{"id":141,"date":"2025-01-17T17:24:14","date_gmt":"2025-01-17T16:24:14","guid":{"rendered":"https:\/\/home.agh.edu.pl\/~kkulak\/?page_id=141"},"modified":"2025-01-17T17:29:10","modified_gmt":"2025-01-17T16:29:10","slug":"book-erratum","status":"publish","type":"page","link":"https:\/\/home.agh.edu.pl\/~kkulak\/book-erratum\/","title":{"rendered":"Book erratum"},"content":{"rendered":"\n<html>\n<style type='text\/css'>\n\/* LyX Provided Styles *\/\ndiv.bibtexentry { margin-left: 2em; text-indent: -2em; }\nspan.bibtexlabel:before{ content: \"[\"; }\nspan.bibtexlabel:after{ content: \"] \"; }\n\n\/* Layout-provided Styles *\/\nh1.title {\nfont-size: x-large;\nmargin-bottom: 1ex;\ntext-align: center;\n\n}\ndiv.author {\nfont-size: large;\nmargin-top: 1.3ex;\nmargin-bottom: 0.7ex;\ntext-align: center;\n\n}\ndiv.abstract {\nfont-size: small;\nmargin-top: 0.7ex;\nmargin-bottom: 0.7ex;\nmargin-left: 3ex;\nmargin-right: 3ex;\ntext-align: left;\n\n}\nspan.abstract_label {\nfont-weight: bold;\nfont-size: large;\ntext-align: center;\n\n}\n\ndiv.abstract {\n\tmargin: 4ex;\n}\ndiv.abstract_item {\n\tfont-size: small;\n\tpadding-top: 1ex;\n}\ndiv.abstract_label {\n\tfont-weight: bold;\n}\nh4.subsubsection_ {\nfont-weight: bold;\nfont-size: medium;\nmargin-top: 0.7ex;\nmargin-bottom: 0.4ex;\ntext-align: left;\n\n}\ndiv.standard {\n\tmargin-bottom: 2ex;\n}\ndiv.example {\ntext-align: left;\n\n}\n\n\n<\/style>\n<\/head>\n<body dir=\"auto\">\n<h1 class=\"title\" id='magicparlabel-45838'>Book Erratum\n<br \/>\n\nUnderstanding The Analytic Hierarchy Process<\/h1>\n<div class=\"author\" id='magicparlabel-45839'>Konrad Ku\u0142akowski<\/div>\n\n<div class=\"abstract\" id='magicparlabel-45840'><span class=\"abstract_label\">Abstract<\/span>\n<div class=\"abstract_item\">Errors found in the book Understanding The Analytic Hierarchy Process [<a href='#LyXCite-Kulakowski2020utahp'><span class=\"bib-label\">1<\/span><\/a>] <\/div>\n<\/div>\n<h4 class=\"subsubsection_\" id='magicparlabel-45841'>Page 40, line 3 from the top<\/h4>\n<div class=\"standard\" id='magicparlabel-45842'><b><div style='height:5ex'><\/div><em>is<\/em><\/b> <\/div>\n\n<div class=\"standard\" id='magicparlabel-45843'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <msub>\n    <mrow><mi>n<\/mi>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>i<\/mi><mi>j<\/mi>\n     <\/mrow>\n    <\/mrow>\n   <\/msub><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true'>{<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>0<\/mn>\n     <\/mtd>\n     <mtd>\n      <mrow>\n       <mstyle mathvariant='normal'>\n        <mrow><mi>i<\/mi><mi>f<\/mi>\n        <\/mrow>\n       <\/mstyle><mspace width=\"6px\" \/><mspace width=\"6px\" \/><mi>i<\/mi><mo>=<\/mo><mi>j<\/mi><mspace width=\"6px\" \/><mspace width=\"6px\" \/>\n       <mstyle mathvariant='normal'>\n        <mrow><mi>o<\/mi><mi>r<\/mi>\n        <\/mrow>\n       <\/mstyle><mspace width=\"6px\" \/><mspace width=\"6px\" \/>{\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow><mi>i<\/mi>\n        <\/mrow>\n       <\/msub><mo>,<\/mo>\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow><mi>j<\/mi>\n        <\/mrow>\n       <\/msub>}<mo> &isin; <\/mo><mi>E<\/mi>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <mrow>\n       <mstyle mathvariant='normal'>\n        <mrow><mi>i<\/mi><mi>f<\/mi>\n        <\/mrow>\n       <\/mstyle><mspace width=\"6px\" \/><mspace width=\"6px\" \/><mi>i<\/mi><mo> &ne; <\/mo><mi>j<\/mi><mspace width=\"6px\" \/><mspace width=\"6px\" \/>\n       <mstyle mathvariant='normal'>\n        <mrow><mi>a<\/mi><mi>n<\/mi><mi>d<\/mi>\n        <\/mrow>\n       <\/mstyle><mspace width=\"6px\" \/><mspace width=\"6px\" \/>{\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow><mi>i<\/mi>\n        <\/mrow>\n       <\/msub><mo>,<\/mo>\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow><mi>j<\/mi>\n        <\/mrow>\n       <\/msub>}<mo> &notin; <\/mo><mi>E<\/mi>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable>\n  <\/mrow>\n <\/mrow><\/math><em><b>should be<\/b> <\/em><\/div>\n\n<div class=\"standard\" id='magicparlabel-45844'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <msub>\n    <mrow><mi>n<\/mi>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>i<\/mi><mi>j<\/mi>\n     <\/mrow>\n    <\/mrow>\n   <\/msub><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true'>{<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>0<\/mn>\n     <\/mtd>\n     <mtd>\n      <mrow>\n       <mstyle mathvariant='normal'>\n        <mrow><mi>i<\/mi><mi>f<\/mi>\n        <\/mrow>\n       <\/mstyle><mspace width=\"6px\" \/><mspace width=\"6px\" \/><mi>i<\/mi><mo>=<\/mo><mi>j<\/mi><mspace width=\"6px\" \/><mspace width=\"6px\" \/>\n       <mstyle mathvariant='normal'>\n        <mrow><mi>o<\/mi><mi>r<\/mi>\n        <\/mrow>\n       <\/mstyle><mspace width=\"6px\" \/><mspace width=\"6px\" \/>{\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow><mi>i<\/mi>\n        <\/mrow>\n       <\/msub><mo>,<\/mo>\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow><mi>j<\/mi>\n        <\/mrow>\n       <\/msub>}<mo> &notin; <\/mo><mi>E<\/mi>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <mrow>\n       <mstyle mathvariant='normal'>\n        <mrow><mi>i<\/mi><mi>f<\/mi>\n        <\/mrow>\n       <\/mstyle><mspace width=\"6px\" \/><mspace width=\"6px\" \/><mi>i<\/mi><mo> &ne; <\/mo><mi>j<\/mi><mspace width=\"6px\" \/><mspace width=\"6px\" \/>\n       <mstyle mathvariant='normal'>\n        <mrow><mi>a<\/mi><mi>n<\/mi><mi>d<\/mi>\n        <\/mrow>\n       <\/mstyle><mspace width=\"6px\" \/><mspace width=\"6px\" \/>{\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow><mi>i<\/mi>\n        <\/mrow>\n       <\/msub><mo>,<\/mo>\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow><mi>j<\/mi>\n        <\/mrow>\n       <\/msub>}<mo> &isin; <\/mo><mi>E<\/mi>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n<h4 class=\"subsubsection_\" id='magicparlabel-45845'>Page 75, the numerical example is faulty. The correct version is: <\/h4>\n<div class=\"standard\" id='magicparlabel-45846'><b><div style='height:5ex'><\/div><\/b><\/div>\n\n<div class=\"example\" id='magicparlabel-45847'>and the constant term vector <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow><mi>r<\/mi>\n <\/mrow><\/math> is given as<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>r<\/mi><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd>\n      <mrow><mo> ln <\/mo><mn>6<\/mn>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow><mo> ln <\/mo>\n       <mfrac>\n        <mrow><mn>21<\/mn>\n        <\/mrow>\n        <mrow><mn>8<\/mn>\n        <\/mrow>\n       <\/mfrac>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow><mo>&#8211;<\/mo><mo> ln <\/mo><mn>3<\/mn>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow><mo> ln <\/mo>\n       <mfrac>\n        <mrow><mn>36<\/mn>\n        <\/mrow>\n        <mrow><mn>7<\/mn>\n        <\/mrow>\n       <\/mfrac>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow><mo>&#8211;<\/mo><mo> ln <\/mo><mn>27<\/mn>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo><mn>.<\/mn>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n\n<div class=\"example\" id='magicparlabel-45848'>Solving <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>G<\/mi>\n   <mover>\n    <mrow><mi>w<\/mi>\n    <\/mrow><mo stretchy=\"true\">&Hat;<\/mo>\n   <\/mover><mo>=<\/mo><mi>r<\/mi>\n  <\/mrow>\n <\/mrow><\/math> leads to the following logarithmized ranking vector<\/div>\n\n\n\n<div class=\"example\" id='magicparlabel-45855'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <mover>\n    <mrow><mi>w<\/mi>\n    <\/mrow><mo stretchy=\"true\">&Hat;<\/mo>\n   <\/mover><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd>\n      <mrow>\n       <mfrac>\n        <mrow><mn>1<\/mn>\n        <\/mrow>\n        <mrow><mn>100<\/mn>\n        <\/mrow>\n       <\/mfrac><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n       <mrow><mn>22<\/mn><mo> ln <\/mo><mn>3<\/mn><mo>+<\/mo><mn>43<\/mn><mo> ln <\/mo><mn>6<\/mn><mo>+<\/mo><mn>2<\/mn><mo> ln <\/mo><mn>27<\/mn><mo>&#8211;<\/mo><mn>7<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>36<\/mn>\n         <\/mrow>\n         <mrow><mn>7<\/mn>\n         <\/mrow>\n        <\/mfrac><mo>+<\/mo><mn>8<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>21<\/mn>\n         <\/mrow>\n         <mrow><mn>8<\/mn>\n         <\/mrow>\n        <\/mfrac>\n       <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow>\n       <mfrac>\n        <mrow><mn>1<\/mn>\n        <\/mrow>\n        <mrow><mn>25<\/mn>\n        <\/mrow>\n       <\/mfrac><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n       <mrow><mn>8<\/mn><mo> ln <\/mo><mn>3<\/mn><mo>+<\/mo><mn>2<\/mn><mo> ln <\/mo><mn>6<\/mn><mo>+<\/mo><mn>3<\/mn><mo> ln <\/mo><mn>27<\/mn><mo>+<\/mo><mn>2<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>36<\/mn>\n         <\/mrow>\n         <mrow><mn>7<\/mn>\n         <\/mrow>\n        <\/mfrac><mo>+<\/mo><mn>12<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>21<\/mn>\n         <\/mrow>\n         <mrow><mn>8<\/mn>\n         <\/mrow>\n        <\/mfrac>\n       <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow>\n       <mfrac>\n        <mrow><mn>1<\/mn>\n        <\/mrow>\n        <mrow><mn>100<\/mn>\n        <\/mrow>\n       <\/mfrac><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n       <mrow><mn>22<\/mn><mo> ln <\/mo><mn>3<\/mn><mo>&#8211;<\/mo><mn>7<\/mn><mo> ln <\/mo><mn>6<\/mn><mo>+<\/mo><mn>2<\/mn><mo> ln <\/mo><mn>27<\/mn><mo>+<\/mo><mn>43<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>36<\/mn>\n         <\/mrow>\n         <mrow><mn>7<\/mn>\n         <\/mrow>\n        <\/mfrac><mo>+<\/mo><mn>8<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>21<\/mn>\n         <\/mrow>\n         <mrow><mn>8<\/mn>\n         <\/mrow>\n        <\/mfrac>\n       <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow>\n       <mfrac>\n        <mrow><mn>1<\/mn>\n        <\/mrow>\n        <mrow><mn>100<\/mn>\n        <\/mrow>\n       <\/mfrac><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n       <mrow><mn>22<\/mn><mo> ln <\/mo><mn>3<\/mn><mo>&#8211;<\/mo><mn>7<\/mn><mo> ln <\/mo><mn>6<\/mn><mo>+<\/mo><mn>2<\/mn><mo> ln <\/mo><mn>27<\/mn><mo>+<\/mo><mn>43<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>36<\/mn>\n         <\/mrow>\n         <mrow><mn>7<\/mn>\n         <\/mrow>\n        <\/mfrac><mo>+<\/mo><mn>8<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>21<\/mn>\n         <\/mrow>\n         <mrow><mn>8<\/mn>\n         <\/mrow>\n        <\/mfrac>\n       <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow>\n       <mfrac>\n        <mrow><mn>1<\/mn>\n        <\/mrow>\n        <mrow><mn>50<\/mn>\n        <\/mrow>\n       <\/mfrac><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n       <mrow><mo>&#8211;<\/mo><mn>4<\/mn><mo> ln <\/mo><mn>3<\/mn><mo>&#8211;<\/mo><mo> ln <\/mo><mn>6<\/mn><mo>&#8211;<\/mo><mn>14<\/mn><mo> ln <\/mo><mn>27<\/mn><mo>&#8211;<\/mo><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>36<\/mn>\n         <\/mrow>\n         <mrow><mn>7<\/mn>\n         <\/mrow>\n        <\/mfrac><mo>&#8211;<\/mo><mn>6<\/mn><mo> ln <\/mo>\n        <mfrac>\n         <mrow><mn>21<\/mn>\n         <\/mrow>\n         <mrow><mn>8<\/mn>\n         <\/mrow>\n        <\/mfrac>\n       <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>1.04<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>1.484<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow><mo>&#8211;<\/mo><mn>2.29<\/mn>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>0.963<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow><mo>&#8211;<\/mo><mn>1.19<\/mn>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo><mn>.<\/mn>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n\n\n\n<div class=\"example\" id='magicparlabel-45861'>Hence, the (unscaled) ranking vector is <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>w<\/mi><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd>\n      <msup>\n       <mrow><mi>e<\/mi>\n       <\/mrow>\n       <mrow><mn>1.04064<\/mn>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <msup>\n       <mrow><mi>e<\/mi>\n       <\/mrow>\n       <mrow><mn>1.48464<\/mn>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <msup>\n       <mrow><mi>e<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mo>&#8211;<\/mo><mn>2.2937<\/mn>\n        <\/mrow>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <msup>\n       <mrow><mi>e<\/mi>\n       <\/mrow>\n       <mrow><mn>0.96356<\/mn>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <msup>\n       <mrow><mi>e<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mo>&#8211;<\/mo><mn>1.19512<\/mn>\n        <\/mrow>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>2.83103<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>4.4134<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>0.100889<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>2.62103<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>0.302668<\/mn>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo><mn>.<\/mn>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n\n<div class=\"example\" id='magicparlabel-45862'>The last step to receive the ranking in the usual form is scaling so that the entries of the ranking vector sum up to <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow><mn>1<\/mn>\n <\/mrow><\/math>. The final form of the ranking vector is as follows: <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <msub>\n    <mrow><mi>w<\/mi>\n    <\/mrow>\n    <mrow>\n     <mstyle mathvariant='italic'>\n      <mrow><mi>g<\/mi><mi>m<\/mi>\n      <\/mrow>\n     <\/mstyle>\n    <\/mrow>\n   <\/msub><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>0.275<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>0.429<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>0.0098<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>0.255<\/mn>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd><mn>0.0294<\/mn>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo><mn>.<\/mn>\n  <\/mrow>\n <\/mrow><\/math>According to the computed ranking, the most preferred alternative is <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <msub>\n   <mrow><mi>a<\/mi>\n   <\/mrow>\n   <mrow><mn>1<\/mn>\n   <\/mrow>\n  <\/msub>\n <\/mrow><\/math> with the ranking value <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>w<\/mi><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n   <msub>\n    <mrow><mi>a<\/mi>\n    <\/mrow>\n    <mrow><mn>2<\/mn>\n    <\/mrow>\n   <\/msub>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n<mo>=<\/mo><mn>0.429<\/mn>\n  <\/mrow>\n <\/mrow><\/math>. The second place is taken by <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <msub>\n   <mrow><mi>a<\/mi>\n   <\/mrow>\n   <mrow><mn>4<\/mn>\n   <\/mrow>\n  <\/msub>\n <\/mrow><\/math> with <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>w<\/mi><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n   <msub>\n    <mrow><mi>a<\/mi>\n    <\/mrow>\n    <mrow><mn>1<\/mn>\n    <\/mrow>\n   <\/msub>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n<mo>=<\/mo><mn>0.275<\/mn>\n  <\/mrow>\n <\/mrow><\/math>, then <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <msub>\n    <mrow><mi>a<\/mi>\n    <\/mrow>\n    <mrow><mn>4<\/mn>\n    <\/mrow>\n   <\/msub><mo>,<\/mo>\n   <msub>\n    <mrow><mi>a<\/mi>\n    <\/mrow>\n    <mrow><mn>5<\/mn>\n    <\/mrow>\n   <\/msub>\n  <\/mrow>\n <\/mrow><\/math> and <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <msub>\n   <mrow><mi>a<\/mi>\n   <\/mrow>\n   <mrow><mn>3<\/mn>\n   <\/mrow>\n  <\/msub>\n <\/mrow><\/math>.<\/div>\n\n<div class=\"example\" id='magicparlabel-45863'>Of course, one may verify that GMM applied to the following matrix <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n  <mtable>\n   <mtr>\n    <mtd><mn>1<\/mn>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>2<\/mn>\n      <\/mrow>\n      <mrow><mn>3<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.275<\/mn>\n      <\/mrow>\n      <mrow><mn>0.0098<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.275<\/mn>\n      <\/mrow>\n      <mrow><mn>0.255<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd><mn>9<\/mn>\n    <\/mtd>\n   <\/mtr>\n   <mtr>\n    <mtd>\n     <mfrac>\n      <mrow><mn>3<\/mn>\n      <\/mrow>\n      <mrow><mn>2<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd><mn>1<\/mn>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.429<\/mn>\n      <\/mrow>\n      <mrow><mn>0.0098<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>7<\/mn>\n      <\/mrow>\n      <mrow><mn>4<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.429<\/mn>\n      <\/mrow>\n      <mrow><mn>0.0294<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n   <\/mtr>\n   <mtr>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.0098<\/mn>\n      <\/mrow>\n      <mrow><mn>0.275<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.0098<\/mn>\n      <\/mrow>\n      <mrow><mn>0.429<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd><mn>1<\/mn>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.0098<\/mn>\n      <\/mrow>\n      <mrow><mn>0.255<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>1<\/mn>\n      <\/mrow>\n      <mrow><mn>3<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n   <\/mtr>\n   <mtr>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.255<\/mn>\n      <\/mrow>\n      <mrow><mn>0.275<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>4<\/mn>\n      <\/mrow>\n      <mrow><mn>7<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.255<\/mn>\n      <\/mrow>\n      <mrow><mn>0.0098<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd><mn>1<\/mn>\n    <\/mtd>\n    <mtd><mn>9<\/mn>\n    <\/mtd>\n   <\/mtr>\n   <mtr>\n    <mtd>\n     <mfrac>\n      <mrow><mn>1<\/mn>\n      <\/mrow>\n      <mrow><mn>9<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>0.0294<\/mn>\n      <\/mrow>\n      <mrow><mn>0.429<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd><mn>3<\/mn>\n    <\/mtd>\n    <mtd>\n     <mfrac>\n      <mrow><mn>1<\/mn>\n      <\/mrow>\n      <mrow><mn>9<\/mn>\n      <\/mrow>\n     <\/mfrac>\n    <\/mtd>\n    <mtd><mn>1<\/mn>\n    <\/mtd>\n   <\/mtr>\n  <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo>\n <\/mrow><\/math>results in <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <msub>\n   <mrow><mi>w<\/mi>\n   <\/mrow>\n   <mrow>\n    <mstyle mathvariant='italic'>\n     <mrow><mi>g<\/mi><mi>m<\/mi>\n     <\/mrow>\n    <\/mstyle>\n   <\/mrow>\n  <\/msub>\n <\/mrow><\/math>.<\/div>\n<h4 class=\"subsubsection_\" id='magicparlabel-45864'>Page 80, line 1 from the top <\/h4>\n<div class=\"standard\" id='magicparlabel-45865'><em><b>is<\/b><\/em><\/div>\n\n<div class=\"standard\" id='magicparlabel-45866'>where <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <msub>\n   <mrow><mi>p<\/mi>\n   <\/mrow>\n   <mrow><mi>i<\/mi>\n   <\/mrow>\n  <\/msub>\n <\/mrow><\/math> is the number of existing comparisons in the i-th row of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow><mi>C<\/mi>\n <\/mrow><\/math>,<\/div>\n\n<div class=\"standard\" id='magicparlabel-45867'><em><b>should be <\/b><\/em><\/div>\n\n<div class=\"standard\" id='magicparlabel-45868'>where <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <msub>\n   <mrow><mi>p<\/mi>\n   <\/mrow>\n   <mrow><mi>i<\/mi>\n   <\/mrow>\n  <\/msub>\n <\/mrow><\/math> is the number of existing comparisons in the i-th row of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow><mi>C<\/mi>\n <\/mrow><\/math> except the diagonal<\/div>\n<h4 class=\"subsubsection_\" id='magicparlabel-45869'>Page 81, line 12 from the bottom<\/h4>\n<div class=\"standard\" id='magicparlabel-45870'><b><div style='height:5ex'><\/div><em>is<\/em><\/b><\/div>\n\n<div class=\"standard\" id='magicparlabel-45871'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <msub>\n    <mrow><mi>q<\/mi>\n    <\/mrow>\n    <mrow><mn>3<\/mn>\n    <\/mrow>\n   <\/msub><mo>=<\/mo>\n   <msubsup>\n    <mrow><mo> &sum; <\/mo>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn>\n     <\/mrow>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>n<\/mi><mo>&#8211;<\/mo><mn>2<\/mn>\n     <\/mrow>\n    <\/mrow>\n   <\/msubsup>\n   <msubsup>\n    <mrow><mo> &sum; <\/mo>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>j<\/mi><mo>=<\/mo><mi>i<\/mi><mo>+<\/mo><mn>1<\/mn>\n     <\/mrow>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>n<\/mi><mo>&#8211;<\/mo><mn>1<\/mn>\n     <\/mrow>\n    <\/mrow>\n   <\/msubsup>\n   <msubsup>\n    <mrow><mo> &sum; <\/mo>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>k<\/mi><mo>=<\/mo><mi>j<\/mi><mo>+<\/mo><mn>1<\/mn>\n     <\/mrow>\n    <\/mrow>\n    <mrow><mi>n<\/mi>\n    <\/mrow>\n   <\/msubsup><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n   <mrow><mn>2<\/mn><mo>&#8211;<\/mo>\n    <mfrac>\n     <mrow>\n      <msub>\n       <mrow><mi>a<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mrow>\n     <mrow>\n      <mrow>\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>i<\/mi><mi>j<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>j<\/mi><mi>k<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n      <\/mrow>\n     <\/mrow>\n    <\/mfrac><mo>&#8211;<\/mo>\n    <mfrac>\n     <mrow>\n      <mrow>\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>i<\/mi><mi>j<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n       <msub>\n        <mrow><mi>a<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>j<\/mi><mi>k<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n      <\/mrow>\n     <\/mrow>\n     <mrow>\n      <msub>\n       <mrow><mi>a<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mrow>\n    <\/mfrac>\n   <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n  <\/mrow>\n <\/mrow><\/math><em><b>should be<\/b><\/em><\/div>\n\n<div class=\"standard\" id='magicparlabel-45872'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <msub>\n    <mrow><mi>q<\/mi>\n    <\/mrow>\n    <mrow><mn>3<\/mn>\n    <\/mrow>\n   <\/msub><mo>=<\/mo>\n   <msubsup>\n    <mrow><mo> &sum; <\/mo>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn>\n     <\/mrow>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>n<\/mi><mo>&#8211;<\/mo><mn>2<\/mn>\n     <\/mrow>\n    <\/mrow>\n   <\/msubsup>\n   <msubsup>\n    <mrow><mo> &sum; <\/mo>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>j<\/mi><mo>=<\/mo><mi>i<\/mi><mo>+<\/mo><mn>1<\/mn>\n     <\/mrow>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>n<\/mi><mo>&#8211;<\/mo><mn>1<\/mn>\n     <\/mrow>\n    <\/mrow>\n   <\/msubsup>\n   <msubsup>\n    <mrow><mo> &sum; <\/mo>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>k<\/mi><mo>=<\/mo><mi>j<\/mi><mo>+<\/mo><mn>1<\/mn>\n     <\/mrow>\n    <\/mrow>\n    <mrow><mi>n<\/mi>\n    <\/mrow>\n   <\/msubsup><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n   <mrow><mn>2<\/mn><mo>&#8211;<\/mo>\n    <mfrac>\n     <mrow>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mrow>\n     <mrow>\n      <mrow>\n       <msub>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>i<\/mi><mi>j<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n       <msub>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>j<\/mi><mi>k<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n      <\/mrow>\n     <\/mrow>\n    <\/mfrac><mo>&#8211;<\/mo>\n    <mfrac>\n     <mrow>\n      <mrow>\n       <msub>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>i<\/mi><mi>j<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n       <msub>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>j<\/mi><mi>k<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n      <\/mrow>\n     <\/mrow>\n     <mrow>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mrow>\n    <\/mfrac>\n   <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n  <\/mrow>\n <\/mrow><\/math><\/div>\n<h4 class=\"subsubsection_\" id='magicparlabel-45873'>Page 113, line 14 from the bottom <\/h4>\n<div class=\"standard\" id='magicparlabel-45874'><b><div style='height:5ex'><\/div><em>is<\/em><\/b><\/div>\n\n<div class=\"standard\" id='magicparlabel-45875'>6.3.8.1 Effectiveness of the Koczkodaj index\n<br \/>\n\n<\/div>\n\n<div class=\"standard\" style='text-align: left;' id='magicparlabel-45876'><em><b>should be<\/b><\/em><\/div>\n\n<div class=\"standard\" id='magicparlabel-45877'>6.3.8.1 Effectiveness and the Koczkodaj index\n<br \/>\n\n<\/div>\n<h4 class=\"subsubsection_\" id='magicparlabel-45878'>Page 123, line 5 from the top<\/h4>\n<div class=\"standard\" id='magicparlabel-45879'><em><b>is<\/b><\/em><\/div>\n\n<div class=\"standard\" id='magicparlabel-45880'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <msub>\n    <mrow><mi>T<\/mi>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>i<\/mi><mi>j<\/mi><mi>k<\/mi>\n     <\/mrow>\n    <\/mrow>\n   <\/msub><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>j<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mtd>\n     <mtd>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow><mn>1<\/mn><mo>\/<\/mo>\n       <msub>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>i<\/mi><mi>j<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n      <\/mrow>\n     <\/mtd>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>k<\/mi><mi>j<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mtd>\n     <mtd>\n      <mrow><mn>1<\/mn><mo>\/<\/mo>\n       <msub>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>k<\/mi><mi>j<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n      <\/mrow>\n     <\/mtd>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo>\n  <\/mrow>\n <\/mrow><\/math><em><b>should be<\/b><\/em> <math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow>\n   <msub>\n    <mrow><mi>T<\/mi>\n    <\/mrow>\n    <mrow>\n     <mrow><mi>i<\/mi><mi>j<\/mi><mi>k<\/mi>\n     <\/mrow>\n    <\/mrow>\n   <\/msub><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>j<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mtd>\n     <mtd>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow><mn>1<\/mn><mo>\/<\/mo>\n       <msub>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>i<\/mi><mi>j<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n      <\/mrow>\n     <\/mtd>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>j<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <msub>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mi>k<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msub>\n     <\/mtd>\n     <mtd>\n      <mrow><mn>1<\/mn><mo>\/<\/mo>\n       <msub>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>j<\/mi><mi>k<\/mi>\n         <\/mrow>\n        <\/mrow>\n       <\/msub>\n      <\/mrow>\n     <\/mtd>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n<h4 class=\"subsubsection_\" id='magicparlabel-45881'>Page 150, line 11 from the bottom<\/h4>\n<div class=\"standard\" id='magicparlabel-45882'><em><b>is<\/b><\/em> <\/div>\n\n<div class=\"standard\" id='magicparlabel-45883'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>C<\/mi><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <msup>\n       <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n        <mrow>\n         <msubsup>\n          <mrow><mo> &prod; <\/mo>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n           <\/mrow>\n          <\/mrow>\n          <mrow><mi>r<\/mi>\n          <\/mrow>\n         <\/msubsup>\n         <msubsup>\n          <mrow><mi>c<\/mi>\n          <\/mrow>\n          <mrow>\n           <mrow><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mi>q<\/mi>\n           <\/mrow>\n          <\/mrow>\n          <mrow>\n           <msub>\n            <mrow><mi> &eta; <\/mi>\n            <\/mrow>\n            <mrow><mi>q<\/mi>\n            <\/mrow>\n           <\/msub>\n          <\/mrow>\n         <\/msubsup>\n        <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n       <\/mrow>\n       <mrow>\n        <mrow><mn>1<\/mn><mo>\/<\/mo><mi>r<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <msup>\n       <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n        <mrow>\n         <msubsup>\n          <mrow><mo> &prod; <\/mo>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n           <\/mrow>\n          <\/mrow>\n          <mrow><mi>r<\/mi>\n          <\/mrow>\n         <\/msubsup>\n         <msubsup>\n          <mrow><mi>c<\/mi>\n          <\/mrow>\n          <mrow>\n           <mrow><mn>1<\/mn><mo>,<\/mo><mi>n<\/mi><mo>,<\/mo><mi>q<\/mi>\n           <\/mrow>\n          <\/mrow>\n          <mrow>\n           <msub>\n            <mrow><mi> &eta; <\/mi>\n            <\/mrow>\n            <mrow><mi>q<\/mi>\n            <\/mrow>\n           <\/msub>\n          <\/mrow>\n         <\/msubsup>\n        <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n       <\/mrow>\n       <mrow>\n        <mrow><mn>1<\/mn><mo>\/<\/mo><mi>r<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <msup>\n       <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n        <mrow>\n         <msubsup>\n          <mrow><mo> &prod; <\/mo>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n           <\/mrow>\n          <\/mrow>\n          <mrow><mi>r<\/mi>\n          <\/mrow>\n         <\/msubsup>\n         <msubsup>\n          <mrow><mi>c<\/mi>\n          <\/mrow>\n          <mrow>\n           <mrow><mn>2<\/mn><mo>,<\/mo><mn>1<\/mn><mo>,<\/mo><mi>q<\/mi>\n           <\/mrow>\n          <\/mrow>\n          <mrow>\n           <msub>\n            <mrow><mi> &eta; <\/mi>\n            <\/mrow>\n            <mrow><mi>q<\/mi>\n            <\/mrow>\n           <\/msub>\n          <\/mrow>\n         <\/msubsup>\n        <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n       <\/mrow>\n       <mrow>\n        <mrow><mn>1<\/mn><mo>\/<\/mo><mi>r<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mi>&vellip;\n      <\/mi>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mi>&vellip;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mi>&dtdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <msup>\n       <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n        <mrow>\n         <msubsup>\n          <mrow><mo> &prod; <\/mo>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n           <\/mrow>\n          <\/mrow>\n          <mrow><mi>r<\/mi>\n          <\/mrow>\n         <\/msubsup>\n         <msubsup>\n          <mrow><mi>c<\/mi>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>n<\/mi><mo>&#8211;<\/mo><mn>1.