Introduction
Preliminaries
\(R(U \times U)\)
|
\(x_{1}\)
|
\(x_{2}\)
|
\(x_{3}\)
|
\(x_{4}\)
|
\(x_{5}\)
|
---|---|---|---|---|---|
\(x_{1}\)
|
\(\left<1,0\right>\)
|
\(\left<0.5,0.7\right>\)
|
\(\left<0.6,0.7\right>\)
|
\(\left<0.4,0.3\right>\)
|
\(\left<0.5,0.3\right>\)
|
\(x_{2}\)
|
\(\left<0.5,0.7\right>\)
|
\(\left<1,0\right>\)
|
\(\left<0.5,0.4\right>\)
|
\(\left<0.5,0.6\right>\)
|
\(\left<0.6,0.4\right>\)
|
\(x_{3}\)
|
\(\left<0.6,0.7\right>\)
|
\(\left<0.5,0.4\right>\)
|
\(\left<1,0\right>\)
|
\(\left<0.7,0.6\right>\)
|
\(\left<0.6,0.5\right>\)
|
\(x_{4}\)
|
\(\left<0.4,0.3\right>\)
|
\(\left<0.5,0.6\right>\)
|
\(\left<0.7,0.6\right>\)
|
\(\left<1,0\right>\)
|
\(\left<0.4,0.3\right>\)
|
\(x_{5}\)
|
\(\left<0.5,0.3\right>\)
|
\(\left<0.6,0.4\right>\)
|
\(\left<0.6,0.5\right>\)
|
\(\left<0.4,0.3\right>\)
|
\(\left<1,0\right>\)
|
\(R(U \times X)\)
|
\(x_{1}\)
|
\(x_{2}\)
|
\(x_{3}\)
|
\(x_{4}\)
|
\(x_{5}\)
|
---|---|---|---|---|---|
\(x_{1}\)
|
\(\left<0,1\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.6,0.7\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.5,0.3\right>\)
|
\(x_{2}\)
|
\(\left<0,1\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.5,0.4\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.6,0.4\right>\)
|
\(x_{3}\)
|
\(\left<0,1\right>\)
|
\(\left<0,1\right>\)
|
\(\left<1,0\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.6,0.5\right>\)
|
\(x_{4}\)
|
\(\left<0,1\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.7,0.6\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.4,0.3\right>\)
|
\(x_{5}\)
|
\(\left<0,1\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.6,0.5\right>\)
|
\(\left<0,1\right>\)
|
\(\left<1,0\right>\)
|
MG-PF-DTRSs based on inclusion measure
Type-I MG-PF-DTRSs
Type-II MG-PF-DTRSs
Type-III MG-PF-DTRSs
Type-IV MG-PF-DTRSs
Uncertainty measures
Decision-making to incomplete multi-source information systems using MG-PF-DTRSs
Incomplete multi-source information systems and the similarity degrees
U
|
\(\mathrm{EC}_{1}\)
|
\(\mathrm{EC}_{2}\)
| ||
---|---|---|---|---|
\(c_{1}\)
|
\(c_{3}\)
|
\(c_{2}\)
|
\(c_{4}\)
| |
\(x_{1}\)
| High | Full | Low | Low |
\(x_{2}\)
| Low | Medium |
\(*\)
| Low |
\(x_{3}\)
|
\(*\)
| Compact |
\(*\)
| Low |
\(x_{4}\)
| High | Full |
\(*\)
| High |
\(x_{5}\)
|
\(*\)
| Full |
\(*\)
| High |
\(x_{6}\)
| Low | Compact | High |
\(*\)
|
\(R_{\mathrm{EC}_{1}}(U \times U)\)
