{"id":2769,"date":"2021-08-31T11:24:55","date_gmt":"2021-08-31T05:54:55","guid":{"rendered":"https:\/\/soulofmathematics.com\/?page_id=2769"},"modified":"2022-08-25T18:54:56","modified_gmt":"2022-08-25T13:24:56","slug":"fuzzy-logic","status":"publish","type":"page","link":"https:\/\/soulofmathematics.com\/index.php\/fuzzy-logic\/","title":{"rendered":"FUZZY LOGIC"},"content":{"rendered":"\n<div class=\"wp-block-cover is-light\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-0 has-background-dim\"><\/span><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<figure class=\"wp-block-pullquote has-border-color has-white-border-color has-black-color has-text-color has-background\" style=\"border-style:solid;background-color:#ffffff00\"><blockquote><p>Fuzzy logic is&nbsp;<strong>an approach to computing based on &#8220;degrees of truth&#8221;<\/strong>&nbsp;rather than the usual &#8220;true or false&#8221; (1 or 0) Boolean logic.<\/p><\/blockquote><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-cover alignfull is-light\" style=\"min-height:850px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-0 has-background-dim has-background-gradient\" style=\"background:linear-gradient(135deg,rgb(0,0,0) 0%,rgb(72,28,114) 100%)\"><\/span><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<h2 class=\"wp-block-heading\">FUZZY SETS<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide\"\/>\n\n\n\n<p>A Fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusions, unions, intersection, complement, relation and convexity are extended to such sets, and various properties of these notions in the context of various fuzzy sets are established.<\/p>\n\n\n\n<p class=\"has-luminous-vivid-amber-color has-text-color has-medium-font-size\">                                                                                                                                                               <a href=\"https:\/\/en.wikipedia.org\/wiki\/Lotfi_A._Zadeh\">&#8211; Lotfi A. Zadeh<\/a><\/p>\n\n\n\n<p>A fuzzy set is a set containing elements that have a varying degree of membership in the set. Elements of a fuzzy set are mapped to a universe of membership values using function &#8211; theoretic form.<\/p>\n\n\n\n<p>A notation convention for fuzzy sets, when the universe of discourse, <em>X<\/em>, is discrete and finite, is as follows for a fuzzy set <em>A<\/em>:<\/p>\n\n\n\n<p> <em>A<\/em>  = {(\u03bc <em><sub>A<\/sub><\/em> (x<sub>1<\/sub>))\/x<sub>1<\/sub> +  (\u03bc <em><sub>A<\/sub><\/em> (x<sub>2<\/sub>))\/x<sub>2<\/sub> + &#8230;&#8230;&#8230;..}<\/p>\n\n\n\n<p> = <strong>\u03a3<\/strong> {(\u03bc <em><sub>A<\/sub><\/em> (x<sub>i<\/sub>))\/x<sub>i<\/sub>}<\/p>\n\n\n\n<p>When the universe is continuous and infinite, the fuzzy set  <em>A<\/em> is denoted by:<\/p>\n\n\n\n<p> <em>A<\/em>  = <strong>\u222b<\/strong> {(\u03bc <em><sub>A<\/sub><\/em> (x))\/x} (the &#8216;division sign&#8217; is not a quotient but a delimiter).<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>The numerator in each term is the membership value in set <em>A<\/em> associated with the element of the universe indicated in the denominator.<\/li><li>The summation symbol is not for algebraic summation but rather a collection\/aggregation.<\/li><\/ul>\n\n\n\n<p><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img data-recalc-dims=\"1\" fetchpriority=\"high\" decoding=\"async\" width=\"485\" height=\"515\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/image-removebg-preview-2.png?resize=485%2C515&#038;ssl=1\" alt=\"fuzzification and defuzzification\" class=\"wp-image-2805\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/image-removebg-preview-2.png?w=485&amp;ssl=1 485w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/image-removebg-preview-2.png?resize=283%2C300&amp;ssl=1 283w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><\/figure><\/div>\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\"><\/div>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/Zadeh_FuzzySetTheory_1965.pdf\" type=\"application\/pdf\" style=\"width:100%;height:639px\" aria-label=\"Embed of Embed of Zadeh_FuzzySetTheory_1965..\"><\/object><a id=\"wp-block-file--media-4ba36e48-1688-493c-8836-6d26dce8fc94\" href=\"https:\/\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/Zadeh_FuzzySetTheory_1965.pdf\">Zadeh_FuzzySetTheory_1965<\/a><a href=\"https:\/\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/Zadeh_FuzzySetTheory_1965.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-4ba36e48-1688-493c-8836-6d26dce8fc94\">Download<\/a><\/div>\n\n\n\n<p><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-cover alignfull is-light has-custom-content-position is-position-bottom-center\" style=\"min-height:850px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-0 has-background-dim has-background-gradient\" style=\"background:linear-gradient(135deg,rgb(68,40,109) 0%,rgb(0,0,0) 100%)\"><\/span><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<h2 class=\"wp-block-heading\">FUZZY SET OPERATION<\/h2>\n\n\n\n<p>Define three fuzzy sets on the universe <em>X<\/em>. For a given element x of the universe, the following function &#8211; theoretic operations for the set-theoretic operations of union, intersection and complement are defined A, <em>B<\/em> and <em>C<\/em> on  <em>X<\/em> :<\/p>\n\n\n\n<div class=\"wp-block-media-text alignwide has-media-on-the-right is-stacked-on-mobile\"><div class=\"wp-block-media-text__content\">\n<p class=\"has-large-font-size\">UNION<\/p>\n\n\n\n<p class=\"has-medium-font-size\"> \u03bc <em><sub>A<\/sub><\/em><sub>\u222a<em>B<\/em><\/sub> (x) =  \u03bc <em><sub>A<\/sub><\/em> (x) \u2228  \u03bc <sub><em>B<\/em><\/sub> (x) <\/p>\n<\/div><figure class=\"wp-block-media-text__media\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"960\" height=\"560\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?resize=960%2C560&#038;ssl=1\" alt=\"union\" class=\"wp-image-2826 size-full\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?resize=1024%2C597&amp;ssl=1 1024w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?resize=300%2C175&amp;ssl=1 300w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?resize=768%2C447&amp;ssl=1 768w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?resize=1536%2C895&amp;ssl=1 1536w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?resize=2048%2C1193&amp;ssl=1 2048w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?resize=1140%2C664&amp;ssl=1 1140w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage.png?w=2880&amp;ssl=1 2880w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-media-text alignwide is-stacked-on-mobile\"><figure class=\"wp-block-media-text__media\"><img data-recalc-dims=\"1\" decoding=\"async\" width=\"960\" height=\"560\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?resize=960%2C560&#038;ssl=1\" alt=\"intersection\" class=\"wp-image-2827 size-full\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?resize=1024%2C597&amp;ssl=1 1024w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?resize=300%2C175&amp;ssl=1 300w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?resize=768%2C447&amp;ssl=1 768w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?resize=1536%2C895&amp;ssl=1 1536w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?resize=2048%2C1193&amp;ssl=1 2048w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?resize=1140%2C664&amp;ssl=1 1140w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-1.png?w=2880&amp;ssl=1 2880w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-large-font-size\">INTERSECTION<\/p>\n\n\n\n<p class=\"has-medium-font-size\"> \u03bc <em><sub>A<\/sub><\/em><sub>\u2229<em>B<\/em><\/sub> (x) =  \u03bc <em><sub>A<\/sub><\/em> (x) <strong>\u2227<\/strong>  \u03bc <sub><em>B<\/em><\/sub> (x) <\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-media-text alignwide has-media-on-the-right is-stacked-on-mobile\"><div class=\"wp-block-media-text__content\">\n<p class=\"has-large-font-size\">COMPLEMENT<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><em>A<\/em> \u2286 X \u2192  \u03bc <em><sub>A<\/sub><\/em> (x) <strong>\u2264<\/strong>  \u03bc <em><sub>X<\/sub><\/em> (x) <\/p>\n<\/div><figure class=\"wp-block-media-text__media\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"560\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?resize=960%2C560&#038;ssl=1\" alt=\"complement\" class=\"wp-image-2830 size-full\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?resize=1024%2C597&amp;ssl=1 1024w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?resize=300%2C175&amp;ssl=1 300w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?resize=768%2C447&amp;ssl=1 768w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?resize=1536%2C895&amp;ssl=1 1536w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?resize=2048%2C1193&amp;ssl=1 2048w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?resize=1140%2C664&amp;ssl=1 1140w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/imageonline-co-invertedimage-2-1.png?w=2880&amp;ssl=1 2880w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/figure><\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table class=\"has-background has-fixed-layout\" style=\"background-color:#ffffff00\"><thead><tr><th> LAW OF CONTRADICTION <\/th><th> LAW OF EXCLUDED MIDDLE <\/th><\/tr><\/thead><tbody><tr><td> <em>A<\/em> \u2229 <em>A<\/em>&#8216; = <em>\u03d5<\/em> <\/td><td> <em>A<\/em> \u222a <em>A<\/em>&#8216; = <em>X<\/em> <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table is-style-regular\"><table><thead><tr><th><span style=\"text-decoration: underline;\">OPERATION<\/span><\/th><th><span style=\"text-decoration: underline;\">CRISP RELATION<\/span><\/th><th><span style=\"text-decoration: underline;\">FUZZY RELATION<\/span><\/th><\/tr><\/thead><tbody><tr><td>UNION<\/td><td>X <sub>A\u222aB<\/sub> (x, y) : X <sub>A\u222aB<\/sub> (x, y) <br>= max [ X <sub>A<\/sub> (x, y) ,  X <sub>B<\/sub> (x, y) ] <\/td><td> \u03bc <em><sub>A<\/sub><\/em><sub>\u222a<em>B<\/em><\/sub> (x, y) = max ( \u03bc <em><sub>A<\/sub><\/em> (x, y) ,  \u03bc <sub><em>B<\/em><\/sub> (x, y)) <\/td><\/tr><tr><td>INTERSECTION<\/td><td> X <sub>A\u2229B<\/sub> (x, y) : X <sub>A\u2229B<\/sub> (x, y)<br>= min [ X <sub>A<\/sub> (x, y) ,  X <sub>B<\/sub> (x, y) ]<\/td><td> \u03bc <em><sub>A<\/sub><\/em><sub>\u2229<em>B<\/em><\/sub> (x, y) = min ( \u03bc <em><sub>A<\/sub><\/em> (x, y) ,  \u03bc <sub><em>B<\/em><\/sub> (x, y))<\/td><\/tr><tr><td>COMPLEMENT<\/td><td> X <sub>A&#8217;<\/sub> (x, y) : X <sub>A&#8217;<\/sub> (x, y) <br>= 1 &#8211;  X <sub>A<\/sub> (x, y) <\/td><td> \u03bc <em><sub>A<\/sub><\/em><sub>&#8216;<\/sub> (x, y) = 1 &#8211;  \u03bc <em><sub>A<\/sub><\/em> (x, y) <\/td><\/tr><tr><td>CONTAINMENT<\/td><td> X <sub>A<\/sub> (x, y) : X <sub>A<\/sub> (x, y) <strong>\u2264<\/strong> X <sub>B<\/sub> (x, y) <\/td><td> <em>A<\/em> \u2286 <em>B<\/em> \u2192  \u03bc <em><sub>A<\/sub><\/em> (x) <strong>\u2264<\/strong>  \u03bc <em><sub><em>B<\/em><\/sub><\/em> (x) <\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-cover alignfull is-light is-position-center-center\" style=\"min-height:900px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-0 has-background-dim has-background-gradient\" style=\"background:linear-gradient(135deg,rgb(255,255,255) 0%,rgb(31,1,56) 100%)\"><\/span><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\"><div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"960\" height=\"505\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?resize=960%2C505&#038;ssl=1\" alt=\"membership