An Application of Classical Logic’s Laws in Formulas of Fuzzy Implications

<div>Intersection between families of <i>QL</i>- and <span class="nowrap"><svg height="13.5868pt" id="M628" style="vertical-align:-2.1507pt" version="1.1" viewbox="-0.0498162 -11.4361 20.2713 13.5868" width="20.2713pt" 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"></path></g><g transform="matrix(.013,0,0,-0.013,9.125,0)"><path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,16.31,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g></svg>-</span>operations (respectively, implications).</div>

Journal of Mathematics

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Figure 3

Figure 3: An Application of Classical Logic’s Laws in Formulas of Fuzzy Implications 