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[EN] With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see "Am. Math. Month. 1967, 74, 436-437") that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see "Fixed Point Theory 2005, 6, 71-78") also allows us to characterize the fuzzy metric completeness.

[EN] We obtain a fixed point theorem for complete fuzzy metric spaces, in the sense of Kramosiland Michalek, that extends the classical Kannan fixed point theorem. We also show that, in fact, ourtheorem allows to characterize the fuzzy metric completeness, extending in this way the well-known Reich-Subrahmanyam theorem that a metric space is complete if and only if every Kannan contraction on it has afixed point.

[EN] We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi.

[EN] In this paper, we introduce the notion of G-fuzzy H-quasi-contractions using directed graphs in the setting of fuzzy metric spaces endowed with a graph and we show that this new type of contraction generalizes a large number of different types of contractions. Subsequently, we investigate some results concerning the existence of fixed points for this class of contractions under two different conditions in M-complete fuzzy metric spaces endowed with a graph. Our main results of the work significantly generalize many known comparable results in the existing literature. Examples are given to support the usability of our results and to show that they are improvements of some known ones.

[EN] With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see "Am. Math. Month. 1967, 74, 436-437") that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see "Fixed Point Theory 2005, 6, 71-78") also allows us to characterize the fuzzy metric completeness.

[EN] We obtain a fixed point theorem for complete fuzzy metric spaces, in the sense of Kramosiland Michalek, that extends the classical Kannan fixed point theorem. We also show that, in fact, ourtheorem allows to characterize the fuzzy metric completeness, extending in this way the well-known Reich-Subrahmanyam theorem that a metric space is complete if and only if every Kannan contraction on it has afixed point.

[EN] We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi.

[EN] In this paper we present an example of a fuzzy psi-contractive sequence in the sense of D. Mihet, which is not Cauchy in a fuzzy metric space in the sense of George and Veeramani. To overcome this drawback we introduce and study a concept of strictly fuzzy contractive sequence. Then, we also make an appropriate correction to Lemma 3.2 of Gregori and Minana (2016) [5]. (C) 2019 Elsevier B.V. All rights reserved.

[EN] In this paper we present an example of a fuzzy psi-contractive sequence in the sense of D. Mihet, which is not Cauchy in a fuzzy metric space in the sense of George and Veeramani. To overcome this drawback we introduce and study a concept of strictly fuzzy contractive sequence. Then, we also make an appropriate correction to Lemma 3.2 of Gregori and Minana (2016) [5]. (C) 2019 Elsevier B.V. All rights reserved.

[EN] In this paper, we introduce the notion of G-fuzzy H-quasi-contractions using directed graphs in the setting of fuzzy metric spaces endowed with a graph and we show that this new type of contraction generalizes a large number of different types of contractions. Subsequently, we investigate some results concerning the existence of fixed points for this class of contractions under two different conditions in M-complete fuzzy metric spaces endowed with a graph. Our main results of the work significantly generalize many known comparable results in the existing literature. Examples are given to support the usability of our results and to show that they are improvements of some known ones.

[EN] In this paper, we introduce the notion of G-fuzzy H-quasi-contractions using directed graphs in the setting of fuzzy metric spaces endowed with a graph and we show that this new type of contraction generalizes a large number of different types of contractions. Subsequently, we investigate some results concerning the existence of fixed points for this class of contractions under two different conditions in M-complete fuzzy metric spaces endowed with a graph. Our main results of the work significantly generalize many known comparable results in the existing literature. Examples are given to support the usability of our results and to show that they are improvements of some known ones.

[EN] In this paper, we introduce the notion of G-fuzzy H-quasi-contractions using directed graphs in the setting of fuzzy metric spaces endowed with a graph and we show that this new type of contraction generalizes a large number of different types of contractions. Subsequently, we investigate some results concerning the existence of fixed points for this class of contractions under two different conditions in M-complete fuzzy metric spaces endowed with a graph. Our main results of the work significantly generalize many known comparable results in the existing literature. Examples are given to support the usability of our results and to show that they are improvements of some known ones.

