fuzzy relation

fuzzy relation

[¦fəz·ē ri′lā·shən]
(mathematics)
A fuzzy subset of the cartesian product X × Y, denoted as a relation from a set X to a set Y.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Hila, "On fuzzy relation and fuzzy quotient [GAMMA]-groups," Quasigroups and Related Systems, vol.
C1 C2 C3 C1 -- -- SC IM SC IM C2 IM MC -- -- SC EL C3 IM MC EU MC -- -- C4 MC MC IM ML ML EL C5 IM MC IM ML MC EL C4 C5 C1 SC SC SC IM C2 VLC IM VLC IM C3 EU VLC EU SC C4 -- -- VLC IM C5 IM ML -- -- Table 6: Collective evaluation with fuzzy relation [20].
A fuzzy preference relation on the attributes is a binary fuzzy relation P on C, where P is a mapping C x C [right arrow] [0, 1] and [p.sub.jr] denotes the preference degree of attribute [c.sub.j] over [c.sub.r].
where I denotes implication, P denotes premise, and C denotes conclusion, while "[omicron]" is a max-min composition, defined on the sets X, Y, and Z, whose result for fuzzy relations A [subset] X x Y and B [subset] Y x Z is a fuzzy relation A [omicron] B [subset] x Z with a membership function:
Since fuzzy relation equations with max-min composition were firstly introduced by Sanchez [1-3], they have attracted much research attention.
Since the membership function is applicable to all evaluation objects, an evaluation matrix can be obtained as a fuzzy relation, that is, R: Q x U [right arrow] [0,1], which is defined as
In the formula, [u.sub.i] as the characteristic value, [r.sub.ik] is the form the membership degree of the fuzzy relation matrix, the fuzzy relation matrix is obtained, which is not enough for the evaluation of the things.
A fuzzy graph is a pair of functions G = ([sigma], [mu]) where [sigma] is a fuzzy subset of a nonempty set V and [mu] is a symmetric fuzzy relation on [sigma], i.e.
Apart from sets, another basic element used by the model is the fuzzy relation. Just as the fuzzy set is a generalization of a non-fuzzy set, so is the fuzzy relation a generalization of a non-fuzzy relation.
Similarly, assume that experts evaluate scientific research conditions guarantee, the scientific research achievement and the project management situation, then the evaluation results constitute the fuzzy relation matrix of project guarantee index valuation results:

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