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

<table>Choosing optimal matrix <svg height="20.9" id="M263" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 15.8875 20.9" width="15.8875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,3.287,16.662)"><path d="M470 619q-46 -79 -133 -79q-39 0 -115 22q-59 16 -92 16q-57 0 -111 -46l-19 23q56 78 138 78q43 0 110 -21q62 -17 100 -17q60 0 103 46z" id="xF5C11"></path></g><g transform="matrix(.017,-0,0,-.017,.625,20.275)"><path d="M594 511q0 -122 -171 -157l1 -2q158 -33 158 -159q0 -52 -34.5 -95t-90.5 -65q-76 -33 -217 -33h-223l8 28q63 5 79.5 19t26.5 72l83 426q9 48 -2.5 60t-77.5 17l6 28h259q195 0 195 -139zM499 509q0 59 -37 83t-91 24q-36 0 -51 -9q-17 -9 -22 -44l-35 -195h62
q82 0 128 37t46 104zM481 199q0 71 -48 102.5t-121 31.5h-56l-37 -201q-11 -58 7.5 -77t80.5 -19q76 0 125 44.5t49 118.5z" id="x1D435"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.112,10.05)"><path d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" id="x2032"></path></g>
</svg> which is closest to matrix <svg height="16.1875" id="M264" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 13.7 16.1875" width="13.7" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,3.212,11.65)"><path d="M658 624q-60 -84 -176 -84q-59 0 -166 25q-89 21 -140 21q-80 0 -159 -54l-17 25q75 84 184 84q57 0 158 -26q100 -20 151 -20q87 0 148 54z" id="xF5C12"></path></g><g transform="matrix(.017,-0,0,-.017,.625,15.563)"><path d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" id="x1D434"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig2

Figure 2

Figure 2: Optimal Inconsistency Repairing of Pairwise Comparison Matrices Using Integrated Linear Programming and Eigenvector Methods 