[EN] In this paper, we introduce the notion of G-fuzzy H-quasi-contractions using directed graphs in the setting of fuzzy metric spaces endowed with a graph and we show that this new type of contraction generalizes a large number of different types of contractions. Subsequently, we investigate some results concerning the existence of fixed points for this class of contractions under two different conditions in M-complete fuzzy metric spaces endowed with a graph. Our main results of the work significantly generalize many known comparable results in the existing literature. Examples are given to support the usability of our results and to show that they are improvements of some known ones.

[EN] In this paper, we introduce the notion of G-fuzzy H-quasi-contractions using directed graphs in the setting of fuzzy metric spaces endowed with a graph and we show that this new type of contraction generalizes a large number of different types of contractions. Subsequently, we investigate some results concerning the existence of fixed points for this class of contractions under two different conditions in M-complete fuzzy metric spaces endowed with a graph. Our main results of the work significantly generalize many known comparable results in the existing literature. Examples are given to support the usability of our results and to show that they are improvements of some known ones.

"This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of General Systems on 01 Dec 2018, available online: https://doi.org/10.1080/03081079.2018.1552687", [EN] In this paper we provide a concept of fuzzy partial metric space (X, P, ¿) as an extension to fuzzy setting in the sense of Kramosil and Michalek, of the concept of partial metric due to Matthews. This extension has been defined using the residuum operator ¿¿ associated to a continuous t-norm ¿ and without any extra condition on ¿. Similarly, it is defined the stronger concept of GV -fuzzy partial metric (fuzzy partial metric in the sense of George and Veeramani). After defining a concept of open ball in (X, P, ¿), a topology TP on X deduced from P is constructed, and it is showed that (X, TP) is a T0-space.

"This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of General Systems on 01 Dec 2018, available online: https://doi.org/10.1080/03081079.2018.1552687", [EN] In this paper we provide a concept of fuzzy partial metric space (X, P, ¿) as an extension to fuzzy setting in the sense of Kramosil and Michalek, of the concept of partial metric due to Matthews. This extension has been defined using the residuum operator ¿¿ associated to a continuous t-norm ¿ and without any extra condition on ¿. Similarly, it is defined the stronger concept of GV -fuzzy partial metric (fuzzy partial metric in the sense of George and Veeramani). After defining a concept of open ball in (X, P, ¿), a topology TP on X deduced from P is constructed, and it is showed that (X, TP) is a T0-space.

"This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of General Systems on 01 Dec 2018, available online: https://doi.org/10.1080/03081079.2018.1552687", [EN] In this paper we provide a concept of fuzzy partial metric space (X, P, ¿) as an extension to fuzzy setting in the sense of Kramosil and Michalek, of the concept of partial metric due to Matthews. This extension has been defined using the residuum operator ¿¿ associated to a continuous t-norm ¿ and without any extra condition on ¿. Similarly, it is defined the stronger concept of GV -fuzzy partial metric (fuzzy partial metric in the sense of George and Veeramani). After defining a concept of open ball in (X, P, ¿), a topology TP on X deduced from P is constructed, and it is showed that (X, TP) is a T0-space.

[EN] Different types of fuzzy uniformities have been introduced in the literature standing out the notions due to Hutton, Hohle and Lowen. The main purpose of this paper is to study several methods to endow a fuzzy metric space (X, M, *), in the sense of George and Veeramani, with a probabilistic uniformity and with a Hutton [0, 1](-quasi)-uniformity. We will show the functorial behavior of these constructions as well as its relation with respect to Lowen's functors and Katsaras's functors, which establish a relationship between the categories of probabilistic uniformities and Hutton [0, 1](-quasi)-uniformities with the category of classical uniformities respectively. Furthermore, we also study the fuzzy topologies associated with these fuzzy uniformities. (C) 2017 Elsevier B.V. All rights reserved.

