Fuzzy pogroupoids

Authors:
Hee Sik Kim;J. Neggers
Affiliations:
Department of Mathematics, Hanyang University, Seoul, South Korea;Department of Mathematics, University of Alabama, Tuscaloosa, AL
Venue:
Information Sciences: an International Journal
Year:
2005

Citing 6
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Abstract

In this paper we show that, for given a pogroupoid (X, ċ), the associated poset (X, ≤) is (C2 + 1)-free if and only if the relation ⊳µ is transitive for any fuzzy subset µ of X. Also we determine the set C(X, ċ) of fuzzy subsets µ such that µ(xċy) = µ(yċx) for all x,y ∈ X. Furthermore, with a given finite poset (X, ≤) or the associated pogroupoid (X, ċ) we may then associate a polynomial whose coefficients count the number of congruence classes mod(X,ċ) of fuzzy subsets of X along with another polynomial invariant of interest.