A New Approach to Decision-Making Problem under Complex Pythagorean Fuzzy Information

<table class="table-group" id="tab8"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left">Operator</td><td class="align_center">Order relation of <svg height="12.5794pt" id="M531" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 81.0517 12.5794" width="81.0517pt" 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="M825 658L642 407C494 204 398 112 329 112C309 112 300 126 300 141C300 166 316 203 386 292C491 424 526 479 526 541C526 625 446 687 347 687C219 687 91 607 91 487C91 426 141 380 205 380C277 380 351 424 380 535H360C329 452 280 410 211 410C166 410 132 442 132 485C132 589 221 652 340 652C399 652 466 614 466 569C466 534 451 503 352 375C274 273 245 224 245 175C245 115 278 82 330 82C387 82 468 139 538 236L541 232C497 156 479 117 438 36C323 -1 123 -39 123 -161C123 -200 156 -226 204 -226C336 -226 470 -82 531 38C585 62 632 81 698 142L683 157C639 120 589 93 546 77C637 261 748 431 916 658H825ZM419 -2C355 -118 290 -196 204 -196C181 -196 165 -178 165 -159C165 -84 276 -50 419 -2Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.038,3.132)"><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(.013,0,0,-0.013,15.094,0)"><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,-0.013,19.592,0)"><path d="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 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transform="matrix(.013,0,0,-0.013,59.705,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,64.881,0)"><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,-0.013,70.024,0)"><path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z"></path></g><g transform="matrix(.013,0,0,-0.013,76.265,0)"><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></td><td class="align_center">Most optimal</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">CPFMSM operator</td><td class="align_center"><span style="width: 112.988ptpx;"><svg height="12.3054pt" id="M532" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -9.01432 112.988 12.3054" width="112.988pt" 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="M825 658L642 407C494 204 398 112 329 112C309 112 300 126 300 141C300 166 316 203 386 292C491 424 526 479 526 541C526 625 446 687 347 687C219 687 91 607 91 487C91 426 141 380 205 380C277 380 351 424 380 535H360C329 452 280 410 211 410C166 410 132 442 132 485C132 589 221 652 340 652C399 652 466 614 466 569C466 534 451 503 352 375C274 273 245 224 245 175C245 115 278 82 330 82C387 82 468 139 538 236L541 232C497 156 479 117 438 36C323 -1 123 -39 123 -161C123 -200 156 -226 204 -226C336 -226 470 -82 531 38C585 62 632 81 698 142L683 157C639 120 589 93 546 77C637 261 748 431 916 658H825ZM419 -2C355 -118 290 -196 204 -196C181 -196 165 -178 165 -159C165 -84 276 -50 419 -2Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.038,3.132)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,20.616,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.879,0)"><path d="M825 658L642 407C494 204 398 112 329 112C309 112 300 126 300 141C300 166 316 203 386 292C491 424 526 479 526 541C526 625 446 687 347 687C219 687 91 607 91 487C91 426 141 380 205 380C277 380 351 424 380 535H360C329 452 280 410 211 410C166 410 132 442 132 485C132 589 221 652 340 652C399 652 466 614 466 569C466 534 451 503 352 375C274 273 245 224 245 175C245 115 278 82 330 82C387 82 468 139 538 236L541 232C497 156 479 117 438 36C323 -1 123 -39 123 -161C123 -200 156 -226 204 -226C336 -226 470 -82 531 38C585 62 632 81 698 142L683 157C639 120 589 93 546 77C637 261 748 431 916 658H825ZM419 -2C355 -118 290 -196 204 -196C181 -196 165 -178 165 -159C165 -84 276 -50 419 -2Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,43.917,3.132)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,52.496,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"></path></g><g transform="matrix(.013,0,0,-0.013,63.758,0)"><path d="M825 658L642 407C494 204 398 112 329 112C309 112 300 126 300 141C300 166 316 203 386 292C491 