Regivan H N Santiago

Universidade Federal do Rio Grande do Norte | IIP · Department of Computer Science and Applied Mathematics

The concept of alpha-order has been recently introduced as a binary relation that allows ranking fuzzy sets with bounded support and whose \(\beta \)-cuts are closed subsets with a finite number of connected components. This paper explores some key properties of such alpha-order. Specifically, we will focus on admissibility, a fundamental property...

This paper introduces the concept of conditional monotonicity and other related relaxed monotonicities within the framework of intervals equipped with admissible orders. It generalizes the work of Sesma-Sara et al., who introduced weak/directional monotonicity on intervals endowed with the Kulisch–Miranker order, and the work of Santiago et al., wh...

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...

In this paper, a novel methodology (that we call \(\alpha \)-ordering) for ranking two fuzzy quantities is introduced and studied. Although this methodology is applicable to all pairs of fuzzy numbers, it has been designed to be applied to a wide family \(\mathscr {C}\) of fuzzy sets of the real line. Concretely, this class is characterized by the...

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...

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...

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.

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...

In this paper we develop the idea of abstract homogeneity in the context of interval-valued (IV) functions endowed with admissible orders. We investigate some of its properties and the notion of self-homogeneity. We show how this framework behaves with respect to some fuzzy connectives. We show that some properties of the usual notions of $\min$ an...

In this paper we introduce the notion of conditional monotonicity and from it the concepts of conditional monotonicity given a vector of degenerated intervals and conditional monotonicity given a constant vector of functions to the setting of intervals endowed with admissible orders. This work is a step after the contribution of Sesma-Sara et al.,...

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...

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...

Traditionally, Convolutional Neural Networks make use of the maximum or arithmetic mean in order to reduce the features extracted by convolutional layers in a downsampling process known as pooling. However, there is no strong argument to settle upon one of the two functions and, in practice, this selection turns to be problem dependent. Further, bo...

Fuzzy Switch Graphs (FSGs) are reactive fuzzy graphs that model systems in which accessibility relations and fuzzy values are changed whenever an edge is crossed [17]. Reversal Fuzzy Switch Graphs (RFSGs) were presented in [6] and model fuzzy reactive systems which provide the activation and deactivation of resources, a functionality that FSGs do n...

Fuzzy Switch Graphs (FSG) generalize the notion of Fuzzy Graphs by adding high-order arrows and aggregation functions which update the fuzzy values of arrows whenever a zero-order arrow is crossed. In this paper, we propose a more general structure called Reversal Fuzzy Switch Graph (RFSG), which promotes other actions in addition to updating the f...

A function that takes n numbers as input and outputs one number is said to be homogeneous whenever the result of multiplying each input by a certain factor λ yields the original output multiplied by that same factor. This concept has been extended by the notion of abstract homogeneity, which generalizes the product in the expression of homogeneity...

In this paper we proposed a concept of Agnesi quasi-fuzzy numbers based on Agnesi’s curve. Also, in the set of all Agnesi quasi-fuzzy numbers is defined an arithmetic where field properties are satisfied.

Fuzzy Mathematical Morphology extends binary morphological operators to grayscale and color images using concepts from fuzzy logic. To define the morphological operators of erosion and fuzzy dilation, the R-implications and fuzzy T-norm respectively are used. This work presents the application of the fuzzy morphological operators of Lukasiewicz, Gö...

This paper discuss on Interval Arithmetic by Moore under two main principles: inclusion isotonicity and quick computations under algebraic cost. In 1999, to overcome Moore difficulties Lodwick introduced constrained interval arithmetic. This paper discuss on Lodwick’s theory under these principles.

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...

Automatic image detection is one of the most important areas in computing due to its potential application in numerous real-world scenarios. One important tool to deal with that is called overlap indices . They were introduced as a procedure to provide the maximum lack of knowledge when comparing two fuzzy objects. They have been successfully app...

In this work we generalize the notion of restricted equivalence function for type-2 fuzzy sets, leading to the notion of extended restricted equivalence functions. We also study how under suitable conditions, these new functions recover the standard axioms for restricted equivalence functions in the real setting. Extended restricted equivalence fun...

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...

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...

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...

In this paper, we propose a generalization for fuzzy graphs in order to model reactive systems with fuzziness. As we will show, the resulting fuzzy structure, called fuzzy reactive graphs (FRG), is able to model dynamical aspects of some entities which generally appear in: biology, computer science and some other fields. The dynamical aspect is cap...

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...

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...

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...

The impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact va...

Fuzzy Switch Graphs (FSG) generalize the notion of Fuzzy Graphs by adding high-order arrows and aggregation functions which update the fuzzy values of arrows whenever a zero-order arrow is crossed. In this paper, we propose a more general structure called Reversal Fuzzy Switch Graph (RFSG), which promotes other actions in addition to updating the f...

This paper is an investigation about primeness in quantales environment. It is proposed a new definition for prime ideal in noncommutative setting. As a consequence, fuzzy primeness can be defined in similar way to ring theory.