[EN] Different types of fuzzy uniformities have been introduced in the literature standing out the notions due to Hutton, Hohle and Lowen. The main purpose of this paper is to study several methods to endow a fuzzy metric space (X, M, *), in the sense of George and Veeramani, with a probabilistic uniformity and with a Hutton [0, 1](-quasi)-uniformity. We will show the functorial behavior of these constructions as well as its relation with respect to Lowen's functors and Katsaras's functors, which establish a relationship between the categories of probabilistic uniformities and Hutton [0, 1](-quasi)-uniformities with the category of classical uniformities respectively. Furthermore, we also study the fuzzy topologies associated with these fuzzy uniformities. (C) 2017 Elsevier B.V. All rights reserved.

[EN] In this paper we discuss the concept of Cauchy sequence due to Grabiec, that we call G-Cauchy, in the context of fuzzy metric spaces. It leads to introduce and study a concept of weak $-completeness in fuzzy and classical context. Then, we generalize the celebrated Grabiec's fuzzy Banach Contraction Principle. Also, we extend the Mihet's fixed point theorem given for weak B-contractive mappings.

[EN] 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. Dobos. Besides, the new generated fuzzy metric spaces are strong and completable, and if we add an extra condition, they are principal. Appropriate examples of such fuzzy metric spaces are given in order to illustrate the exposed technique.

[EN] 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. Dobos. Besides, the new generated fuzzy metric spaces are strong and completable, and if we add an extra condition, they are principal. Appropriate examples of such fuzzy metric spaces are given in order to illustrate the exposed technique.

[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].

[EN] In this paper we survey some results on contractive sequences in fuzzy metric spaces in the sense of George and Veeramani.

[EN] In the context of fuzzy metrics in the sense of George and Veeramani, we introduce the concept of stratified fuzzy metric. Many well-known fuzzy metrics are stratified. We prove that stratified strong fuzzy metric spaces (X, M, *) are completable, under the assumption that * is integral (positive). In particular, stratified fuzzy ultrametric spaces are completable. (C) 2017 Elsevier B.V. All rights reserved.

[EN] In this paper we survey some results on contractive sequences in fuzzy metric spaces in the sense of George and Veeramani.

[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].

[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].

[EN] In this paper we survey some results on contractive sequences in fuzzy metric spaces in the sense of George and Veeramani.

[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].

[EN] In this paper we survey some results on contractive sequences in fuzzy metric spaces in the sense of George and Veeramani.

[EN] In the context of fuzzy metrics in the sense of George and Veeramani, we introduce the concept of stratified fuzzy metric. Many well-known fuzzy metrics are stratified. We prove that stratified strong fuzzy metric spaces (X, M, *) are completable, under the assumption that * is integral (positive). In particular, stratified fuzzy ultrametric spaces are completable. (C) 2017 Elsevier B.V. All rights reserved.

[EN] In this paper we survey some results on contractive sequences in fuzzy metric spaces in the sense of George and Veeramani.

[EN] Usually, fuzzy metric spaces are endowed with crisp topologies or crisp uniformities. Nevertheless, some authors have shown how to construct in this context different kinds of fuzzy uniformities like a Hutton [0, 1]- quasi-uniformity or a probabilistic uniformity. In 2010, J. Guti´errez Garc´ıa, S. Romaguera and M. Sanchis [7] proved that the category of uniform spaces is isomorphic to a category whose objects are sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, we obtain a factorization of some functors introduced in [6].

[EN] In this paper we introduce and study the concept of strong convergence in fuzzy metric spaces (X, M,*) in the sense of George and Veeramani. This concept is related with the condition Lambda M-t > 0(x, y, t) > 0, which frequently is required or missing in this context. Among other results we characterize the class of s-fuzzy metrics by the strong convergence defined here and we solve partially the question of finding explicitly a compatible metric with a given fuzzy metric.

[EN] In this paper we introduce and study the concept of strong convergence in fuzzy metric spaces (X, M,*) in the sense of George and Veeramani. This concept is related with the condition Lambda M-t > 0(x, y, t) > 0, which frequently is required or missing in this context. Among other results we characterize the class of s-fuzzy metrics by the strong convergence defined here and we solve partially the question of finding explicitly a compatible metric with a given fuzzy metric.

