioner must adopt an intermediate position between two fixed postures, that may even be opposite, in order to achieve an agreement and a working decision. In 2003, J.J. Nieto and A. Torres developed a mathematical technique for decision making in the aforementioned case by means of the use of the notion of midpoint b...
Conference Paper
Generalized dissimilarities have been used successfully as efficient tools in modeling in Computer Science. In fact, partial metrics and quasi-metrics have shown to be useful in the study of recursive denotational specifications for programming languages and to discuss the complexity analysis of algorithms, respectively. The aforesaid models were p...
Article
In this paper, we study those functions that allows us to combine a family of quasi-metrics, defined all of them on the same set, into a single one, which will be called quasi-metric aggregation functions. In particular, we characterize the quasi-metric aggregation functions and, in addition, we discuss a few of their properties. Moreover, a few me...
Article
Full-text available
In 1982, Trillas introduced the notion of indistinguishability operator with the main aim of fuzzifying the crisp notion of equivalence relation. In the study of such a class of operators, an outstanding property must be stressed. Concretely, there exists a duality relationship between indistinguishability operators and metrics. The aforesaid relat...
Article
The celebrated Kleene fixed point theorem is crucial in the mathematical modelling of recursive specifications in Denotational Semantics. In this paper we discuss whether the hypothesis of the aforementioned result can be weakened. An affirmative answer to the aforesaid inquiry is provided so that a characterization of those properties that a self-...
Article
Full-text available
Many G-metric fixed point results can be retrieved from classical ones given in the (quasi-)metric framework. Indeed, many G-contractive conditions can be reduced to a quasi-metric counterpart assumed in the statement of celebrated fixed point results. In this paper, we show that the existence of fixed points for the most part in the aforesaid G-me...
Article
In 1981, J. Borsík and J. Doboš analyzed what properties a function must satisfy in order to merge a collection of metric spaces into a single one. Later on, E. Castiñeira, A. Pradera and E. Trillas studied a variant of the same problem in which each metric of the collection to be merged is defined on the same non-empty set. In this, paper we conti...
Conference Paper
We consider the aggregation problem of relaxed Ti –indistinguishability operators where each member of the collection to be merged is a relaxed indistinguishability operator with respect to a different t-norm Ti . Thus we provide sufficient conditions to merge a collection such an indistinguishability operators. Moreover, we give a characterization...
Article
A fuzzy set on a finite universe can be interpreted as a vector in a unit cube. This gives rise to a huge variety of approaches in order to aggregate finite fuzzy sets or to modify a given one. We analyze several geometrical methods and discuss possible applications in a multidisciplinary setting.
Article
In 1970, a qualitative fixed point technique useful to model the recursive specifications in denotational semantics was developed by means of the celebrated Kleene‘s fixed point theorem. Later on, in 1994 and 1995, quantitative counterparts of the aforesaid technique, but now based on generalized versions of Banach fixed point theorem, were obtaine...
Article
Based on the duality relationship between indistinguishability operators and (pseudo-)metrics, we address the problem of establishing whether there is a relationship between the last ones and fuzzy (pseudo-)metrics. We give a positive answer to the posed question. Concretely, we yield a method for generating fuzzy (pseudo-)metrics from (pseudo)-met...
Article
In 1972, D.S. Scott developed a qualitative mathematical technique for modeling the meaning of recursive specifications in Deno-tational Semantics. In this paper we show that the same original Scott’s technique remains helpful for Asymptotic Complexity Analy-sis of algorithms requiring really a reduced number of hypotheses and elementary arguments....
Article
In this paper we present a new �fixed point theorem in quasi-metric spaces which captures the spirit of Kleene's �fixed point theorem. To this end, we explore the fundamental assumptions in the aforesaid result when we consider quasi-metric spaces endowed with the specialization partial order. Thus, we introduce an appropriate notion of order-compl...
Article
In this paper we develop a new technique for constructing fuzzy metric spaces, in the sense of George and Veeramani, from metric spaces and by means of the Lukasievicz t-norm. In particular such a technique is based on the use of metric preserving functions in the sense of J. Doboš. Besides, the new generated fuzzy metric spaces are strong and comp...
Article
Full-text available
The notion of indistinguishability operator was introduced by E. Trillas in 1982, with the aim of fuzzifying the crisp notion of equivalence relation. Such operators allow for measuring the similarity between objects when there is a limitation on the accuracy of the performed measurement or a certain degree of similarity can be only determined betw...
Article
Full-text available
Selecting the best task to execute (task allocation problem) is one of the main problems in multi-robot systems. Typical ways to address this problem are based on swarm intelligence and very especially using the so-called response threshold method. In the aforementioned method a robot has a certain probability of executing a task which depends on a...