424 526 479 526 541C526 625 446 687 347 687C219 687 91 607 91 487C91 426 141 380 205 380C277 380 351 424 380 535H360C329 452 280 410 211 410C166 410 132 442 132 485C132 589 221 652 340 652C399 652 466 614 466 569C466 534 451 503 352 375C274 273 245 224 245 175C245 115 278 82 330 82C387 82 468 139 538 236L541 232C497 156 479 117 438 36C323 -1 123 -39 123 -161C123 -200 156 -226 204 -226C336 -226 470 -82 531 38C585 62 632 81 698 142L683 157C639 120 589 93 546 77C637 261 748 431 916 658H825ZM419 -2C355 -118 290 -196 204 -196C181 -196 165 -178 165 -159C165 -84 276 -50 419 -2Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,75.796,3.132)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,84.375,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"></path></g><g transform="matrix(.013,0,0,-0.013,95.638,0)"><path d="M825 658L642 407C494 204 398 112 329 112C309 112 300 126 300 141C300 166 316 203 386 292C491 424 526 479 526 541C526 625 446 687 347 687C219 687 91 607 91 487C91 426 141 380 205 380C277 380 351 424 380 535H360C329 452 280 410 211 410C166 410 132 442 132 485C132 589 221 652 340 652C399 652 466 614 466 569C466 534 451 503 352 375C274 273 245 224 245 175C245 115 278 82 330 82C387 82 468 139 538 236L541 232C497 156 479 117 438 36C323 -1 123 -39 123 -161C123 -200 156 -226 204 -226C336 -226 470 -82 531 38C585 62 632 81 698 142L683 157C639 120 589 93 546 77C637 261 748 431 916 658H825ZM419 -2C355 -118 290 -196 204 -196C181 -196 165 -178 165 -159C165 -84 276 -50 419 -2Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,107.676,3.132)"><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"></path></g></svg></span></td><td class="align_center"><span style="width: 17.1292ptpx;"><svg height="12.1958pt" id="M533" style="vertical-align:-3.181479pt" 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175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg></span></td></tr><tr><td class="align_left">CPFDMSM operator</td><td class="align_center"><span style="width: 112.988ptpx;"><svg height="12.3054pt" id="M534" style="vertical-align:-3.29108pt" version="1.1" viewbox="-0.0498162 -9.01432 112.988 12.3054" width="112.988pt" 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="M825 658L642 407C494 204 398 112 329 112C309 112 300 126 300 141C300 166 316 203 386 292C491 424 526 479 526 541C526 625 446 687 347 687C219 687 91 607 91 487C91 426 141 380 205 380C277 380 351 424 380 535H360C329 452 280 410 211 410C166 410 132 442 132 485C132 589 221 652 340 652C399 652 466 614 466 569C466 534 451 503 352 375C274 273 245 224 245 175C245 115 278 82 330 82C387 82 468 139 538 236L541 232C497 156 479 117 438 36C323 -1 123 -39 123 -161C123 -200 156 -226 204 -226C336 -226 470 -82 531 38C585 62 632 81 698 142L683 157C639 120 589 93 546 77C637 261 748 431 916 658H825ZM419 -2C355 -118 290 -196 204 -196C181 -196 165 -178 165 -159C165 -84 276 -50 419 -2Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.038,3.132)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,20.616,0)"><path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z"></path></g><g transform="matrix(.013,0,0,-0.013,31.879,0)"><path d="M825 658L642 407C494 204 398 112 329 112C309 112 300 126 300 141C300 166 316 203 386 292C491 424 526 479 526 541C526 625 446 687 347 687C219 687 91 607 91 487C91 426 141 380 205 380C277 380 351 424 380 535H360C329 452 280 410 211 410C166 410 132 442 132 485C132 589 221 652 340 652C399 652 466 614 466 569C466 534 451 503 352 375C274 273 245 224 245 175C245 115 278 82 330 82C387 82 468 139 538 236L541 232C497 156 479 117 438 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290 -196 204 -196C181 -196 165 -178 165 -159C165 -84 276 -50 419 -2Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.038,3.132)"><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"></path></g></svg></span></td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Complexity

tab8

Table 8

Table 8: A New Approach to Decision-Making Problem under Complex Pythagorean Fuzzy Information 