In this paper we give a fixed point theorem in the context of fuzzy metric spaces in the sense of George and Veeramani. As a consequence of our result we obtain a fixed point theorem due to D. Mihet and generalize a fixed point theorem due to D. Wardowski. Also, we answer in a positive way to a question posed by D. Wardowski, and solve partially an open question on Cauchyness and contractivity. (C) 2015 Elsevier B.V. All rights reserved.

In this paper we give a fixed point theorem in the context of fuzzy metric spaces in the sense of George and Veeramani. As a consequence of our result we obtain a fixed point theorem due to D. Mihet and generalize a fixed point theorem due to D. Wardowski. Also, we answer in a positive way to a question posed by D. Wardowski, and solve partially an open question on Cauchyness and contractivity. (C) 2015 Elsevier B.V. All rights reserved.

In this paper we give a characterization of the class of completable strong (non-Archimedean) fuzzy metric spaces, in the sense of George and Veeramani.

In this paper we give a characterization of the class of completable strong (non-Archimedean) fuzzy metric spaces, in the sense of George and Veeramani.

[EN] We introduce and study the notions of lower Wijsman topology, upper Wijsman topology and Wijsman topology of a fuzzy metric space in the sense of Kramosil and Michalek. In particular, quasi-uniformizability, uniformizability, quasi-metrizability and metrizability of these topologies are discussed. Their relations with other hypertopologies are also analyzed. Corresponding results to the Wijsman topology of a metric space are deduced from our approach with the help of the standard fuzzy metric.

[EN] We introduce and study the notions of lower Wijsman topology, upper Wijsman topology and Wijsman topology of a fuzzy metric space in the sense of Kramosil and Michalek. In particular, quasi-uniformizability, uniformizability, quasi-metrizability and metrizability of these topologies are discussed. Their relations with other hypertopologies are also analyzed. Corresponding results to the Wijsman topology of a metric space are deduced from our approach with the help of the standard fuzzy metric.

In this note we show a fixed point theorem for multivalued Caristi's type mappings on a large class of complete fuzzy metric spaces. In fact, this result allows us to characterize complete fuzzy metric spaces with continuous t-norm greater than or equal to the Lukasiewicz t-norm.

In this note we answer two recent questions posed by Morillas and Sapena [10] related to standard convergence in fuzzy metric spaces in the sense of George and Veeramani. The obtained results lead us to establish what conditions must satisfy a concept about sequential convergence to be considered compatible with a concept of Cauchyness.

In this paper we construct a non-completable fuzzy metric space in the sense of George and Veeramani which allows to answer an open question related to continuity on the real parameter t. In addition, the constructed space is not strong (non-Archimedean).

Tesis por compendio, [EN] Fuzzy mathematics has constituted a wide field of research, since L. A. Zadeh introduced in 1965 the concept of fuzzy set. In particular, the problem of constructing a satisfactory theory of fuzzy metric spaces has been investigated by several authors. In 1994, George and Veeramani introduced and studied a notion of fuzzy metric space that constituted a modification of the one given by Kramosil and Michalek. Several authors have contributed to the study of this kind of fuzzy metrics, from the mathematical point of view and for their applications. In this thesis we have contributed to develop the study of these fuzzy metrics, from the mathematical point of view, and we approached the problem of measuring perceptual colour-difference between samples of colour using one of these fuzzy metrics. The contributions of the study carried out in this thesis is summarized as follows: \begin{enumerate} \item[(i)] We have made a detailed study of the fuzzy metric space $(X,M,\cdot)$ where $M$ is given on $X=[0,\infty[$ by $M(x,y,t)=\frac{\min\{x,y\}+t}{\max\{x,y\}+t}$ and others related to it. As a consequence we have introduced five questions in fuzzy metrics related to continuity, extension, contractivity and completion. \item[(ii)] We have answered an open question constructing a fuzzy metric space $(X,M,\ast)$ in which the assignment $f(t)=\lim_n M(a_n,b_n,t)$, where $\{a_n\}$ and $\{b_n\}$ are $M$-Cauchy sequences in $X$, is not a continuous function on $t$. The response to this question has allowed us to characterize the class of completable strong fuzzy metric spaces. \item[(iii)] We have introduced and studied a stronger concept than convergence of sequences in fuzzy metric spaces, which we call $s$-convergence. In our study, we have gotten a characterization of those spaces in which every convergent sequence is $s$-convergent and we have given a classification of fuzzy metrics attending to the behaviour of the fuzzy metric with respect to the different types of con, [ES] La matemática fuzzy ha constituido un amplio campo en la investigación, desde que en 1965 L. A. Zadeh introdujo el concepto de conjunto fuzzy. En particular, la construcción de una teoría satisfactoria de espacios métricos fuzzy ha sido un problema investigado por muchos autores. En 1994, George y Veeramani introdujeron y estudiaron una noción de espacio métrico fuzzy que constituía una modificación de la anteriormente dada por Kramosil y Michalek. Muchos autores han contribuido al estudio de este tipo de métricas fuzzy, desde el punto de vista matemático y de sus aplicaciones. En esta tesis hemos contribuido al desarrollo del estudio de estas métricas fuzzy, desde el punto de vista matemático, y hemos abordado el problema de la medida de la diferencia perceptual de color utilizando una de estas métricas. Las contribuciones que aportamos en esta tesis a dicho estudio, se resumen a continuación: \begin{enumerate} \item[(i)] Hemos hecho un estudio detallado del espacio métrico fuzzy $(X,M,\cdot)$ donde $M$ está dada sobre $[0,\infty[$ por la expresión $M(x,y,t)=\frac{\min\{x,y\}+t}{\max\{x,y\}+t}$ y de otros espacios métricos fuzzy relacionados con el. Como consecuencia de este estudio hemos introducido cinco cuestiones en la teoría de las métricas fuzzy relacionadas con continuidad, extensión, contractividad y completación. \item[(ii)] Hemos respondido a una cuestión abierta construyendo un espacio métrico fuzzy $(X,M,\ast)$ en el cual la asignación $f(t)=\lim_n M(a_n,b_n,t)$, donde $\{a_n\}$ y $\{b_n\}$ son sucesiones $M$-Cauchy, no es una función continua sobre $t$. La respuesta a esta cuestión nos ha permitido caracterizar la clase de los espacios métricos fuzzy strong completables. \item[(iii)] Hemos introducido y estudiado un concepto más fuerte que el de convergencia de sucesiones en espacios métricos fuzzy, al que hemos llamado $s$-convergencia. En nuestro estudio hemos conseguido una caracterización de aquellos espacios métricos fuzzy en los cuales toda, [CA] La matemàtica fuzzy ha constituït un ampli camp en la investigació, des que el 1965 L. A. Zadeh va introduir el concepte de conjunt fuzzy. En particular, la construcció d'una teoria satisfactòria d'espais mètrics fuzzy ha estat un problema investigat per molts autors. El 1994, George i Veeramani introduiren i estudiaren una noció d'espai mètric fuzzy que constituïa una modificació de la donada per Kramosil i Michalek anteriorment. Molts autors han contribuït a l'estudi d'aquest tipus de mètriques fuzzy, des del punt de vista matemàtic i de les seves aplicacions. En aquesta tesi hem contribuït al desenvolupament de l'estudi d'aquestes mètriques fuzzy, des del punt de vista matemàtic, i hem abordat el problema de la mesura de la diferència perceptiva de color utilitzant aquestes mètriques. Les contribucions que aportem en aquesta tesi a tal estudi es resumeixen a continuació: \begin{enumerate} \item[(i)] Hem fet un estudi detallat de l'espai mètric fuzzy $(X,M,\cdot)$ on $M$ està donada sobre $[0,\infty[$ per l'expressió $M(x,y,t)=\frac{\min\{x,y\}+t}{\max\{x,y\}+t}$ i d'altres espais mètrics fuzzy relacionats amb ell. Com a conseqüència d'aquest estudi hem introduït cinc qüestions en la teoria de les mètriques fuzzy relacionades amb continuïtat, extensió, contractividad i completació. \item[(ii)] Hem respost a una qüestió oberta construint un espai mètric fuzzy $ (X, M, \ast) $ en el qual l'assignació $ f (t) = \lim_n M (a_n, b_n, t) $, on $ \{a_n\} $ i $ \{b_n \} $ són successions $ M $-Cauchy, no és una funció contínua sobre $ t $. La resposta a aquesta qüestió ens ha permès caracteritzar la classe dels espais mètrics fuzzy strong completables. \item[(iii)] Hem introduït i estudiat un concepte més fort que el de convergència de successions en espais mètrics fuzzy, al qual hem anomenat $ s $-Convergència. En el nostre estudi hem aconseguit una caracterització d'aquells espais mètrics fuzzy en els quals tota successió convergent és $ s $-convergente i hem donat