|
\(x_{1}\)
|
\(x_{2}\)
|
\(x_{3}\)
|
\(x_{4}\)
|
\(x_{5}\)
|
\(x_{6}\)
|
---|---|---|---|---|---|---|
\(x_{1}\)
|
\(\left<1,0\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.2500,0.9330\right>\)
|
\(\left<1,0\right>\)
|
\(\left<0.7500,0.4303\right>\)
|
\(\left<0,1\right>\)
|
\(x_{2}\)
|
\(\left<1,0\right>\)
|
\(\left<0.2500,0.6330\right>\)
|
\(\left<0,1\right>\)
|
\(\left<0.2500,0.9330\right>\)
|
\(\left<0.5000,0.5000\right>\)
| |
\(x_{3}\)
|
\(\left<1,0\right>\)
|
\(\left<0.2500,0.9330\right>\)
|
\(\left<0.1250,0.9841\right>\)
|
\(\left<0.2500,0.9330\right>\)
| ||
\(x_{4}\)
|
\(\left<1,0\right>\)
|
\(\left<0.7500,0.4330\right>\)
|
\(\left<0,1\right>\)
| |||
\(x_{5}\)
|
\(\left<1,0\right>\)
|
\(\left<0.2500,0.9330\right>\)
| ||||
\(x_{6}\)
|
\(\left<1,0\right>\)
|
An algorithm
An illustrative example
Problem description
Decision analysis
U
|
\(\mathrm{EC}_{1}\)
|
\(\mathrm{EC}_{2}\)
|
\(\mathrm{EC}_{3}\)
| |||||||
---|---|---|---|---|---|---|---|---|---|---|
\(c_{1}\)
|
\(c_{2}\)
|
\(c_{6}\)
|
\(c_{7}\)
|
\(c_{3}\)
|
\(c_{5}\)
|
\(c_{8}\)
|
\(c_{4}\)
|
\(c_{9}\)
|
\(c_{10}\)
| |
\(x_{1}\)
| High | Average | Fine | Moderate | Moderate | Low | Fine | Fine | Moderately high | Fine |
\(x_{2}\)
| High |
\(*\)
| Fine | Moderately high | Moderate |
\(*\)
| Fine | Good | High |
\(*\)
|
\(x_{3}\)
| Low |
\(*\)
| Fine |
\(*\)
|
\(*\)
| Moderate |
\(*\)
| Good | Moderately low | Good |
\(x_{4}\)
|
\(*\)
| Low | Poor |
\(*\)
|
\(*\)
| Moderately low |
\(*\)
| Fine |
\(*\)
| Fine |
\(x_{5}\)
| High | Average | Good | Low |
\(*\)
| High | Good |
\(*\)
| High |
\(*\)
|
\(x_{6}\)
|
\(*\)
| Low | Fine |
\(*\)
| Moderately low |
\(*\)
|
\(*\)
| Fine | Moderate |
\(*\)
|
\(x_{7}\)
|
\(*\)
|
\(*\)
| Good | High |
\(*\)
|
\(*\)
| Fine |
\(*\)
| Moderately high | Fine |
\(x_{8}\)
| Low |
\(*\)
| Fine | Moderately high | Moderate |
\(*\)
| Good | Fine |
\(*\)
|
\(*\)
|
\(x_{9}\)
|
\(*\)
| Average | Good |
\(*\)
|
\(*\)
| Low | Poor |
\(*\)
| Low |
\(*\)
|
\(x_{10}\)
| Low | Low | Fine |
\(*\)
|
\(*\)
| Moderate |
\(*\)
| Fine | Moderate | Fine |
\(R_{1}(U)\)
|
\(x_{1}\)
|
\(x_{2}\)
|
\(x_{3}\)
|
\(x_{4}\)
|
\(x_{5}\)
|
\(x_{6}\)
|
\(x_{7}\)
|
\(x_{8}\)
|
\(x_{9}\)
|
\(x_{10}\)
|
---|---|---|---|---|---|---|---|---|---|---|
\(x_{1}\)
| \(<1\), | \(<0.6250\), | \(<0.4250\), | \(<0.1750\), | \(<0.5000\), | \(<0.4250\), | \(<0.2500\), | \(<0.3750\), | \(<0.4250\), | \(<0.3000\), |
\(0>\)
|
\(0.4665>\)
|
\(0.7115>\)
|
\(0.9615>\)
|
\(0.5000>\)
|
\(0.7115>\)
|
\(0.9330>\)
|
\(0.7165>\)
|
\(0.7115>\)
|
\(0.7449>\)
| |
\(x_{2}\)
| \(<1\), | \(<0.3625\), | \(<0.3000\), | \(<0.3750\), | \(<0.5500\), | \(<0.1875\), | \(<0.5625\), | \(<0.3000\), | \(<0.4250\), | |
\(0>\)
|
\(0.7370>\)
|
\(0.9280>\)
|
\(0.7165>\)
|
\(0.6780>\)
|
\(0.9586>\)
|
\(0.4921>\)
|
\(0.9280>\)
|
\(0.7115>\)
| ||
\(x_{3}\)
| \(<1\), | \(<0.2600\), | \(<0.1750\), | \(<0.5100\), | \(<0.2375\), | \(<0.6125\), | \(<0.2600\), | \(<0.635\), | ||
\(0>\)
|
\(0.9328>\)
|
\(0.9615>\)
|
\(0.6828>\)
|
\(0.9535>\)
|
\(0.4870>\)
|
\(0.9328>\)
|
\(0.4663>\)
| |||
\(x_{4}\)
| \(<1\), | \(<0.1750\), | \(<0.3225\), | \(<0.2375\), | \(<0.3000\), | \(<0.0725\), | \(<0.385\), | |||
\(0>\)
|
\(0.9615>\)
|
\(0.7419>\)
|
\(0.9535>\)
|
\(0.9280>\)
|
\(0.9919>\)
|
\(0.7163>\)
| ||||
\(x_{5}\)
| \(<1\), | \(<0.1750\), | \(<0.5000\), | \(<0.1250\), | \(<0.6750\), | \(<0.0500\), | ||||
\(0>\)
|
\(0.9615>\)
|
\(0.6380>\)
|
\(0.9665>\)
|
\(0.4615>\)
|
\(0.9949>\)
| |||||
\(x_{6}\)
| \(<1\), | \(<0.2375\), | \(<0.5500\), | \(<0.0725\), | \(<0.6350\), | |||||
\(0>\)
|
\(0.9535>\)
|
\(0.6780>\)
|
\(0.9919>\)
|
\(0.4663>\)
| ||||||
\(x_{7}\)
| \(<1\), | \(<0.1875\), | \(<0.4875\), | \(<0.3000\), | ||||||
\(0>\)
|
\(0.9586>\)
|
\(0.7035>\)
|
\(0.9280>\)
| |||||||
\(x_{8}\)
| \(<1\), | \(<0.3000\), | \(<0.6750\), | |||||||
\(0>\)
|
\(0.9280>\)
|
\(0.4615>\)
| ||||||||
\(x_{9}\)
| \(<1\), | \(<0.1350\), | ||||||||
\(0>\)
|
\(0.9663>\)
| |||||||||
\(x_{10}\)
| \(<1\), | |||||||||
\(0>\)
|
\(R_{2}(U)\)
|
\(x_{1}\)
|
\(x_{2}\)
|
\(x_{3}\)
|
\(x_{4}\)
|
\(x_{5}\)
|
\(x_{6}\)
|
\(x_{7}\)
|
\(x_{8}\)
|
\(x_{9}\)
|
\(x_{10}\)
|
---|---|---|---|---|---|---|---|---|---|---|
\(x_{1}\)
| \(<1\), | \(<0.7333\), | \(<0.2778\), | \(<0.2778\), | \(<0.1667\), | \(<0.1778\), | \(<0.5667\), | \(<0.4000\), | \(<0.5000\), | \(<0.2778\), |
\(0>\)
|
\(0.3266>\)
|
\(0.9363>\)
|
\(0.9363>\)
|
\(0.9553>\)
|
\(0.9742>\)
|
\(0.6153>\)
|
\(0.6599>\)
|
\(0.6220>\)
|
\(0.9363>\)
| |
\(x_{2}\)
| \(<1\), | \(<0.3444\), | \(<0.3444\), | \(<0.2333\), | \(<0.1244\), | \(<0.5133\), | \(<0.3467\), | \(<0.2333\), | \(<0.3444\), | |
\(0>\)
|
\(0.9295>\)
|
\(0.9295>\)
|
\(0.9486>\)
|
\(0.9807>\)
|
\(0.6217>\)
|
\(0.6664>\)
|
\(0.9486>\)
|
\(0.9295>\)
| ||
\(x_{3}\)