function basic\" class=\"wp-image-2845\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?resize=1024%2C539&amp;ssl=1 1024w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?resize=300%2C158&amp;ssl=1 300w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?resize=768%2C404&amp;ssl=1 768w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?resize=1536%2C809&amp;ssl=1 1536w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?resize=2048%2C1078&amp;ssl=1 2048w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?resize=1140%2C600&amp;ssl=1 1140w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?w=1920&amp;ssl=1 1920w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/08\/2880px-Fuzzy_crisp.svg.png?w=2880&amp;ssl=1 2880w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\">MEMBERSHIP FUNCTION<\/h2>\n\n\n\n<p>Membership functions represent&nbsp;fuzzy subsets&nbsp;of&nbsp;<em>X<\/em>. The membership function which represents a fuzzy set <em>A<\/em>&nbsp;is usually denoted by \u03bc <em><sub>A<\/sub><\/em>.&nbsp;For an element&nbsp;<em>x<\/em> of&nbsp;<em>X<\/em>, the value&nbsp; \u03bc <em><sub>A<\/sub><\/em> (x) &nbsp;is called the&nbsp;<em>membership degree<\/em>&nbsp;of&nbsp;<em>x<\/em>&nbsp;in the fuzzy set&nbsp;<em>A<\/em>&nbsp;The membership degree  \u03bc <em><sub>A<\/sub><\/em> (x) &nbsp;quantifies the grade of membership of the element&nbsp;<em>x<\/em>&nbsp;to the fuzzy set&nbsp;<em>A<\/em>.&nbsp;The value 0 means that&nbsp;<em>x<\/em>&nbsp;is not a member of the fuzzy set; the value 1 means that&nbsp; <em>x<\/em>&nbsp; is fully a member of the fuzzy set. The values between 0 and 1 characterize fuzzy members, which belong to the fuzzy set only partially.<\/p>\n\n\n\n<p>Since all information contained in a fuzzy set is described by its membership function, it is useful to develop a lexicon of terms to describe various special features of this function. For purposes of simplicity, the functions shown in the following figures will all be continuous, but the terms apply equally for both discrete and continuous fuzzy sets.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"610\" height=\"310\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/pr-7-2-edited.png?resize=610%2C310&#038;ssl=1\" alt=\"core, support and boundary\" class=\"wp-image-2852\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/pr-7-2-edited.png?w=610&amp;ssl=1 610w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/pr-7-2-edited.png?resize=300%2C152&amp;ssl=1 300w\" sizes=\"(max-width: 610px) 100vw, 610px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\"><li>The core of a membership function for some fuzzy set <em>A<\/em> is defined as that region of the universe that is characterized by complete and full membership in the set <em>A<\/em>. That is, the core comprises those elements x of the universe such that \u03bc<em><sub>A<\/sub><\/em>(x) = 1.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li>The support of a membership function for some fuzzy set <em>A<\/em> is defined as that region of the universe that is characterized by nonzero membership in the set <em>A<\/em>. That is, the support comprises those elements x of the universe such that \u03bc<em><sub>A<\/sub><\/em>(x) &gt; 0.