New Distance Measures between the Interval-Valued Complex Fuzzy Sets with Applications to Decision-Making

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center">Reflectional invariance</td><td class="align_center">Rotational invariance</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left">Distances in [<a href="/journals/mpe/2021/6685793/#B22" target="_blank">22</a>]</td><td class="align_center"><span style="width: 10.0689ptpx;"><svg height="12.4959pt" id="M154" style="vertical-align:-2.92051pt" version="1.1" viewbox="-0.0498162 -9.57539 10.0689 12.4959" width="10.0689pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.013)"><path d="M782 731H740L476 -79H474L280 352L133 274L151 239L242 286L473 -219L782 731Z"></path></g></svg></span></td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M155" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" 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="M528 54L331 254L528 455L492 493L294 291L96 493L60 455L257 254L60 54L96 16L294 217L492 16L528 54Z"></path></g></svg></span></td></tr><tr><td class="align_left"><span style="width: 15.4971ptpx;"><svg height="10.8649pt" id="M156" style="vertical-align:-1.57657pt" version="1.1" viewbox="-0.0498162 -9.28833 15.4971 10.8649" width="15.4971pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.708,0)"><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,-0.013,11.851,0)"><path d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z"></path></g></svg></span></td><td class="align_center"><span style="width: 10.0689ptpx;"><svg height="12.4959pt" id="M157" style="vertical-align:-2.92051pt" version="1.1" viewbox="-0.0498162 -9.57539 10.0689 12.4959" width="10.0689pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.013)"><path d="M782 731H740L476 -79H474L280 352L133 274L151 239L242 286L473 -219L782 731Z"></path></g></svg></span></td><td class="align_center"><span style="width: 7.75925ptpx;"><svg height="7.35473pt" id="M158" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 7.75925 7.35473" width="7.75925pt" 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="M528 54L331 254L528 455L492 493L294 291L96 493L60 455L257 254L60 54L96 16L294 217L492 16L528 54Z"></path></g></svg></span></td></tr><tr><td class="align_left"><span style="width: 17.063ptpx;"><svg height="9.39034pt" id="M159" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 17.063 9.39034" width="17.063pt" 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="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.382,0)"><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,-0.013,10.525,0)"><path d="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z"></path></g></svg></span></td><td class="align_center"><span style="width: 10.0689ptpx;"><svg height="12.4959pt" id="M160" style="vertical-align:-2.92051pt" version="1.1" viewbox="-0.0498162 -9.57539 10.0689 12.4959" width="10.0689pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.013)"><path d="M782 731H740L476 -79H474L280 352L133 274L151 239L242 286L473 -219L782 731Z"></path></g></svg></span></td><td class="align_center"><span style="width: 10.0689ptpx;"><svg height="12.4959pt" id="M161" style="vertical-align:-2.92051pt" version="1.1" viewbox="-0.0498162 -9.57539 10.0689 12.4959" width="10.0689pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,.013)"><path d="M782 731H740L476 -79H474L280 352L133 274L151 239L242 286L473 -219L782 731Z"></path></g></svg></span></td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Two properties of distance measures between IVCFSs.</div>

Mathematical Problems in Engineering

tab1

Table 1

Table 1: New Distance Measures between the Interval-Valued Complex Fuzzy Sets with Applications to Decision-Making 