Conference paper accepted
26/07/22/09:27 Filed in: Conference paper
F. Pérez-Gámez, P. Cordero, M. Enciso, A. Mora, M. Ojeda-Aciego. Grading unknown information via an intuitionistic approah. European Symposium on Computational Intelligence and Mathematics (ESCIM), Naples, Italy, 2022.
ABSTRACT Information is not always precise and exact and, in many cases, some data are missed or unknown. To manage this data, fuzzy logic introduces a set of (infinitely many) values between the two Boolean truth values. Other authors use a three-valued approach, by adding an intermediate value to the set of Boolean truth-values. We propose a formal framework strongly based on Atanassov fuzzy sets, associating each proposition with a pair of degrees characterizing our knowledge about the two truth-values, since this logic does not include the law of the excluded middle.
Our starting point is the crisp Formal Concept Analysis, which provides a formal framework for knowledge representation and reasoning. Information is described by means of a binary relation characterizing the relationship among a set of objects and a set of attributes. We extend the crisp framework considering a pair of degrees for each element in the relation.
Formal concept analysis provides a twofold representation of knowledge: the so-called concept lattice and the implication set. In this paper we choose the second option since it better provides a symbolic manipulation of the information. Here, we introduce the syntax and semantics for a new intuitionistic implication. This notion of implication allows a further definition of an intuitionistic logic to manage this kind of information with great expressive power, but avoiding the complexity problems of classical propositional logic.
ABSTRACT Information is not always precise and exact and, in many cases, some data are missed or unknown. To manage this data, fuzzy logic introduces a set of (infinitely many) values between the two Boolean truth values. Other authors use a three-valued approach, by adding an intermediate value to the set of Boolean truth-values. We propose a formal framework strongly based on Atanassov fuzzy sets, associating each proposition with a pair of degrees characterizing our knowledge about the two truth-values, since this logic does not include the law of the excluded middle.
Our starting point is the crisp Formal Concept Analysis, which provides a formal framework for knowledge representation and reasoning. Information is described by means of a binary relation characterizing the relationship among a set of objects and a set of attributes. We extend the crisp framework considering a pair of degrees for each element in the relation.
Formal concept analysis provides a twofold representation of knowledge: the so-called concept lattice and the implication set. In this paper we choose the second option since it better provides a symbolic manipulation of the information. Here, we introduce the syntax and semantics for a new intuitionistic implication. This notion of implication allows a further definition of an intuitionistic logic to manage this kind of information with great expressive power, but avoiding the complexity problems of classical propositional logic.