Comments on “A note on “Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP” ”

A very recent note by Pandey and Kumar [3] pointed out some mathematical incorrect assumptions with respect to the statement and proof of the results given by Wang and Chen [8]. Furthermore, the note had modified the statement and proof of the results. This paper shows that the modified results are technically and logically incorrect. New properties of fuzzy linguistic preference relations are developed to correct flaws in the existing results, and a triangular fuzzy addition based transitivity equation is introduced to define additively consistent fuzzy linguistic preference relations.