We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name “modal interval trapezoidal fuzzy numbers”. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this context, it is difficult to...

In this paper, fuzzy morpuhological image processing is explained and reviewed. Based on the mathematical morphology rules, fuzzy sets and fuzzy logic theorem fuzzy morphology operations are defined. In general mathematical morphology operation definitions are similar structures set theory and set operations definitions. For this reason fuzzy set theory is easly applied to the mathematical morp...

In integer programming, the elementary closure associated with a family of cuts is the convex set de ned by the intersection of all the cuts in the family. In this paper, we compare the elementary closures arising from several classical families of cuts: three versions of Gomory’s fractional cuts, three versions of Gomory’s mixed integer cuts, two versions of intersection cuts and their strengt...