Journal papers accepted
30/05/22/10:10 Filed in: Journal papers
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero and E. Muñoz-Velasco. Fuzzy Closure Relations. Fuzzy Sets and Systems, 2022. To appear
ABSTRACT The concept of closure operator is key in several branches of mathematics. In this paper, closure operators are extended to relational structures, more specifically to fuzzy relations in the framework of complete fuzzy lattices. The core of the work is the search for a suitable definition of (strong) fuzzy closure relation, that is, a fuzzy relation whose relation with fuzzy closure systems is one-to-one.The study of the properties of fuzzy closure systems and fuzzy relations helps narrow down this exploration until an appropriate definition is settled.
W. Conradie, D. Della Monica, E. Muñoz-Velasco, G. Sciavicco, I.E. Stan. Fuzzy Halpern and Shoham’s Interval Temporal Logics. Fuzzy Sets and Systems, 2022. To appear
ABSTRACT The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal re- lations and propositional labels in a definite, crisp way. In this paper, follow- ing the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications.
ABSTRACT The concept of closure operator is key in several branches of mathematics. In this paper, closure operators are extended to relational structures, more specifically to fuzzy relations in the framework of complete fuzzy lattices. The core of the work is the search for a suitable definition of (strong) fuzzy closure relation, that is, a fuzzy relation whose relation with fuzzy closure systems is one-to-one.The study of the properties of fuzzy closure systems and fuzzy relations helps narrow down this exploration until an appropriate definition is settled.
W. Conradie, D. Della Monica, E. Muñoz-Velasco, G. Sciavicco, I.E. Stan. Fuzzy Halpern and Shoham’s Interval Temporal Logics. Fuzzy Sets and Systems, 2022. To appear
ABSTRACT The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal re- lations and propositional labels in a definite, crisp way. In this paper, follow- ing the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications.