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].

Step 2 (establishment of the

fuzzy relation matrix R : C [right arrow] V).

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: