Bi-Level Programming Model of Cloud Manufacturing Services Based on Extension Theory

<table class="fixed-width table-group" id="tab7"><tr><td><table class="table"><colgroup><col style="width:9.68em"/><col style="width:6.98em"/><col style="width:40.68em"/></colgroup><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_center" colspan="2">Evaluation method</td><td class="align_center">The sorted results</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left" colspan="2">TOPSIS method</td><td class="align_center">s19&gt; s8&gt; s6&gt; s10&gt; s17&gt; s14&gt; s2&gt; s11&gt; s15&gt; s20&gt; s5&gt; s13&gt; s9&gt; s4&gt; s18&gt; s1&gt; s7&gt; s12&gt; s16&gt; s3</td></tr><tr><td class="align_left" colspan="3"><hr/></td></tr><tr><td class="align_left" colspan="2">Variable precision rough set method</td><td class="align_center">s19&gt; s8&gt; s6&gt; s10&gt; s14&gt; s2&gt; s11&gt; s17&gt; s15&gt; s20&gt; s5&gt; s4&gt; s13&gt; s9&gt; s1&gt; s12&gt; s7&gt; s18&gt; s16&gt; s3</td></tr><tr><td class="align_left" colspan="3"><hr/></td></tr><tr><td class="align_left" colspan="2">Intuitionistic fuzzy method</td><td class="align_center">s6&gt; s8&gt; s19&gt; s17&gt; s10&gt; s2&gt; s14&gt; s11&gt; s15&gt; s20&gt; s5&gt; s13&gt; s9&gt; s4&gt; s18&gt; s1&gt; s12&gt; s7&gt; s16&gt; s3</td></tr><tr><td class="align_left" colspan="3"><hr/></td></tr><tr><td class="align_left" rowspan="4">Extension evaluation</td><td class="align_center"><svg height="12.4698pt" id="M237" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.2229 12.4698" width="12.2229pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg></td><td class="align_center">s9&gt; s13&gt; s11&gt; s5&gt; s18&gt; s2&gt; s19&gt; s20&gt; s15&gt; s10&gt; s14&gt; s7&gt; s6&gt; s8&gt; s16&gt; s17&gt; s1&gt; s4&gt; s12&gt; s3</td></tr><tr><td class="align_center"><svg height="12.4698pt" id="M238" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.2229 12.4698" width="12.2229pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg></td><td class="align_center">s19&gt; s9&gt; s13&gt; s11&gt; s2&gt; s5&gt; s14&gt; s20&gt; s10&gt; s18&gt; s8&gt; s6&gt; s7&gt; s17&gt; s15&gt; s4&gt; s1&gt; s16&gt; s12&gt; s3</td></tr><tr><td class="align_center"><svg height="12.5794pt" id="M239" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 12.2229 12.5794" width="12.2229pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z" id="g50-52"></path></g></svg></td><td class="align_center">s9&gt; s13&gt; s11&gt; s5&gt; s2&gt; s19&gt; s20&gt; s14&gt; s18&gt; s10&gt; s7&gt; s8&gt; s6&gt; s17&gt; s1&gt; s4&gt; s16&gt; s15&gt; s12&gt; s3</td></tr><tr><td class="align_center"><svg height="12.4698pt" id="M240" style="vertical-align:-3.18147pt" version="1.1" viewbox="-0.0498162 -9.28833 12.2229 12.4698" width="12.2229pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z" id="g50-53"></path></g></svg></td><td class="align_center">s19&gt; s9&gt; s13&gt; s5&gt; s11&gt; s2&gt; s10&gt; s14&gt; s8&gt; s18&gt; s20&gt; s6&gt; s17&gt; s15&gt; s7&gt; s1&gt; s4&gt; s16&gt; s12&gt; s3</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The sorted results of four methods.</div>

Mathematical Problems in Engineering

tab7

Table 7

Table 7: Bi-Level Programming Model of Cloud Manufacturing Services Based on Extension Theory 