Ordered Semigroups Based on <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.2055pt" id="M1" height="21.3863pt" version="1.1" viewBox="-0.0657574 -16.1808 67.3926 21.3863" width="67.3926pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.017,0,0,-0.017,5.937,0)"><path id="g117-173" d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z"/></g><g transform="matrix(.017,0,0,-0.017,14.998,0)"><path id="g113-45" 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"/></g><g transform="matrix(.017,0,0,-0.017,21.787,0)"><use xlink:href="#g117-173"/></g><g transform="matrix(.017,0,0,-0.017,35.641,0)"><path id="g117-64" d="M574 548H512L295 69H293L76 548H14L263 0H325L574 548Z"/></g><g transform="matrix(.017,0,0,-0.017,45.714,0)"><path id="g113-114" 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"/></g><g transform="matrix(.012,0,0,-0.012,54.14,-7.578)"><path id="g50-226" d="M501 517C491 587 426 710 310 710C240 710 175 662 175 601C175 561 201 517 250 452C219 438 187 423 157 404C88 360 24 280 24 178C24 71 90 -12 195 -12C250 -12 297 6 334 32C412 87 452 170 452 249C452 335 408 396 333 481C259 565 229 601 229 621C229 642 245 652 275 652C359 652 427 583 490 499L501 517ZM364 233C364 142 323 33 222 33C173 33 119 81 119 178C119 265 156 335 193 374C213 395 242 413 272 425C308 384 364 319 364 233Z"/></g><g transform="matrix(.012,0,0,-0.012,54.054,4.995)"><path id="g50-108" d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"/></g><g transform="matrix(.017,0,0,-0.017,61.128,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g></svg>-Fuzzy Ideals

<div>Order relation of <span class="nowrap"><svg height="8.8423pt" id="M199" 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></div>

Advances in Fuzzy Systems

fig1

Figure 1

Figure 1: Ordered Semigroups Based on <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.2055pt" id="M1" height="21.3863pt" version="1.1" viewBox="-0.0657574 -16.1808 67.3926 21.3863" width="67.3926pt"><g transform="matrix(.017,0,0,-0.017,0,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.017,0,0,-0.017,5.937,0)"><path id="g117-173" d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z"/></g><g transform="matrix(.017,0,0,-0.017,14.998,0)"><path id="g113-45" 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"/></g><g transform="matrix(.017,0,0,-0.017,21.787,0)"><use xlink:href="#g117-173"/></g><g transform="matrix(.017,0,0,-0.017,35.641,0)"><path id="g117-64" d="M574 548H512L295 69H293L76 548H14L263 0H325L574 548Z"/></g><g transform="matrix(.017,0,0,-0.017,45.714,0)"><path id="g113-114" 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"/></g><g transform="matrix(.012,0,0,-0.012,54.14,-7.578)"><path id="g50-226" d="M501 517C491 587 426 710 310 710C240 710 175 662 175 601C175 561 201 517 250 452C219 438 187 423 157 404C88 360 24 280 24 178C24 71 90 -12 195 -12C250 -12 297 6 334 32C412 87 452 170 452 249C452 335 408 396 333 481C259 565 229 601 229 621C229 642 245 652 275 652C359 652 427 583 490 499L501 517ZM364 233C364 142 323 33 222 33C173 33 119 81 119 178C119 265 156 335 193 374C213 395 242 413 272 425C308 384 364 319 364 233Z"/></g><g transform="matrix(.012,0,0,-0.012,54.054,4.995)"><path id="g50-108" d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"/></g><g transform="matrix(.017,0,0,-0.017,61.128,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g></svg>-Fuzzy Ideals 

Advances in Fuzzy Systems

Ordered Semigroups Based on -Fuzzy Ideals

Figure 1