The Uncertainty Measure of Hierarchical Quotient Space Structure

<table>The hierarchical quotient space structure <svg height="16.275" id="M62" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 49.262501 16.275" width="49.262501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.137)"><path d="M574 449q-23 -58 -38 -79q-16 -4 -79 -4q-27 -100 -46 -219q-14 -87 7 -87t74 36l13 -27q-74 -81 -139 -81q-48 0 -48 62q0 22 8 59l60 258l-154 4q-21 -103 -54.5 -209t-64.5 -151q-38 -23 -83 -23l-7 15q46 36 94 152.5t64 216.5q-81 0 -138 -54l-18 23q22 27 39.5 43
t61.5 33.5t100 17.5q43 0 131.5 -2.5t129.5 -2.5q23 0 33.5 5t24.5 25z" id="x1D70B"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.113,16.212)"><path d="M775 650l-6 -28q-60 -6 -81.5 -16t-61.5 -54l-175 -191l125 -243q30 -58 48.5 -71t82.5 -19l-5 -28h-275l7 28l35 4q31 4 37 12t-6 34l-108 216q-140 -165 -177 -219q-16 -22 -10.5 -30.5t41.5 -13.5l22 -3l-7 -28h-244l8 28q52 4 75 15.5t67 52.5q48 46 206 231
l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g>
<g transform="matrix(.017,-0,0,-.017,20.15,12.137)"><path d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" id="x28"></path></g><g transform="matrix(.017,-0,0,-.017,26.032,12.137)"><path d="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117
t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" id="x1D445"></path></g>
<g transform="matrix(.012,-0,0,-.012,36.988,16.212)"><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>
<g transform="matrix(.017,-0,0,-.017,43.312,12.137)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
</svg> of <svg height="15.25" id="M63" style="vertical-align:-3.27605pt" version="1.1" viewbox="0 0 17.4 15.25" width="17.4" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M627 18l-10 -26q-79 6 -116 27t-69 76q-41 71 -71 138q-13 29 -27.5 39t-42.5 10h-46l-27 -145q-13 -74 -2.5 -88.5t78.5 -20.5l-6 -28h-271l5 28q66 6 82.5 21.5t30.5 87.5l71 387q12 66 2 78.5t-77 19.5l8 28h233q102 0 147 -29q65 -43 65 -129q0 -69 -45.5 -117
t-115.5 -72q40 -86 66 -133q39 -68 65 -101q28 -37 73 -51zM491 483q0 67 -33.5 101t-91.5 34q-35 0 -51 -10q-13 -8 -20 -48l-45 -245h49q71 0 113 28q79 52 79 140z" id="x1D445"></path></g>
<g transform="matrix(.012,-0,0,-.012,11.013,15.187)"><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>.</table>

Mathematical Problems in Engineering

The Uncertainty Measure of Hierarchical Quotient Space Structure

Figure 1