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...

Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modeled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from the literature that there is an incompatibility between some algebraic structures and its interval counterpart. Th...

Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modelled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from literature that there is a incompatibility between some algebraic structures and its interval counterpart. This p...

In the literature, there are several forms of extensions of the classical bi-implication for the fuzzy logic, as for example, the axiomatization proposed by Fodor and Roubens [1]. Another way to obtain a generalization is to provide a definition based on the classical equivalence , in which the classical operators of conjunction and implication are...

In this paper we discuss the incompatibility between the notions of validity and impreciseness in the context of Dynamic Logics. To achieve that we consider the Łukasiewicz action lattice and its interval counterpart, we show how some validities fail in the context of intervals. In order to capture the properties of action lattices that remain vali...

In this paper we propose a new concept of primeness in quantales. It is proved that this concept coincide with classical definition in commutative quantales, but no longer valid in the noncommutative setting. Also, the notions of strong and uniform strong primeness are investigated.

The notion of semi-BCI algebras is introduced and some of its properties are investigated. This notion is a generalization of BCI algebras, suggested by the process of intervalization of BCI algebras. Semi-BCI algebras have a similar structure to pseudo-BCI algebras, however they are not the same. In this paper we investigate the similarities betwe...

Overlap functions were introduced as class of bivariate aggregation functions on [0, 1] to be applied in image processing. This paper has as main objective to present appropriates definitions of overlap functions considering the scope of lattices and introduced a more general definition, called of quasi-overlaps, which arise of abolishes the contin...

The use of fuzzy implications is widespread as easily found in the literature. The study of fuzzy implications attracts the attention of many authors probably because of their theoretical features and also the diversity of applications where they can be applied. In the present work we continue the study of a type of fuzzy implication, called (T, N)...

Generalized Mixture (GM) and Bounded Generalized Mixture (BGM) functions, as well as OWA and Choquet integrals, are weighted averaging functions which provide a broad class of fusion functions. However, both, OWA and Choquet Integrals, satisfy the monotonicity condition, which fails for some GM and BGM functions. In this paper we investigate two ge...

Implications play an important role in fuzzy logics as they can be used both in practical and theoretical works. There exist many works in the literature where fuzzy implications behave in a crisp manner, i.e., implications that map to either zero or one. In this sense, we call those implications as crisp fuzzy implications and our goal is to study...

Fuzzy implications has drawn attention of many authors along the years, as their theoretical features seem to be a useful tool in a fair amount of applications. Meanwhile, functional equations are those in which the unknowns are functions instead of a traditional variable, and within the fuzzy logic, they can be considered generalizations of some t...

This paper introduces briefly the notion of SBCI algebras and its role as candidate to model Fuzzy and Interval Fuzzy Logics. Its main goal is to provide how such algebraic structures behaves from the categorical theoretical standpoint.

In this paper we introduce a class of operators on complete lattices called Dynamic Ordered Weighted Averaging (DYOWA) functions. These functions provide a generalized form of an important class of aggregation functions: The Ordered Weighted Averaging (OWA) functions, whose applications can be found in several areas like: Image Processing and Decis...

Classifier ensembles are pattern recognition structures composed of a set of classification algorithms (members), organized in a parallel way, and a combination method with the aim of increasing the classification accuracy of a classification system. In this study, we investigate the application of a generalized mixture (GM) functions as a new appr...

In literature, it is common to find problems which require a way to encode a finite set of information into a single data; usually means are used for that. An important generalization of means are the so called Aggregation Functions, with a noteworthy subclass called OWA functions. There are, however, further functions which are able to provide suc...

Classifier ensembles are pattern recognition structures composed of a set of classification algorithms (members), organized in a parallel way, and a combination method with the aim of increasing the classification accuracy of a classification system. In this study, we investigate the application of a generalized mixture (GM)functions as a new appro...

Ensemble of Classifiers are composed of parallel-organized components (individual classifiers) whose outputs are combined using a combination method that provides the final output for an ensemble. In this context, Dynamic Ensemble Systems (DES) is an ensemble-based system that, for each test pattern, a different ensemble structure is defined, in wh...

It is not hard to see that implications can be obtained by means of other operators. To name a few, we can mention (S,N)-, R- and QL-implications, which has been widely investigated. The aim of this work is to study a fuzzy implication called (T,N)-implication, obtained from the composition of a fuzzy negation and a t-norm. It is also discussed the...

Some functions commonly found in the literature have the ability to aggregate a finite amount of information into a single data, e.g. OWA functions, mixture functions, generalized mixture functions and bounded generalized mixture functions. OWA functions can be characterized as aggregation functions, while the others cannot because of the lack of m...

Boolean-like laws is inspired by many works in Fuzzy Logic. In this paper, we investigate the fuzzy generalization of: x→(y→z)≡(x→y)→(x→z) law. More precisely, we will show under which conditions such Boolean-like law holds for the following classes of fuzzy implications: (S,N)-, R-, QL-, D-, (T,N)- and H. To achieve that we introduce a new fuzzy p...

