Fuzzy ordered sets. (English) Zbl 0765.06008

The author introduces a definition of fuzzy ordered set (foset) \((P,\mu)\) and presents an example on the set of positive integers. He extends this concept to obtain a fuzzy lattice upon which he defines a (fuzzy) similarity relation as a generalization of equivalence. A few propositions of these topics are followed by a section on the fuzzy interval topology generated by fuzzy sets \(P\backslash \downarrow e\) and \(P\backslash \uparrow e\), where, for a fuzzy point \(e=x_ \lambda\), \(\downarrow e(y)=(\mu(y,x)+\lambda-1)\vee 0\) and \(\uparrow e(y)=(\mu(x,y)+\lambda-1)\vee 0\). All fuzziness is taken with respect to the unit interval.


06A99 Ordered sets
54A40 Fuzzy topology
06B99 Lattices
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