<\/li><\/ul>\n\n\n\n<p><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-cover alignfull is-light\" style=\"min-height:950px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-0 has-background-dim has-background-gradient\" style=\"background:linear-gradient(135deg,rgb(0,0,0) 0%,rgb(155,81,224) 100%)\"><\/span><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<h2 class=\"wp-block-heading\">Implementing a Linguistic<\/h2>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide\"\/>\n\n\n\n<p>Control strategy sensors for the crane head position\u00a0<code>Distance\u00a0<\/code>and the\u00a0<code>angle\u00a0<\/code>of the container sway\u00a0<code>Angle\u00a0<\/code>are employed to automate the control of this crane. Using these inputs to describe the current condition of the crane, for example,<\/p>\n\n\n\n<pre id=\"pre408747\" class=\"wp-block-preformatted\">IF Distance = medium AND Angle = neg_small THEN Power = pos_high <\/pre>\n\n\n\n<p>The figure below shows the complete structure of a fuzzy logic controller:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted has-normal-font-size\">\/\/CODE SAMPLE\n\n\/\/Fuzzy function to produce optimized power\npublic double fuzzy()\n{\n\/\/Fuzzification of variables, distance and angle\n\nif((angle&lt;-60)&amp;&amp;(angle&gt;=-90))\nneg_small=0;\nelse if((angle&lt;-10)&amp;&amp;(angle&gt;=-60))\nneg_small=(0.02*angle+1.2);\nelse if((angle&lt;0)&amp;&amp;(angle&gt;=-10))\nneg_small=(-0.1*angle);\nelse if((angle&lt;=90)&amp;&amp;(angle&gt;=0))\nneg_small=0;\nif((angle&lt;-60)&amp;&amp;(angle&gt;=-90))\nneg_big=1;\nelse if((angle&gt;=-60)&amp;&amp;(angle&lt;-10))\nneg_big=(-0.02*angle-0.2);\nelse if((angle&gt;=-10)&amp;&amp;(angle&lt;=90))\nneg_big=0;\nif((distance&lt;5)&amp;&amp;(distance&gt;=-10))\nmedium=0;\nelse if((distance&lt;10)&amp;&amp;(distance&gt;=5))\nmedium=(0.2*distance-1);\nelse if((distance&lt;22)&amp;&amp;(distance&gt;=10))\nmedium=((-1\/12)*distance+(11\/6));\nelse if((distance&lt;=30)&amp;&amp;(distance&gt;=22))\nmedium=0;\nif((distance&lt;10)&amp;&amp;(distance&gt;=-10))\nfar=0;\nelse if((distance&lt;22)&amp;&amp;(distance&gt;=10))\nfar=((1\/12)*distance-(5\/6));\nelse if((distance&lt;=30)&amp;&amp;(distance&gt;=22))\nfar=1;\n\/\/... other if_ then_else clauses for other terms of  distance and angle to be\n\/\/ continued .\n\n\/\/Defuzzification of variable, power\nreturn \nSystem.Math.Round(System.Math.Max(System.Math.Min(pos_small,zerodis),\n    System.Math.Min(pos_small,close))*neg_medium_pow+System.Math.Max(\n    System.Math.Min(zero,zerodis),System.Math.Min(zero,close))*zero_pow+System.Math.Max(\n    System.Math.Max(System.Math.Min(neg_small,close),System.Math.Min(neg_big,medium)),\n    System.Math.Min(zero,far))*pos_medium_pow+System.Math.Max(System.Math.Min(neg_small,\n    medium),System.Math.Min(neg_small,far))*pos_high_pow,2);\n}<\/pre>\n\n\n\n<div class=\"wp-block-columns alignwide are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:52%\">\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-outline is-style-outline--1\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/www.codeproject.com\/Articles\/23387\/Introduction-to-C-and-Fuzzy-Logic\" target=\"_blank\" rel=\"noreferrer noopener\">FOR THE ENTIRE ARTICLE<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:48%\">\n<figure class=\"wp-block-image size-large is-resized\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/image.png?resize=461%2C190&#038;ssl=1\" alt=\"\" class=\"wp-image-2856\" width=\"461\" height=\"190\" srcset=\"https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/image.png?resize=1024%2C422&amp;ssl=1 1024w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/image.png?resize=300%2C124&amp;ssl=1 300w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/image.png?resize=768%2C317&amp;ssl=1 768w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/image.png?resize=1536%2C633&amp;ssl=1 1536w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/image.png?resize=1140%2C470&amp;ssl=1 1140w, https:\/\/i0.wp.com\/soulofmathematics.com\/wp-content\/uploads\/2021\/09\/image.png?w=1616&amp;ssl=1 1616w\" sizes=\"(max-width: 461px) 100vw, 461px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"class_list":["post-2769","page","type-page","status-publish","hentry"],"ams_acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v23.6 - 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