An Extended Analytical Approach to Evaluating Monotonic Functions of Fuzzy Numbers

<table>Membership functions of <svg height="15.425" id="M283" style="vertical-align:-3.135pt" version="1.1" viewbox="0 0 13.6375 15.425" width="13.6375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,-1.937,11.1)"><path d="M658 624q-60 -84 -176 -84q-59 0 -166 25q-89 21 -140 21q-80 0 -159 -54l-17 25q75 84 184 84q57 0 158 -26q100 -20 151 -20q87 0 148 54z" id="xF5C12"></path></g><g transform="matrix(.017,-0,0,-.017,.062,11.288)"><path d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26
q13 -21 0 -43z" id="x1D45F"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.238,15.362)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg> and <svg height="15.425" id="M284" style="vertical-align:-3.135pt" version="1.1" viewbox="0 0 13.6375 15.425" width="13.6375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,-1.937,11.1)"><path d="M658 624q-60 -84 -176 -84q-59 0 -166 25q-89 21 -140 21q-80 0 -159 -54l-17 25q75 84 184 84q57 0 158 -26q100 -20 151 -20q87 0 148 54z" id="xF5C12"></path></g><g transform="matrix(.017,-0,0,-.017,.062,11.288)"><path d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26
q13 -21 0 -43z" id="x1D45F"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.238,15.362)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg>.</table>

Advances in Fuzzy Systems

fig10

Figure 10

Figure 10: An Extended Analytical Approach to Evaluating Monotonic Functions of Fuzzy Numbers 