This paper presents the concept of partition of a nonempty fuzzy set in nonempty convex fuzzy subsets. We restrict our discussion when the universal set, where are defined the fuzzy sets, is the real n-dimensional Euclidean space. We also show that a nonempty fuzzy set has a least one partition in nonempty convex fuzzy subsets.

The notion of an n-ary group is a natural generalization of the notion of a group and has many applications in different branches. In this paper, the notion of (normal) fuzzy n-ary subgroup of an n-ary group is introduced and some related properties are investigated. Characterizations of fuzzy n-ary subgroups are given.

Contrapositive symmetry (CPS) is a tautology in classical logic. In fuzzy logic, not all fuzzy implications have CPS with respect to a given strong negation. Given a fuzzy implication J , towards imparting contrapositive symmetry to J with respect to a strong negation N two techniques, viz., upper and lower contrapositivisation, have been proposed by Bandler and Kohout [Semantics of implication...

We consider the fuzzification of the notion of an n-fold implicative ideal, an n-fold (weak) commutative ideal. We give characterizations of an n-fold fuzzy implicative ideal. We establish an extension property for n-fold fuzzy commutative ideals. 2000 Mathematics Subject Classification. 06F35, 03G25, 03E72.

in this paper, we compute the number of fuzzy subgroups of some classes of non-abeilan groups. explicit formulas are givenfor dihedral groups $d_{2n}$, quasi-dihedral groups $qd_{2^n}$, generalized quaternion groups $q_{4n}$ and modular $p$-groups $m_{p^n}$.

0020-0255/$ see front matter 2008 Elsevier Inc doi:10.1016/j.ins.2008.05.028 * Corresponding author. Tel.: +886 7 6577711x65 E-mail addresses: [email protected], dr.deor@g The lack of consistency in decision making can lead to inconsistent conclusions. In fuzzy analytic hierarchy process (fuzzy AHP) method, it is difficult to ensure a consistent pairwise comparison. Furthermore, establishing a ...

s In respect of the de finition of intuitionistic fuzzy n-norm [9] , the definition of generalised intuitionistic fuzzy ψ norm ( in short GIFψN ) is introduced over a linear space and there after a few results on generalized intuitionistic fuzzy ψ normed linear space and finite dimensional generalized intuitionistic fuzzy ψ normed linear space have been developed. Lastly, we have introduced the...