Site Selection of Waste-to-Energy (WtE) Plant considering Public Satisfaction by an Extended VIKOR Method

<div>The 2-tuples <span class="nowrap"><svg height="15.065194pt" id="M461" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.049816 -11.774084 45.933219 15.065194" width="45.933219pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.515,0)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.609,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.664,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.013,0,0,-0.013,19.844,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.998,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,32.084,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.139,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.013,0,0,-0.013,41.319,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg>,</span> <svg height="17.76757pt" id="M462" style="vertical-align:-5.993486pt" version="1.1" viewbox="-0.049816 -11.774084 42.235872 17.76757" width="42.235872pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.515,0)"><path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.696,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,12.631,5.885)"><path d="M256 606C256 635 239 657 207 657C171 657 147 619 147 593C147 563 173 543 194 543C234 543 256 573 256 606ZM233 98L216 125C191 101 156 75 139 75C133 75 132 82 139 107L214 377C226 420 224 454 198 454C169 454 98 415 31 351L46 323C81 353 110 372 116 372C129 372 126 356 121 338L57 101C31 5 47 -12 72 -12C115 -12 197 52 233 98Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.876,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,24.03,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,31.442,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,31.116,5.885)"><path d="M256 606C256 635 239 657 207 657C171 657 147 619 147 593C147 563 173 543 194 543C234 543 256 573 256 606ZM233 98L216 125C191 101 156 75 139 75C133 75 132 82 139 107L214 377C226 420 224 454 198 454C169 454 98 415 31 351L46 323C81 353 110 372 116 372C129 372 126 356 121 338L57 101C31 5 47 -12 72 -12C115 -12 197 52 233 98Z"></path></g><g transform="matrix(.013,0,0,-0.013,37.621,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> and <svg height="15.065194pt" id="M463" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.049816 -11.774084 49.195415 15.065194" width="49.195415pt" 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="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,4.515,0)"><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"></path></g><g transform="matrix(.0091,0,0,-0.0091,13.871,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.927,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.106,0)"><path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.26,0)"><path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,35.346,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,38.401,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.013,0,0,-0.013,44.581,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> of public assessments.</div>

Mathematical Problems in Engineering

tab10

Table 10

Table 10: Site Selection of Waste-to-Energy (WtE) Plant considering Public Satisfaction by an Extended VIKOR Method 