Optimal Inconsistency Repairing of Pairwise Comparison Matrices Using Integrated Linear Programming and Eigenvector Methods

Algorithm 1

Find modified PCM.

Algorithm Find Modified_Matrix( 𝑍_max,𝑍_min,𝜉,𝐴 )

Input: 𝑍_max, 𝑍_min, ξ, original matrix 𝐴

Output: 𝑍_max, 𝑍_min, optimal matrix 𝐵

BEGIN

(1) If ( 𝑍_max−𝑍_min<𝜉) & (𝑋=0)

 Then

 The current 𝜔^𝑀_𝑖 is the desired optimal solution of weight vector.

 Adopt (16) to get 𝑏^𝑀′_𝑖𝑗.

 Use Theorem 3 to obtain 𝑏^𝐿′_𝑖𝑗 and 𝑏^𝑈′_𝑖𝑗.

 Adjustable PCM 𝐵^′=(𝑏^𝐿′_𝑖𝑗,𝑏^𝑀′_𝑖𝑗,𝑏^𝑈′_𝑖𝑗).

 Obtain Modified PCM 𝐵 by Definition 2.

 Stop.

(2) Else Search segment tree

   Find the greatest lower value of 𝑍 when 𝑋=0

    𝑍_max = upper bound of the interval; 𝑍_min = lower bound of the interval

     Solve the problem (29)–(34),

     Save the new value of 𝜔^𝑀_𝑖

END