Usually, the evaluation of the classifiers performance is not an easy task to be performed, mainly when we analyze different criteria (output parameters). In this evaluation process, we can use quantitative measures (accuracy, specificity, among others), however when the output values are very close and we have several criteria, the results are dif...

The wide number of languages and programming paradigms, as well as the heterogeneity of ‘programs’ and ‘executions’ require new generalisations of propositional dynamic logic. The dynamisation method, introduced in [20], contributed on this direction with a systematic parametric way to construct Many-valued Dynamic Logics able to handle systems whe...

Na literatura existem diversos tipos de funções com a finalidade quantificar uma coleção finita de informações em um único dado, como for exemplo, as funções OWA, as funções mistura, as funções mistura generalizada e as funções mistura generalizada limitada. As funções OWA, são na verdade exemplos de uma classe mais ampla de funções, denominadas de...

A common problem found in literature is the reduction and minimization of automata. In fuzzy finite automata those processes are more complex; it is not always possible to minimize a given fuzzy automaton, M. In this paper we define a notion of order for the set of fuzzy Mealy machines type L-Valued and we prove the existence of a residuated functi...

The Generalized Mixture functions — GM, proposed by Pereira et al. [1], are a generalized form an important type of aggregation function, defined by Yager and called Ordered Weighted Averaging functions — OWA [4]. While an OWA consists of a calculable function starting from a finite collection of fixed weights, in a GM, the vector of weights is dyn...

There are several variations of fuzzy Turing machines in the literature, many of them require a t-norm in order to establish their accepted language. This paper generalize the concept of non-deterministic fuzzy Turing machine-NTFM, replacing the t-norm operator for several aggregation functions. We establish the languages accepted by these machines...

Generalized Mixture (GM) functions beyond to generalize the Mixture functions, also generalizes an important type of aggregation functions, called Ordered Weighted Averaging (OWA). An OWA is a parametrized average, it uses previously defined weights. A GM is also parametrized average, but with a not fixed predefined vector of weights. Whereas appli...

The linearity contained in the natural order of unit interval plays an important role in many concepts and applications of fuzzy theory. Besides, it is very important in concepts like ordered weighted aggregation operators (OWA) and fuzzy decision making. However, this linearity is not inherited by most of fuzzy logics which extend the standard one...

In this paper we present a new generalization of the mathematical notion of distance. It is based on the abstraction of the codomain of the distance function. The resulting functions must satisfy a generalized triangular inequality, which depends only on the order structure of the valuation space, i.e a monoid structure is not required. This type o...

In this paper, we propose a generalized quasi-metric in spaces of strings, which is based on edit operations (insertion and deletions) and taking values as pairs of non-negative integers. We show that with such a generalization is possible to carry more information about similarity between strings than in the usual case where the distance between t...

In this paper we propose a special type of aggregation function which generalizes the notion of Ordered Weighted Averaging Function - OWA. The resulting functions are called Dynamic Ordered Weighted Averaging Functions --- DYOWAs. This generalization will be developed in such way that the weight vectors are variables depending on the input vector....

The main aim of this investigation is to propose the notion of uniform and strong prime- ness in fuzzy environment. First, it is proposed and investigated the concept of fuzzy strongly prime and fuzzy uniformly strongly prime ideal. As an additional tool, the concept of t/m systems for fuzzy environment gives an alternative way to deal with primene...

The main goal of using data with interval nature is to represent numeric information endowed with impreciseness, which are normally captured from measures of real world. However, in order to do this, it is necessary to adapt real-valued techniques to be applied on interval-based data. For interval-based clustering applications, for instance, it is...

In this paper we consider the notion of Fuzzy Lattices, which was introduced by Chon (Korean J. Math 17 (2009), No. 4, 361-374). We propose some new notions for Fuzzy Ideals and Filters and provide a characterization of Fuzzy Ideals via α-level Sets and Support. Some types of ideals and filters, such as: Fuzzy Principal Ideals (Filters), Proper Fuz...

In this paper we introduce a new notion of generalized metric, called i-metric. This generalization is made by changing the valuation space of the distance function. The result is an interesting distance function for the set of fuzzy numbers of Interval Type with non negative fuzzy numbers as values. This example of i-metric generates a topology in...

In 2013, Bergamaschi and Santiago proposed Strongly Prime Fuzzy(SP) ideals for commutative and noncommutative rings with unity, and investigated their properties. This paper goes a step further since it provides the concept of Strongly Prime Radical of a fuzzy ideal and its properties are investigated. It is shown that Zadeh's extension preserves s...

In this paper, some results about interval uninorms with the additional property of monotonicity inclusion are introduced; e.g construction of interval uninorms from usual uninorms and constructions of interval t-norms and t-conorms from interval uninorms. It is also shown that the neutral element of this type of interval uninorm must be a degenera...