Completion of ordered structures by cuts of fuzzy sets: an overview

We deal with rectangular × boards of square cells, using the cut technics of the height function. We investigate combinatorial properties of this function, and in particular we give lower and upper bounds for the number of essentially different cuts. This number turns out to be the cardinality of the height function's range, in case the height function has maximally many rectangular islands. MSC:05D99, 05C05

show abstract

“…More details can be found, e.g., in [6,10,19,20]. We take the whole board to be a rectangular island (of size × ).…”

Section: Height Function and Cutsmentioning

confidence: 99%

Cardinality of height function’s range in case of maximally many rectangular islands — computed by cuts

2012

Self Cite

View full text Add to dashboard Cite

show abstract

“…They provided an algorithm for the construction of a fuzzy set corresponding to a given partially ordered set, [26]. They have also investigated several algebraic properties of the given partially ordered set and the corresponding fuzzy set [27]. A survey of results on the representation of a family of partially ordered sets by a fuzzy set has been recently published in [28].…”

Section: Introductionmentioning

confidence: 99%

Uniqueness results in the representation of families of sets by fuzzy sets

Jaballah

Saidi

2006

Fuzzy Sets and Systems

View full text Add to dashboard Cite

“…Further, * * = * , because * * (x) = * * (x) = {y ∈ U | * (x) ⊇ * (y)} = y ∈ U | {y} ⊆ {x} = {x} = * (x). Therefore, following Šešelja and Tepavčević [30,31], the mapping * : U →T op can be identified as a canonical representation of .…”

Section: Proposition 43 Let Be a Preorder On U Then There Exists Amentioning

confidence: 99%