Tesis por compendio, Mathematical models have extensively been used in problems related to engineering, computer sciences, economics, social, natural and medical sciences etc. It has become very common to use mathematical tools to solve, study the behavior and different aspects of a system and its different subsystems. Because of various uncertainties arising in real world situations, methods of classical mathematics may not be successfully applied to solve them. Thus, new mathematical theories such as probability theory and fuzzy set theory have been introduced by mathematicians and computer scientists to handle the problems associated with the uncertainties of a model. But there are certain deficiencies pertaining to the parametrization in fuzzy set theory. Soft set theory aims to provide enough tools in the form of parameters to deal with the uncertainty in a data and to represent it in a useful way. The distinguishing attribute of soft set theory is that unlike probability theory and fuzzy set theory, it does not uphold a precise quantity. This attribute has facilitated applications in decision making, demand analysis, forecasting, information sciences, mathematics and other disciplines. In this thesis we will discuss several algebraic and topological properties of soft sets and fuzzy soft sets. Since soft sets can be considered as setvalued maps, the study of fixed point theory for multivalued maps on soft topological spaces and on other related structures will be also explored. The contributions of the study carried out in this thesis can be summarized as follows: i) Revisit of basic operations in soft set theory and proving some new results based on these modifications which would certainly set a new dimension to explore this theory further and would help to extend its limits further in different directions. Our findings can be applied to develop and modify the existing literature on soft topological spaces ii) Defining some new classes of mappings and then proving the existence

Tesis por compendio, Mathematical models have extensively been used in problems related to engineering, computer sciences, economics, social, natural and medical sciences etc. It has become very common to use mathematical tools to solve, study the behavior and different aspects of a system and its different subsystems. Because of various uncertainties arising in real world situations, methods of classical mathematics may not be successfully applied to solve them. Thus, new mathematical theories such as probability theory and fuzzy set theory have been introduced by mathematicians and computer scientists to handle the problems associated with the uncertainties of a model. But there are certain deficiencies pertaining to the parametrization in fuzzy set theory. Soft set theory aims to provide enough tools in the form of parameters to deal with the uncertainty in a data and to represent it in a useful way. The distinguishing attribute of soft set theory is that unlike probability theory and fuzzy set theory, it does not uphold a precise quantity. This attribute has facilitated applications in decision making, demand analysis, forecasting, information sciences, mathematics and other disciplines. In this thesis we will discuss several algebraic and topological properties of soft sets and fuzzy soft sets. Since soft sets can be considered as setvalued maps, the study of fixed point theory for multivalued maps on soft topological spaces and on other related structures will be also explored. The contributions of the study carried out in this thesis can be summarized as follows: i) Revisit of basic operations in soft set theory and proving some new results based on these modifications which would certainly set a new dimension to explore this theory further and would help to extend its limits further in different directions. Our findings can be applied to develop and modify the existing literature on soft topological spaces ii) Defining some new classes of mappings and then proving the existence

In this note we show a fixed point theorem for multivalued Caristi's type mappings on a large class of complete fuzzy metric spaces. In fact, this result allows us to characterize complete fuzzy metric spaces with continuous t-norm greater than or equal to the Lukasiewicz t-norm.

[EN] We present a procedure to construct a compatible metric from a given fuzzy metric space. We use this approach to obtain a characterization of a large class of complete fuzzy metric spaces by means of a fuzzy version of Caristi’s fixed point theorem, obtaining, in this way, partial solutions to a recent question posed in the literature. Some illustrative examples are also given.