Person: Callejas Bedregal, Benjamin
Loading...
Email Address
person.page.identifierURI
Birth Date
Research Projects
Organizational Units
Job Title
Last Name
Callejas Bedregal
First Name
Benjamin
person.page.departamento
IngenierĆa ElĆ©ctrica, ElectrĆ³nica y de ComunicaciĆ³n
person.page.instituteName
ORCID
0000-0002-6757-7934
person.page.upna
811677
Name
4 results
Search Results
Now showing 1 - 4 of 4
Publication Open Access Towards interval uncertainty propagation control in bivariate aggregation processes and the introduction of width-limited interval-valued overlap functions(Elsevier, 2021) Da Cruz Asmus, Tiago; Pereira Dimuro, GraƧaliz; Callejas Bedregal, Benjamin; Sanz Delgado, JosĆ© Antonio; Mesiar, Radko; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; EstadĆstica, InformĆ”tica y MatemĆ”ticas; Universidad PĆŗblica de Navarra / Nafarroako Unibertsitate PublikoaOverlap 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 express the overlapping of interval-valued data, and they have been usually applied when there is uncertainty regarding the assignment of membership degrees, as in interval-valued fuzzy rule-based classification systems. In this context, the choice of a total order for intervals can be significant, which motivated the recent developments on interval-valued aggregation functions and interval-valued overlap functions that are increasing to a given admissible order, that is, a total order that refines the usual partial order for intervals. Also, width preservation has been considered on these recent works, in an intent to avoid the uncertainty increase and guarantee the information quality, but no deeper study was made regarding the relation between the widths of the input intervals and the output interval, when applying interval-valued functions, or how one can control such uncertainty propagation based on this relation. Thus, in this paper we: (i) introduce and develop the concepts of width-limited interval-valued functions and width limiting functions, presenting a theoretical approach to analyze the relation between the widths of the input and output intervals of bivariate interval-valued functions, with special attention to interval-valued aggregation functions; (ii) introduce the concept of (a,b)-ultramodular aggregation functions, a less restrictive extension of one-dimension convexity for bivariate aggregation functions, which have an important predictable behaviour with respect to the width when extended to the interval-valued context; (iii) define width-limited interval-valued overlap functions, taking into account a function that controls the width of the output interval and a new notion of increasingness with respect to a pair of partial orders (ā¤1,ā¤2); (iv) present and compare three construction methods for these width-limited interval-valued overlap functions, considering a pair of orders (ā¤1,ā¤2), which may be admissible or not, showcasing the adaptability of our developments.Publication Open Access On fuzzy implications derived from general overlap functions and their relation to other classes(MDPI, 2023) Pinheiro, Jocivania; Santos, Helida; Pereira Dimuro, GraƧaliz; Callejas Bedregal, Benjamin; Santiago, Regivan; FernĆ”ndez FernĆ”ndez, Francisco Javier; Bustince Sola, Humberto; EstadĆstica, InformĆ”tica y MatemĆ”ticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISCThere 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, such as decision making, classification and image processing, the idea of this work is to continue previous studies related to fuzzy implication functions derived from general overlap functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions, obtaining the so-called (GO, N)-implication functions. We also investigate their properties, the aggregation of (GO, N)-implication functions, their characterization and the intersections with other classes of fuzzy implication functions.Publication Open Access The law of O-conditionality for fuzzy implications constructed from overlap and grouping functions(Elsevier, 2019) Pereira Dimuro, GraƧaliz; Callejas Bedregal, Benjamin; FernĆ”ndez FernĆ”ndez, Francisco Javier; Sesma Sara, Mikel; Pintor Borobia, JesĆŗs MarĆa; Bustince Sola, Humberto; Estatistika, Informatika eta Matematika; Ingeniaritza; Institute of Smart Cities - ISC; EstadĆstica, InformĆ”tica y MatemĆ”ticas; IngenierĆaOverlap and grouping functions are special kinds of non necessarily associative aggregation operators proposed for many applications, mainly when the associativity property is not strongly required. The classes of overlap and grouping functions are richer than the classes of t-norms and t-conorms, respectively, concerning some properties like idempotency, homogeneity, and, mainly, the self-closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap/grouping functions. In previous works, we introduced some classes of fuzzy implications derived by overlap and/or grouping functions, namely, the residual implications R-0-implications, the strong implications (G, N)-implications and the Quantum Logic implications QL-implications, for overlap functions O, grouping functions G and fuzzy negations N. Such implications do not necessarily satisfy certain properties, but only weaker versions of these properties, e.g., the exchange principle. However, in general, such properties are not demanded for many applications. In this paper, we analyze the so-called law of O-Conditionality, O(x, 1(x, y)) <= y, for any fuzzy implication I and overlap function O, and, in particular, for Ro-implications, (G, N)-implications, QL-implications and D-implications derived from tuples (O, G, N), the latter also introduced in this paper. We also study the conditional antecedent boundary condition for such fuzzy implications, since we prove that this property, associated to the left ordering property, is important for the analysis of the O-Conditionality. We show that the use of overlap functions to implement de generalized Modus Ponens, as the scheme enabled by the law of O-Conditionality, provides more generality than the laws of T-conditionality and U-conditionality, for t-norms T and uninorms U, respectively.Publication Open Access The evolution of the notion of overlap functions(Springer, 2021) Bustince Sola, Humberto; Mesiar, Radko; Pereira Dimuro, GraƧaliz; FernĆ”ndez FernĆ”ndez, Francisco Javier; Callejas Bedregal, Benjamin; EstadĆstica, InformĆ”tica y MatemĆ”ticas; Estatistika, Informatika eta MatematikaIn 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 discuss further theoretical developments that have appeared to deal with other types of problems.