November 2021
Conference papers accepted
02/11/21/10:10 Filed in: Conference papers
O. Krídlo, M. Ojeda-Aciego. Lower Sugeno-like Integral for Multi-Adjoint FCA. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2022.
ABSTRACT The proposed relationship between L-fuzzy measures, integrals and isotone concept-forming operators on a Girard monoid has recently been used to define a generalized notion of Sugeno integral for Atanassov Intuitionistic L-fuzzy sets. We further continue generalizing the construction aiming at the framework of multi-adjoint formal concept analysis. At this level of generality it is still possible to define a multi-adjoint analogy for lower Sugeno integral at the price of slight modifications in the definition of the underlying adjoint triple. The notion of upper Sugeno integral requires a much more complete treatment including negations, implications with many properties, etc. and is an interesting piece of future work.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Fuzzy closure relations. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2022.
ABSTRACT The concept of closure operator is extended to a fuzzy relation in a complete fuzzy lattice, and the existence of a one-to-one relation between fuzzy closure systems and fuzzy closure relations is studied. First, a suitable definition of fuzzy closure relation must be established, using the existing definitions in the literature as a start point. Next, once the definition is set, one must find two functions such that fuzzy closure systems map to fuzzy closure relations and vice versa. Finally, this correspondence is proved to be one-to-one.
ABSTRACT The proposed relationship between L-fuzzy measures, integrals and isotone concept-forming operators on a Girard monoid has recently been used to define a generalized notion of Sugeno integral for Atanassov Intuitionistic L-fuzzy sets. We further continue generalizing the construction aiming at the framework of multi-adjoint formal concept analysis. At this level of generality it is still possible to define a multi-adjoint analogy for lower Sugeno integral at the price of slight modifications in the definition of the underlying adjoint triple. The notion of upper Sugeno integral requires a much more complete treatment including negations, implications with many properties, etc. and is an interesting piece of future work.
M. Ojeda-Hernández, I.P. Cabrera, P. Cordero, E. Muñoz-Velasco. Fuzzy closure relations. Fuzzy Set Theory and Applications (FSTA), Liptovský Ján, Slovak Republic, 2022.
ABSTRACT The concept of closure operator is extended to a fuzzy relation in a complete fuzzy lattice, and the existence of a one-to-one relation between fuzzy closure systems and fuzzy closure relations is studied. First, a suitable definition of fuzzy closure relation must be established, using the existing definitions in the literature as a start point. Next, once the definition is set, one must find two functions such that fuzzy closure systems map to fuzzy closure relations and vice versa. Finally, this correspondence is proved to be one-to-one.