Article
In 1970, D.S. Scott gave applications of Kleene’s fixed point theorem to describe the meaning of recursive denotational specifications in programming languages. Later on, in 1994, S.G. Matthews and, in 1995, M.P. Schellekens gave quantitative counterparts of the Kleene fixed point theorem which allowed to apply partial metric and quasi-metric fixed...
Article
Full-text available
In this paper we show an application of indistinguishability operators to model response functions. Such functions are used in the mathematical modeling of the task allocation problem in multi-agent systems when the stimulus, perceived by the agent, to perform a task is assessed by means of the response threshold model. In particular, we propose th...
Conference Paper
One of the main problems to solve in multi-robot systems is to select the best robot to execute each task (task allocation). Several ways to address this problem have been proposed in the literature. This paper focuses on one of them, the so-called response threshold methods. In a recent previous work, it was proved that the possibilistic Markov ch...
Conference Paper
This paper addresses one of the main problems to solve in a multi-robot system, allocating tasks to a set of robots (multi-robot task allocation-MRTA). Among all the approaches proposed in the literature to face up MRTA problem, this paper is focused on swarm-like methods called response threshold algorithms. The task allocation algorithms inspired...
Article
We show that the definition of a fuzzy set is directly related to the existence of a weightable quasi-metric on a universe. This relationship is also explored in terms of functional equations coming either from the membership function of a fuzzy set or from the disymmetry function of a quasi-metric.
Article
We study finite partial orders and the concept of indistinguishability. In particular, we focus on SP-orders. These orderings can be represented by means of Hasse diagrams and numerical labels. Since these numerical representations can be interpreted by means of permutations, we extend the study to the field of group theory. Through this point of v...
Article
Full-text available
Multi-robot task allocation is one of the main problems to address in order to design a multi-robot system, very especially when robots form coalitions that must carry out tasks before a deadline. A lot of factors affect the performance of these systems and among them, this paper is focused on the physical interference effect, produced when two or...
Data
Mean, standard deviation and median for experiments with soft deadline and Nt = 30. These results show the ratio between the utility obtained with MDRA and the utility of the optimal strategy. (PDF)
Data
Mean, standard deviation and median of the execution with hard deadline. These results show the ratio between the utility obtained with MDRA and the utility of the optimal strategy. (PDF)
Data
Mean, standard deviation and median of the execution with hard deadline using the 50 environments with the highest deadline values. These results show the ratio between the utility obtained with MDRA and the utility of the optimal strategy. (PDF)
Data
Parameters of the uniform random variables (U(a, b)) used to generate the experiments. (PDF)
Data
Mean, standard deviation and median for experiments with soft deadline and Nt = 15. These results show the ratio between the utility obtained with MDRA and the utility of the optimal strategy. (PDF)
Data
Mean, standard deviation and median of the execution time with soft deadline and Nt = 30. (PDF)
Chapter
In 1981, J. Borsík and J. Doboš studied the problem of how to merge, by means of a function, a family of distances into a single one. To this end, they introduced the notion of distance aggregation function and gave a characterization of such functions. Later on, in 2010, the notion of distance aggregation function was extended to the framework of...
Article
Full-text available
In "Denotational semantics for programming languages, balanced quasi-metrics and fixed points" (International Journal of Computer Mathematics 85 (2008), 623-630), J. Rodr\'{i}guez-L\'{o}pez, S. Romaguera and O. Valero introduced and studied a balanced quasi-metric on any domain of (finite and infinite) words, denoted by $q_{b}$. In this paper we sh...
Article
In this paper we continue the study of fixed point theory in partial quasi-metric spaces and its usefulness in complexity analysis of algorithms. Concretely we prove two new fixed point results for monotone and continuous self-mappings in 0-complete partial quasi-metric spaces and, in addition, we show that the assumptions in the statement of such...
Article
We show that the poset of formal balls of the Sorgenfrey quasi-metric space is an ω-continuous domain, and deduce that it is also a computational model, in the sense of R.C. Flagg and R. Kopperman, for the Sorgenfrey line. Furthermore, we study its structure of quantitative domain in the sense of P. Waszkiewicz.
Article
Full-text available
In 1994, Matthews obtained an extension of the celebrated Banach fixed point theorem to the partial metric framework (Ann. N.Y. Acad. Sci. 728:183-197, 1994). Motivated by the Matthews extension of the Banach theorem, we present a Nemytskii-Edelstein type fixed point theorem for self-mappings in partial metric spaces in such a way that the classica...
Article
Full-text available
In 1981, Borsík and Doboš studied the aggregation problem for metric spaces. Thus, they characterized those functions that allow one to merge a collection of metrics providing a single metric as a result (Borsík and Doboš in Math. Slovaca 31:193-205, 1981). Later on, in 1994, the notion of partial metric space was introduced by Matthews with the ai...
Article
Full-text available
In this paper we present a few fixed point results in the framework of topological posets. To this end, we introduce an appropriate notion of completeness and order-continuity. Special attention is paid to the case that the topology of the topological poset is induced by an extended quasi-metric. Finally, the applicability of the exposed results is...
Article
Abstract Scott (1970) [11] introduced qualitative fixed point techniques as a suitable mathematical tool for program verification. Inspired by the fact that the Scott mathematical tools do not include metric implements, Matthews (1994) [8] introduced the concept of partial metric space with the aim of reconciling the Scott fixed point techniques wi...
Article
Full-text available
Starting from the definition of a weightable quasi-metric we observe that several functional equations are induced in a natural way. Studying these equations we characterize weightable quasi-metrics and show that they define representable total preorders. We also analyze how to retrieve weightable quasi-metrics from real-valued functions satisfying...
Conference Paper
The task allocation problem is one of the main issues in multi-robot systems. Typical ways to address this problem are based on Swarm Intelligence. One of them is the so-called Response Threshold Method. In the aforementioned method every robot has associated a task response threshold and a task stimuli in such a way that the robot’s probability of...
Article
Full-text available
Asymmetric normed semilinear spaces are studied. A description of biBanach, left K -sequentially complete, and Smyth complete asymmetric normed semilinear spaces is provided and three appropriate notions of absolute convergence in the asymmetric normed framework are introduced. Some characterizations of completeness are also obtained via absolutely...
Article
Many fields in applied sciences, like Artificial Intelligence and Computer Science, use aggregation methods to provide new generalized metrics from a collection of old ones. Thus, the problem of merging by means of a function a collection of generalized metrics into a single one has been recently studied in depth. Moreover, the mipoint sets for a g...
Article
Full-text available
In Cerdà-Uguet et al. (Theory Comput. Syst. 50:387-399, 2012), a new mathematical fixed point technique, that uses the so-called Baire partial quasi-metric space, was introduced with the aim of providing the asymptotic complexity of a class of recursive algorithms. The aforementioned technique presents the advantage that requires less calculations...
Conference Paper
Full-text available
In 1981, Borsík and Doboš studied the problem of how to combine, by means of a function, two metrics in order to obtain a single one as output. To this end, they introduced the notion of metric aggregation function and gave a characterization of such functions. Recently, in [“Aggregation of asymmetric distances in computer science”, Inform. Sci. 18...
Article
The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsik and J. Dobos [On a product of metric spaces, Math. Slovaca31 (1981) 193-205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsik and Dobos study was extended to the quasi-metric context in such a way that...
Article
Full-text available
In 1994, Matthews introduced the notion of a partial metric space in order to obtain a suitable mathematical tool for program verification (Matthews in Ann. N.Y. Acad. Sci. 728:183-197, 1994). He gave an application of this new structure to formulate a suitable test for lazy data flow deadlock in Kahn’s model of parallel computation by means of a p...
Article
Full-text available
In 1981, J. Borsík and J. Doboš studied and solved the problem of how to merge, by means of a function, a (not necessarily finite) collection of metrics in order to obtain a single one as output. Later on, in 2010, G. Mayor and O. Valero proposed and solved the Borsík and Doboš problem in the context of quasi-metrics. In this paper, we focus our at...
Article
Full-text available
In 1994, Matthews introduced the notion of partial metric space with the aim of providing a quantitative mathematical model suitable for program verification. Concretely, Matthews proved a partial metric version of the celebrated Banach fixed point theorem which has become an appropriate quantitative fixed point technique to capture the meaning of...
Article
Full-text available
In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. Concretely, we present fixed point results for weakly contractive and weakly Kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Special attention to the cyclical case is paid. Mo...
Article
Schellekens [The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electron. Notes Theor. Comput. Sci. 1 (1995), pp. 211–232.] introduced the theory of complexity (quasi-metric) spaces as a part of the development of a topological foundation for the asymptotic complexity analysis of programs and algorithms in...
Article
Full-text available
We show that the domain of formal balls of a complete partial metric space (X, p) can be endowed with a complete partial metric that extends p and induces the Scott topology. This result, that generalizes well-known constructions of Edalat and Heckmann [A computational model for metric spaces, Theoret. Comput. Sci. 193 (1998), pp. 53–73] and Heckma...
Conference Paper