| \(<1\), | \(<0.1204\), | \(<0.1944\), | \(<0.2704\), | \(<0.2611\), | \(<0.3444\), | \(<0.1944\), | \(<0.4537\), | ||
\(0>\)
|
\(0.9874>\)
|
\(0.9704>\)
|
\(0.9465>\)
|
\(0.9636>\)
|
\(0.9295>\)
|
\(0.9704>\)
|
\(0.6540>\)
| |||
\(x_{4}\)
| \(<1\), | \(<0.1204\), | \(<0.2704\), | \(<0.2611\), | \(<0.3444\), | \(<0.1944\), | \(<0.1204\), | |||
\(0>\)
|
\(0.9874>\)
|
\(0.9465>\)
|
\(0.9636>\)
|
\(0.9295>\)
|
\(0.9704>\)
|
\(0.9874>\)
| ||||
\(x_{5}\)
| \(<1\), | \(<0.3444\), | \(<0.2611\), | \(<0.5667\), | \(<0.0833\), | \(<0.1944\), | ||||
\(0>\)
|
\(0.9295>\)
|
\(0.9636>\)
|
\(0.6153>\)
|
\(0.9894>\)
|
\(0.9704>\)
| |||||
\(x_{6}\)
| \(<1\), | \(<0.2911\), | \(<0.1244\), | \(<0.3444\), | \(<0.2704\), | |||||
\(0>\)
|
\(0.9360>\)
|
\(0.9807>\)
|
\(0.9295>\)
|
\(0.9465>\)
| ||||||
\(x_{7}\)
| \(<1\), | \(<0.1800\), | \(<0.1500\), | \(<0.2611\), | ||||||
\(0>\)
|
\(0.9551>\)
|
\(0.9827>\)
|
\(0.9636>\)
| |||||||
\(x_{8}\)
| \(<1\), | \(<0.2333\), | \(<0.2333\), | |||||||
\(0>\)
|
\(0.9486>\)
|
\(0.9486>\)
| ||||||||
\(x_{9}\)
| \(<1\), | \(<0.1944\), | ||||||||
\(0>\)
|
\(0.9704>\)
| |||||||||
\(x_{10}\)
| \(<1\), | |||||||||
\(0>\)
|
\(R_{3}(U)\)
|
\(x_{1}\)
|
\(x_{2}\)
|
\(x_{3}\)
|
\(x_{4}\)
|
\(x_{5}\)
|
\(x_{6}\)
|
\(x_{7}\)
|
\(x_{8}\)
|
\(x_{9}\)
|
\(x_{10}\)
|
---|---|---|---|---|---|---|---|---|---|---|
\(x_{1}\)
| \(<1\), | \(<0.1111\), | \(<0\), | \(<0.7333\), | \(<0.2778\), | \(<0.4444\), | \(<0.8333\), | \(<0.5111\), | \(<0.2778\), | \(<0.6667\), |
\(0>\)
|
\(0.9809>\)
|
\(1>\)
|
\(0.3266>\)
|
\(0.9363>\)
|
\(0.6476>\)
|
\(0.2887>\)
|
\(0.6409>\)
|
\(0.9363>\)
|
\(0.3333>\)
| |
\(x_{2}\)
| \(<1\), | \(<0.4444\), | \(<0.1778\), | \(<0.5370\), | \(<0.3704\), | \(<0.2778\), | \(<0.1037\), | \(<0.2704\), | \(<0.1111\), | |
\(0>\)
|
\(0.6476>\)
|
\(0.9742>\)
|
\(0.6199>\)
|
\(0.6646>\)
|
\(0.9363>\)
|
\(0.9912>\)
|
\(0.9465>\)
|
\(0.9809>\)
| ||
\(x_{3}\)
| \(<1\), | \(<0.0667\), | \(<0.2778\), | \(<0.1111\), | \(<0.1667\), | \(<0.1778\), | \(<0.2778\), | \(<0\), | ||
\(0>\)
|
\(0.9933>\)
|
\(0.9363>\)
|
\(0.9809>\)
|
\(0.9553>\)
|
\(0.9742>\)
|
\(0.9363>\)
|
\(1>\)
| |||
\(x_{4}\)
| \(<1\), | \(<0.3444\), | \(<0.5111\), | \(<0.5667\), | \(<0.4578\), | \(<0.3444\), | \(<0.7333\), | |||
\(0>\)
|
\(0.9295>\)
|
\(0.6409>\)
|
\(0.6153>\)
|
\(0.6473>\)
|
\(0.9295>\)
|
\(0.3266>\)
| ||||
\(x_{5}\)
| \(<1\), | \(<0.2037\), | \(<0.1944\), | \(<0.2704\), | \(<0.1204\), | \(<0.1944\), | ||||
