Pairwise Comparison Matrices and their Fuzzy Extension by Jana Krejčí

Author:Jana Krejčí
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Since the fuzzy maximal eigenvalue obtained by the formulas (4.46)–(4.49) has all desired properties, it can be used in the formulas (4.35) and (4.36) for computing and respectively, in order to verify acceptable inconsistency of FMPCMs.

Fig. 4.6Fuzzy maximal eigenvalues and of the FMPCM (4.55)

Theorem 38

Fuzzy consistency index given by the formula (4.35) with the fuzzy maximal eigenvalue given by the formulas (4.46)–(4.49) is invariant under permutation of objects in FMPCMs.

Proof

According to Theorem 37, the fuzzy maximal eigenvalue obtained by the formulas (4.46)–(4.49) is invariant under permutation of objects in FMPCMs. Thus, also the expressions and in the formula (4.35) are invariant under permutation of objects. This means that given by the formula (4.35) is invariant under permutation of objects in FMPCMs.

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