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Publications (389)
In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers R0+. More precisely, we prove several new results concerning these theories. We introduce to the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing how to compute them. The topol...
Multidimensional fuzzy sets (MFS) is a new extension of fuzzy sets on which the membership values of an element in the universe of discourse are increasingly ordered vectors on the set of real numbers in the interval $[0,1]$. This paper aims to investigate fuzzy negations on the set of increasingly ordered vectors on $[0,1]$, i.e. on $\mathcal{L}_\...
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. We also propose a new hyperstructure for...
A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic properties, and orders. It is show...
Saminger-Platz, Klement, and Mesiar (2008) extended t-norms from a complete sublattice to its respective lattice using the conventional definition of sublattice. In contrast, Palmeira and Bedregal (2012) introduced a more inclusive sublattice definition, via retractions. They expanded various important mathematical operators, including t-norms, t-c...
The discrete Choquet Integral (CI) and its generalizations have been successfully applied in many different fields, with particularly good results when considered in Fuzzy Rule-Based Classification Systems (FRBCSs). One of those functions is the CC-integral, where the product operations in the expanded form of the CI are generalized by copulas. Rec...
Generalizamos a noção de linguagem fuzzy associada a autômatos fuzzy considerando uma função de agregação conjuntiva C em lugar de uma t-norma e uma função de agregação disjuntiva D em lugar de uma t-conorma e a chamamos de linguagem (C,D)-fuzzy. Depois investigamos condições suficientes e necessárias sobre C e D para a classe das linguagens (C,D)-...
The idea of nondeterministic typical hesitant fuzzy automata is a generalization of the fuzzy automata presented by Costa and Bedregal. This paper, presents the sufficient and necessary conditions for a typical hesitant fuzzy language to be computed by nondeterministic typical hesitant fuzzy automata. Besides, the paper introduces a new class of ty...
This paper explores a strict relation between two core notions of the semantics of programs and of fuzzy logics: Kleene Algebras and (pseudo) uninorms. It shows that every Kleene algebra induces a pseudo uninorm, and that some pseudo uninorms induce Kleene algebras. This connection establishes a new perspective on the theory of Kleene algebras and...
The interval-valued fuzzy sets and Atanassov intuitionistic fuzzy sets can be extended to a more general framework to simultaneously deal with uncertainty in both membership and non-membership values. This fact leads to the concept of interval-valued Atanassov intuitionistic fuzzy sets (IVAIFS), as given by Atanassov and Gargov (Fuzzy Sets Syst, 31...
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 conce...
There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy. Since these possibly non-associative operators have been successfully used in many applications, su...
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.
From the more than two hundred partial orders for fuzzy numbers proposed in the literature, only a few are total. In this article, we introduce the notion of admissible order for fuzzy numbers equipped with a partial order, i.e., a total order which refines the partial order. In particular, it is given special attention to the partial order propose...
We introduce a new contrapositivisation technique for fuzzy implications constructed from a pair of bivariate aggregation functions and a fuzzy negation, which we call bi-aggregated contrapositivisation. We show that the bi-aggregated contrapositivisation generalizes the upper, lower, medium and aggregated contrapositivisations. We characterize thi...
Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as g...
In order to get a more general result related on fuzzy implications that induced by aggregation functions, we relax the definition of general overlap functions, more precisely, removing its right-continuous, and introduce a new kind of aggregation function, which called semi-overlap function. Subsequently, we explore some of their related algebraic...
After the research on naBL-algebras gained by the non-associative t-norms and overlap functions, inflationary BL-algebras were also studied as a recent kind of non-associative generalization of BL-algebras, which can be obtained by general overlap functions. In this paper, we show that not every inflationary general overlap function can induce an i...
The essential idea of the residuation principle plays a fundamental role in the residuated lattice theory based on R-implications, which are derived from left-continuous t-norms providing a general logical framework frequently applied to achieve solutions for multiple criteria and decision-making problems. The definition of n-dimensional fuzzy R-im...
