|Title:||On a representation of posets by fuzzy sets||Journal:||Fuzzy Sets and Systems||Volume:||98||Issue:||1||First page:||127||Last page:||132||Issue Date:||1-Jan-1998||Rank:||M22||ISSN:||0165-0114||DOI:||10.1016/S0165-0114(96)00385-5||Abstract:||
The aim of the paper is to present an application of fuzzy sets in mathematics, namely, in the theory of ordered sets. An algorithm for the construction of P-fuzzy sets with distinct levels is given. In connection with this, every finite poset can be mapped, by an anti-isotone bijection, onto the poset of levels of a suitable fuzzy set. Moreover, it is proved that every finite partially ordered set (P, ≤) can be represented by the poset of levels of a particular fuzzy set, defined on the collection of meet-irreducible elements of (P, ≤).
|Keywords:||Cs-carrying cations | Fuzzy set | Irradiation | Level-sets | Meet-irreducible | Partially ordered set | Sputtering||Publisher:||Elsevier|
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