\(0>\)
|
\(0.9533>\)
|
\(0.9704>\)
|
\(0.9465>\)
|
\(0.9874>\)
|
\(0.9704>\)
| |||||
\(x_{6}\)
| \(<1\), | \(<0.2778\), | \(<0.4370\), | \(<0.2037\), | \(<0.7778\), | |||||
\(0>\)
|
\(0.9363>\)
|
\(0.6579>\)
|
\(0.9533>\)
|
\(0.3143>\)
| ||||||
\(x_{7}\)
| \(<1\), | \(<0.3444\), | \(<0.1944\), | \(<0.5000\), | ||||||
\(0>\)
|
\(0.9295>\)
|
\(0.9704>\)
|
\(0.6220>\)
| |||||||
\(x_{8}\)
| \(<1\), | \(<0.2704\), | \(<0.5111\), | |||||||
\(0>\)
|
\(0.9465>\)
|
\(0.6409>\)
| ||||||||
\(x_{9}\)
| \(<1\), | \(<0.2778\), | ||||||||
\(0>\)
|
\(0.9363>\)
| |||||||||
\(x_{10}\)
| \(<1\), | |||||||||
\(0>\)
|
\([x_{i}]_{\cap _{k=1}^{3}R_{k}(U\times X)}\)
|
\(x_{1}\)
|
\(x_{2}\)
|
\(x_{3}\)
|
\(x_{4}\)
|
\(x_{5}\)
|
\(x_{6}\)
|
\(x_{7}\)
|
\(x_{8}\)
|
\(x_{9}\)
|
\(x_{10}\)
|
---|---|---|---|---|---|---|---|---|---|---|
\(x_{1}\)
| \(<1\), | \(<0.1111\), | \(<0\), | \(<0.1750\), | \(<0.1667\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0>\)
|
\(0.9809>\)
|
\(1>\)
|
\(0.9615>\)
|
\(0.9553>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
| |
\(x_{2}\)
| \(<0.1111\), | \(<1\), | \(<0.3444\), | \(<0.1778\), | \(<0.2333\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0.9809>\)
|
\(0>\)
|
\(0.9295>\)
|
\(0.9742>\)
|
\(0.9486>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
| |
\(x_{3}\)
| \(<0\), | \(<0.3444\), | \(<1\), | \(<0.0667\), | \(<0.1750\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(1>\)
|
\(0.9295>\)
|
\(0>\)
|
\(0.9933>\)
|
\(0.9704>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
| |
\(x_{4}\)
| \(<0.1750\), | \(<0.1778\), | \(<0.0667\), | \(<1\), | \(<0.1204\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0.9615>\)
|
\(0.9742>\)
|
\(0.9933>\)
|
\(0>\)
|
\(0.9874>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
| |
\(x_{5}\)
| \(<0.1667\), | \(<0.2333\), | \(<0.1750\), | \(<0.1204\), | \(<1\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0.9553>\)
|
\(0.9486>\)
|
\(0.9704>\)
|
\(0.9874>\)
|
\(0>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
| |
\(x_{6}\)
| \(<0.1778\), | \(<0.1244\), | \(<0.1111\), | \(<0.2704\), | \(<0.1750\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0.9742>\)
|
\(0.9807>\)
|
\(0.9809>\)
|
\(0.9465>\)
|
\(0.9615>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
| |
\(x_{7}\)