We introduce a new contrapositivisation technique for fuzzy implications constructed from grouping functions and fuzzy negations, which generalizes the (S,N)-contrapositivisation, and we study some of its properties; we present some characterizations of the (G,N)-contrapositivisators concerning N-compatibility and the action of an automorphism. Fin...
The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo...
Fusion functions and their most important subclass, aggregation functions, have been successfully applied in fuzzy modeling. However, there are practical problems, such as classification via Convolutional Neural Networks (CNNs), where the data to be aggregated are not modeling membership degrees in the unit interval. In this scenario, systems could...
In the literature it is very common to see problems in which it is necessary to aggregate a set of data into a single one. An important tool able to deal with these issues is the aggregation functions, which we can highlight as the OWA functions. However, there are other functions that are also capable of performing these tasks, such as the preaggr...
In the literature it is very common to see problems in which it is necessary to aggregate a set of data into a single one. An important tool able to deal with these issues is the aggregation functions, which we can highlight as the OWA functions. However, there are other functions that are also capable of performing these tasks, such as t...
General overlap and grouping functions have been proposed by De Miguel et al. as a generalization of overlap and grouping functions respectively. In this paper, we continue to investigate the two functions by their multiplicative generator pairs. First, we introduce the concept of multiplicative generator pairs for general overlap functions and obt...
Ensembles of classifiers have been receiving much attention lately, they consist of a collection of classifiers that process the same information and their output is combined in some manner. The combination method is probably the most important part in a ensemble of classifiers however, many works found in literature focus mostly on the classificat...
Multidimensional fuzzy sets (MFS) is a new extension of fuzzy sets on which the membership values of an element in the discourse universe are increasingly ordered vectors on the set of real numbers in the interval [0,1]. This paper aims to investigate fuzzy negations and, mainly, fuzzy implications on the set of increasingly ordered vectors on [0,1...
The complexity of the procedures for discovering, classifying, and selecting suitable resources to meet customer demands is related to the growing resource offers connected to the Internet. This proposal takes into account the uncertainties in the specification and processing of customer preferences, via consensual analysis. In this work we study t...
It is worth noticing that a fuzzy conjunction and its corresponding fuzzy implication can form a residual pair if and only if it is left-continuous. In order to get a more general result related on residual implications that induced by aggregation functions, we relax the definition of general overlap functions, more precisely, removing its right-co...
We introduce a new contrapositivisation technique for fuzzy implications constructed from triangular conorms, which generalizes the medium contrapositivisation, and we study some of its properties; we present some characterizations of the operator that defines this new contrapositivisation technique concerning N-compatibility and the action of an a...
This paper presents a generalization of the extension principle for fuzzy numbers. The minimum is substituted by a general binary aggregation function. It is used to extend the usual metric for real numbers to fuzzy numbers, generating a new family of fuzzy-valued distances between fuzzy numbers. Then, some conditions on these aggregation functions...
One recent work, Paivaet al. introduced the concept of quasi-overlap functions onbounded lattices and investigated some vital properties of them. In this paper, we continue considerthis research topic and focus on a generalization, called general quasi-overlap functions, whichmeasure the degree of overlapping of several classes in a given classific...
In one recent work, Paiva et al. generalized the notion of overlap functions to the context of lattices and introduced a weaker definition, called a quasi-overlap, that arises from the removal of the continuity condition. In this article, quasi-overlap functions on lattices are equipped with a topological space structure, namely, Alexandroff’s spac...
Este trabalho apresenta um estudo sobre a representabilidade de conectivos fuzzy valorados intervalarmente considerando ordens parciais e admissíveis. Nossa abordagem considera aquelas ordens baseadas em funções de agregação injetivas que permitem a construção de operadores fuzzy valorados intervalarmente. Um resultado imediato é a construção da im...
This work deals with the study of a new total order Triangular Fuzzy Numbers and arithmetic properties that are maintained in relation to the operations of addition and subtraction. Additionally, we present as example of application the shortest path solution for the Travelling Salesman Problem with fuzzy distances.
