We fuzzify the concept of an associative <mml:math alttext="$\mathcal{I}$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x2110;</mml:mi></mml:math>-ideal in
an <mml:math alttext="$\mathbf{IS}$" id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="bold">I</mml:mi><mml:mi mathvariant="bold">S</mml:mi></mml:math>-algebra. We give a relation between a fuzzy
<mml:math alttext="$\mathcal{I}$" id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x2110;</mml:mi></mml:math>-ideal and a fuzzy  associative <mml:math alttext="$\mathcal{I}$" id="E6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x2110;</mml:mi></mml:math>-ideal,
and we investigate some related properties.

Fuzzy associative <mml:math alttext="$\mathcal{I}$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ℐ</mml:mi></mml:math>-ideals of  
            <mml:math alttext="$\mathbf{IS}$" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="bold">I</mml:mi><mml:mi mathvariant="bold">S</mml:mi></mml:math>-algebras

Fuzzy associative <svg style="vertical-align:-0.20474pt" height="11.85" version="1.1" viewBox="0 0 15.375 11.85" width="15.375" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.538)"><path id="x2110" d="M63 95h-2q0 -22 35 -51q35 -28 85 -28q101 0 174 53q72 54 138 202l27 59q-58 12 -91 48.5t-33 92.5q0 91 86 145q64 40 183 40q46 0 118 -8q41 27 76 27q12 0 20.5 -5.5t8.5 -14.5q0 -52 -109 -52q-34 -25 -66 -78t-80 -157q74 20 125 99l16 -10q-51 -100 -157 -124&#xA;q-80 -172 -133 -227q-117 -121 -285 -121q-76 0 -125 35q-48 36 -48 87q0 31 17 51.5t42 20.5q22 0 36.5 -13.5t14.5 -34.5t-11.5 -34.5t-31.5 -13.5q-23 0 -30 12zM729 601v2q-10 1 -53 1q-100 0 -154 -24q-37 -16 -61 -48t-24 -70q0 -36 26.5 -65t72.5 -35&#xA;q46 89 90.5 144.5t102.5 94.5z" /></g></svg>-ideals of              <svg style="vertical-align:-0.25935pt" height="12.2125" version="1.1" viewBox="0 0 16.1875 12.2125" width="16.1875" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,11.825)"><path id="x1D408" d="M370 25v-25h-350v25q56 4 75 20q18 15 18 61v470q0 41 -19 56t-74 19v25h350v-25q-56 -2 -75.5 -17.5t-19.5 -57.5v-470q0 -48 18 -63q20 -14 77 -18z" /></g><g transform="matrix(.017,-0,0,-.017,6.675,11.825)"><path id="x1D412" d="M484 692v-218h-28q-25 83 -70 130q-54 56 -123 56q-51 0 -80.5 -27t-29.5 -72q0 -37 21 -59q23 -25 82 -55q14 -8 68 -36q67 -34 80 -41q50 -28 79.5 -74.5t29.5 -101.5q0 -96 -69 -154q-68 -59 -179 -59q-61 0 -130 24q-30 10 -41 10q-23 0 -30 -34h-29v248h29&#xA;q23 -97 60 -143q57 -72 144 -72q58 0 92 30.5t34 82.5q0 47 -57 88q-30 21 -122 65q-91 44 -131 91.5t-40 118.5q0 95 58.5 148t160.5 53q54 0 117 -23q27 -9 42 -9q14 0 20.5 6.5t11.5 26.5h30z" /></g></svg>-algebras


International Journal of Mathematics and Mathematical Sciences

Fuzzy associative ℐ-ideals of IS-algebras

Abstract

Copyright