| \(<0.2500\), | \(<0.1875\), | \(<0.1667\), | \(<0.2375\), | \(<0.1944\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0.9330>\)
|
\(0.9586>\)
|
\(0.9636>\)
|
\(0.9636>\)
|
\(0.9704>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
| |
\(x_{8}\)
| \(<0.3750\), | \(<0.1037\), | \(<0.1778\), | \(<0.3000\), | \(<0.1250\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0.7165>\)
|
\(0.9912>\)
|
\(0.9742>\)
|
\(0.9295>\)
|
\(0.9665>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
| |
\(x_{9}\)
| \(<0.2778\), | \(<0.2333\), | \(<0.1944\), | \(<0.0725\), | \(<0.0833\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0.9363>\)
|
\(0.9486>\)
|
\(0.9704>\)
|
\(0.9919>\)
|
\(0.9894>\)
|
\(0>\)
|
\(1>\)
| 1 |
\(1>\)
|
\(1>\)
| |
\(x_{10}\)
| \(<0.2778\), | \(<0.1111\), | \(<0\), | \(<0.1204\), | \(<0.0500\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), | \(<0\), |
\(0.9363>\)
|
\(0.9809>\)
|
\(1>\)
|
\(0.9874>\)
|
\(0.9949>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
\(1>\)
|
No. |
X
| Type-I MG-PF-DTRSs | Type-II MG-PF-DTRSs | Type-III MG-PF-DTRSs | Type-IV MG-PF-DTRSs | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
\(\rho _{\mathrm{I}}\)
|
\(\sigma _{\mathrm{I}}\)
|
\(\omega _{\mathrm{I}}\)
|
\(\rho _{\mathrm{II}}\)
|
\(\sigma _{\mathrm{II}}\)
|
\(\omega _{\mathrm{II}}\)
|
\(\rho _{\mathrm{III}}\)
|
\(\sigma _{\mathrm{III}}\)
|
\(\omega _{\mathrm{III}}\)
|
\(\rho _{\mathrm{IV}}\)
|
\(\sigma _{\mathrm{IV}}\)
|
\(\omega _{\mathrm{IV}}\)
| ||
1 |
\(x_{1,2,3,4,5}\)
| 0.7 | 1.4 | 0.7 | 0.2857 | 0.4 | 0.2 | 0.3 | 0.6 | 0.3 | 0.75 | 1.2 | 0.6 |
2 |
\(x_{1,2,5,6,7}\)
| 0.7 | 1.4 | 0.7 | 0.5 | 0.6 | 0.3 | 0.3 | 0.6 | 0.3 | 0.75 | 1.2 | 0.6 |
3 |
\(x_{1,3,5,7,8}\)
| 0.6 | 1.2 | 0.6 | 0.25 | 0.4 | 0.2 | 0.2 | 0.4 | 0.2 | 0.6667 | 1.2 | 0.6 |
4 |
\(x_{1,3,4,6,7}\)
| 0.5 | 1 | 0.5 | 0.5 | 0.4 | 0.2 | 0.2 | 0.4 | 0.2 | 1 | 1 | 0.5 |
5 |
\(x_{2,4,5,6,7}\)
| 0.7 | 1.4 | 0.7 | 0.5 | 0.6 | 0.3 | 0.4 | 0.8 | 0.4 | 1 | 1.2 | 0.6 |
6 |
\(x_{2,4,5,9,10}\)
| 0.6 | 1.2 | 0.6 | 0.1429 | 0.2 | 0.1 | 0.1 | 0.2 | 0.1 | 0.875 | 1.4 | 0.6 |
7 |
\(x_{2,7,8,9,10}\)
| 0.6 | 1.2 | 0.6 | 0 | 0 | 0 | 0.1 | 0.2 | 0.1 | 0.8571 | 1.2 | 0.6 |
8 |
\(x_{3,4,6,8,9}\)
| 0.5 | 1 | 0.5 | 0.25 | 0.2 | 0.1 | 0.2 | 0.4 | 0.2 | 1 | 1 | 0.5 |
9 |
\(x_{3,5,6,9,10}\)
| 0.6 | 1.2 | 0.6 | 0.2 | 0.2 | 0.1 | 0.1 | 0.2 | 0.1 | 0.8571 | 1.2 | 0.6 |
10 |
\(x_{4,6,7,8,9}\)
| 0.5 | 1 | 0.5 | 0 | 0 | 0 | 0.1 | 0.2 | 0.1 | 1 | 1 | 0.5 |