The study of n-dimensional fuzzy logic contributes to overcome the insufficiency of traditional FL in modeling imperfect and imprecise information coming from different experts. Based on representability, we extend results from fuzzy connectives to n-dimensional approach. This research on n-dimensional fuzzy implications (n-DI) pass through the next...
In this paper we propose a new generalization for the notion of homogeneous functions. We show some properties and how it appears in some scenarios. Finally we show how this generalization can be used in order to provide a new paradigm for decision making theory called consistent influenced/disturbed decision making. In order to illustrate the appl...
n-Dimensional fuzzy sets are a type of fuzzy sets where the membership degrees are n-dimensional intervals, i.e., ordered vector of dimension n on [0,1]. A fundamental aspect for aggregation function in types of fuzzy sets is establish the order on the membership valued which be consider. The natural order for n-dimensional intervals is the product...
In this paper, we discussconsensus measures for typical hesitant fuzzy elements (THFE), which are the finite and nonempty fuzzy membership degrees under the scope of typical hesitant fuzzy sets (THFS). In our approach, we present a model that formally constructs consensus measures by means of aggregations functions, fuzzy implication-like functions...
In 2001 and 2002, Daowen Qiu has established a new theory of L-valued automata which is based on complete residuated lattices. Moreover, besides the finite automata, several other classes of machines, grammars and languages have been generalized using the ideas introduced by Qiu. This paper generalizes the concept of linear grammars and linear lang...
Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. They have been successfully applied as a fuzzy conjunction operation in several problems in which associativity is not required, such as image processing and classification. Interval-valued overlap functions were defined as an extension to...
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 integra...
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 Ln([0,1]). This paper aims to investigate semi-vector spaces over a weak semifield and aggregation functions con...
Using the fuzzy lattices defined by Chon, we define fuzzy homomor- phism between fuzzy lattices, the operations of product, collapsed sum, lifting, opposite, interval and intuitionistic on bounded fuzzy lattices. They are conceived as extensions of their analogous opera- tions on the classical theory by using this definition of fuzzy lattices and i...
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 ($S$,$N$,$T$...
The BDI logic is an important and widely used theoretical apparatus to represent and reason about rational agents. However, the BDI logics are incomplete regarding the intention reconsideration, override of intention, the deliberation process, and belief revision. These are essential processes of the BDI model. Also, some rational agents, especiall...
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...
Recently, Paiva et al. generalized the notion of overlap functions in the context of lattices and introduced a weaker definition, called quasi-overlap, that originates from the removal of the continuity condition. In this paper, we introduce the concept of residuated implications related to quasi-overlap functions on lattices and prove some related...
Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative aggregation functions. In order to obtain a more general and flexible context, we extend the class of implications d...
Dynamic consolidation of virtual machines (VMs) is an effective way to improve resource utilization and power efficiency in cloud computing. For example, determining when it is best to relocate VMs from an overloaded host is one aspect of dynamic VM consolidation that directly influences the resource utilization and Quality of Service (QoS) offered...
The idea of nondeterministic typical hesitant fuzzy automata is a generalization of the fuzzy automata presented by Costa and Bedregal. This paper, presents the sufficient and necessary conditions for a typical hesitant fuzzy language to be computed by nondeterministic typical hesitant fuzzy automata. Besides, the paper introduces a new class of Ty...
As an important class of aggregation operators, the notion of overlap functions was first presented in 2009 in order to be considered for applications in image processing context. Later, many other researches arised bringing some variations of those functions for different purposes. Here, our main goal is defining overlap functions on lattices and...
Multi Expert‐Multi Criteria Decision Making (ME‐MCDM) problems have been well explored on hesitant fuzzy environments dealing with membership degrees as subsets which do not necessarily have the same cardinality. Admissible (total) orders collaborate by reducing the collapse in the ranking of alternatives related to preference relations. In such co...
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...
Overlap functions are a type of aggregation functions that are not required to be associative, generally used to indicate the overlapping degree between two values. They have been successfully used as a conjunction operator in several practical problems, such as fuzzy-rule-based classification systems (FRBCSs) and image processing. Some extensions...
