The Application of Fuzzy VIKOR for the Design Scheme Selection in Lean Management

<table class="fixed-width table-group" id="tab15"><tr><td><table class="table"><colgroup><col style="width:5.49em"/><col style="width:2.98em"/><col style="width:4.41em"/><col style="width:3.01em"/><col style="width:4.41em"/><col style="width:2.94em"/><col style="width:4.41em"/><col style="width:2.99em"/><col style="width:4.41em"/><col style="width:3.01em"/><col style="width:4.41em"/></colgroup><tr><td class="thead-hr" colspan="11"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center"><span style="width: 15.3285ptpx;"><svg height="11.8174pt" id="M366" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 15.3285 11.8174" width="15.3285pt" 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="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.244,3.132)"><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></span></td><td class="align_center">ranking</td><td class="align_center"><span style="width: 15.3285ptpx;"><svg height="11.8174pt" id="M367" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 15.3285 11.8174" width="15.3285pt" 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="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.244,3.132)"><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></span></td><td class="align_center">ranking </td><td class="align_center"><span style="width: 15.3285ptpx;"><svg height="11.927pt" id="M368" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 15.3285 11.927" width="15.3285pt" 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="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.244,3.132)"><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></span></td><td class="align_center">ranking</td><td class="align_center"><span style="width: 15.3285ptpx;"><svg height="11.8174pt" id="M369" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 15.3285 11.8174" width="15.3285pt" 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="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.244,3.132)"><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></span></td><td class="align_center">ranking</td><td class="align_center"><span style="width: 15.3285ptpx;"><svg height="11.927pt" id="M370" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 15.3285 11.927" width="15.3285pt" 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="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z" id="g113-66"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.244,3.132)"><path d="M158 548H390L417 615L410 623H122L83 318C105 326 143 337 185 337C296 337 350 275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 397 242 397C214 397 170 382 133 369L158 548Z" id="g50-54"></path></g></svg></span></td><td class="align_center">ranking</td></tr><tr><td class="thead-hr" colspan="11"><hr/></td></tr><tr><td class="align_left"><span style="width: 6.25863ptpx;"><svg height="8.8423pt" id="M371" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 6.25863 8.8423" width="6.25863pt" 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="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path></g></svg></span></td><td class="align_center">4.76</td><td class="align_center">1</td><td class="align_center">6.20</td><td class="align_center">2</td><td class="align_center">9.94</td><td class="align_center">5</td><td class="align_center">6.90</td><td class="align_center">4</td><td class="align_center">6.78</td><td class="align_center">3</td></tr><tr><td class="align_left"><span style="width: 9.02496ptpx;"><svg height="8.8423pt" id="M372" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 9.02496 8.8423" width="9.02496pt" 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="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z" id="g113-72"></path></g></svg></span></td><td class="align_center">2.15</td><td class="align_center">4</td><td class="align_center">2.18</td><td class="align_center">5</td><td class="align_center">2.03</td><td class="align_center">3</td><td class="align_center">1.17</td><td class="align_center">1</td><td class="align_center">1.66</td><td class="align_center">5</td></tr><tr><td class="align_left"><span style="width: 54.8999ptpx;"><svg height="11.5564pt" id="M373" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 54.8999 11.5564" width="54.8999pt" 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="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z" id="g113-82"></path></g><g transform="matrix(.013,0,0,-0.013,9.386,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,13.884,0)"><path d="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z" 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transform="matrix(.013,0,0,-0.013,50.183,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g></svg></span></td><td class="align_center">0.49</td><td class="align_center">3</td><td class="align_center">0.64</td><td class="align_center">4</td><td class="align_center">0.93</td><td class="align_center">5</td><td class="align_center">0.21</td><td class="align_center">1</td><td class="align_center">0.44</td><td class="align_center">2</td></tr><tr class="table-tr"><td colspan="11"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Utility, regret, and VIKOR index and their ranking.</div>

Mathematical Problems in Engineering

tab15

Table 15

Table 15: The Application of Fuzzy VIKOR for the Design Scheme Selection in Lean Management 