Throughout this paper, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first we introduce the concept of a general mean on an abstract set. This new concept conciliates the Social Choice where well-known impossibility results as the Arrovian ones are encountere...
naBL-algebras are non-associative generalizations of BL-algebras obtained from non-associative t-norms (nat-norms). In the present paper we propose a further generalization of BL-algebras where associativity is not required. Such generalization is based on a subclass of bivariate general overlap functions called inflationary. We call this non-assoc...
Nullnorms are aggregation functions which generalize t-norms and t-conorms. For each nullnorm there exists an annihilator element such that, below it, the function behaves like a t-conorm, and, above it, like a t-norm. In this paper, we study some classes of nullnorms which naturally arise from well known classes of t-norms and t-conorms, such as i...
In this chapter we make a review of the notion of overlap function. Although originally developed in order to determine up to what extent a given element belongs to two sets, overlap functions have widely developed in the last years for very different problems. We recall here the motivation that led to the introduction of this new notion and we dis...
The n-dimensional fuzzy logic (n-DFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modelling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership degrees. Thus, n-DFL provides a consolidated logica...
In this paper, in order to generalize the Choquet integral, we replace the difference between inputs in its definition by a restricted dissimilarity function and refer to the obtained function as d-Choquet integral. For some particular restricted dissimilarity function the corresponding d-Choquet integral with respect to a fuzzy measure is just the...
In the theory of Hesitant Fuzzy Sets (HFS), the membership degree of an element is characterized by a membership function which always returns a fuzzy set. This approach enables one to express, for example, the hesitance of several experts in the process of decision making based on multiple attributes and multiple criteria. In this work, we focus o...
Some aggregation functions that are not necessarily associative, namely overlap and grouping functions, have called the attention of many researchers in the recent past. This is probably due to the fact that they are a richer class of operators whenever one compares with other classes of aggregation functions, such as t-norms and t-conorms, respect...
In this paper, we study a new generalization for the notion of fuzzy automata, which we called typical hesitant fuzzy automata. First, we present the formulations of the mathematics framework for the theory of typical hesitant fuzzy automata. Second, we then show a method to transform nondeterministic typical hesitant fuzzy automata (in short nthfa...
Problems can arise in decision-making when a different number of evaluations for the different criteria or alternatives may be available. This is the case, for instance, when for some reason one or more experts refrain from evaluating certain criteria for an alternative. In these situations, approaches using n-dimensional fuzzy sets and hesitant fu...
The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributio...
The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These functions are a generalization of the “standard” Choquet integral obtained by replacing the difference in the definition of the usual Choquet integral by a dissimilarity function. In particular, the class of all d-Choquet integrals encompasses the c...
From the more than two hundred partial orders for fuzzy numbers proposes in the literature, only a few are totals. In this paper, we introduce the notion of admissible orders for fuzzy numbers equipped with a partial order, i.e. a total order which refines the partial order. In particular, is given special attention when thr partial order is the pr...
Overlap functions are aggregation functions that express the overlapping degree between two values. They have been used both as a conjunction in several practical problems (e.g., image processing and decision making), and to generate overlap indices between two fuzzy sets, which can be used to construct fuzzy confidence values to be applied in fuzz...
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-overla...
In this paper, we make some considerations about admissible orders on the set of closed subintervals of the unit interval I[0,1], i.e. linear orders that refine the product order on intervals. We propose a new way to generate admissible orders on I[0,1] which is more general than those we find in the current literature. Also, we deal with the possi...
Supervised machine learning methods, also known as classification algorithms, have been widely used in the literature for many classification tasks. In this context, some aspects of these algorithms, as the used attributes used and the form they were built, have a direct impact in the system performance. Therefore, in this paper, we evaluate the ap...
This work proposes a wavelet-fuzzy power quality (PQ) diagnosis method able to evaluate the PQ impact of steady-state (stationary) PQ events in alternating current (AC) microgrids considering the influence of the power level penetration. The proposed method is composed by a wavelet packet-based signal processing to compute the root mean square (RMS...