<\/mn><mi>n<\/mi><mo>,<\/mo><mi>q<\/mi>\n           <\/mrow>\n          <\/mrow>\n          <mrow>\n           <msub>\n            <mrow><mi> &eta; <\/mi>\n            <\/mrow>\n            <mrow><mi>q<\/mi>\n            <\/mrow>\n           <\/msub>\n          <\/mrow>\n         <\/msubsup>\n        <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n       <\/mrow>\n       <mrow>\n        <mrow><mn>1<\/mn><mo>\/<\/mo><mi>r<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <msup>\n       <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n        <mrow>\n         <msubsup>\n          <mrow><mo> &prod; <\/mo>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n           <\/mrow>\n          <\/mrow>\n          <mrow><mi>r<\/mi>\n          <\/mrow>\n         <\/msubsup>\n         <msubsup>\n          <mrow><mi>c<\/mi>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>n<\/mi><mo>,<\/mo><mn>1<\/mn><mo>,<\/mo><mi>q<\/mi>\n           <\/mrow>\n          <\/mrow>\n          <mrow>\n           <msub>\n            <mrow><mi> &eta; <\/mi>\n            <\/mrow>\n            <mrow><mi>q<\/mi>\n            <\/mrow>\n           <\/msub>\n          <\/mrow>\n         <\/msubsup>\n        <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n       <\/mrow>\n       <mrow>\n        <mrow><mn>1<\/mn><mo>\/<\/mo><mi>r<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msup>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo><mo>,<\/mo>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n\n<div class=\"standard\" id='magicparlabel-45884'><em><b>should be<\/b><\/em> <\/div>\n\n<div class=\"standard\" id='magicparlabel-45885'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>C<\/mi><mo>=<\/mo><mo form='prefix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>(<\/mo>\n   <mtable>\n    <mtr>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <mrow>\n       <msubsup>\n        <mrow><mo> &prod; <\/mo>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n         <\/mrow>\n        <\/mrow>\n        <mrow><mi>r<\/mi>\n        <\/mrow>\n       <\/msubsup>\n       <msubsup>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mn>1<\/mn><mo>,<\/mo><mn>2<\/mn><mo>,<\/mo><mi>q<\/mi>\n         <\/mrow>\n        <\/mrow>\n        <mrow>\n         <msub>\n          <mrow><mi> &eta; <\/mi>\n          <\/mrow>\n          <mrow><mi>q<\/mi>\n          <\/mrow>\n         <\/msub>\n        <\/mrow>\n       <\/msubsup>\n      <\/mrow>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mrow>\n       <msubsup>\n        <mrow><mo> &prod; <\/mo>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n         <\/mrow>\n        <\/mrow>\n        <mrow><mi>r<\/mi>\n        <\/mrow>\n       <\/msubsup>\n       <msubsup>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mn>1<\/mn><mo>,<\/mo><mi>n<\/mi><mo>,<\/mo><mi>q<\/mi>\n         <\/mrow>\n        <\/mrow>\n        <mrow>\n         <msub>\n          <mrow><mi> &eta; <\/mi>\n          <\/mrow>\n          <mrow><mi>q<\/mi>\n          <\/mrow>\n         <\/msub>\n        <\/mrow>\n       <\/msubsup>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow>\n       <msubsup>\n        <mrow><mo> &prod; <\/mo>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n         <\/mrow>\n        <\/mrow>\n        <mrow><mi>r<\/mi>\n        <\/mrow>\n       <\/msubsup>\n       <msubsup>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mn>2<\/mn><mo>,<\/mo><mn>1<\/mn><mo>,<\/mo><mi>q<\/mi>\n         <\/mrow>\n        <\/mrow>\n        <mrow>\n         <msub>\n          <mrow><mi> &eta; <\/mi>\n          <\/mrow>\n          <mrow><mi>q<\/mi>\n          <\/mrow>\n         <\/msub>\n        <\/mrow>\n       <\/msubsup>\n      <\/mrow>\n     <\/mtd>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mi>&vellip;\n      <\/mi>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mi>&vellip;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mi>&dtdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mrow>\n       <msubsup>\n        <mrow><mo> &prod; <\/mo>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n         <\/mrow>\n        <\/mrow>\n        <mrow><mi>r<\/mi>\n        <\/mrow>\n       <\/msubsup>\n       <msubsup>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>n<\/mi><mo>&#8211;<\/mo><mn>1.<\/mn><mi>n<\/mi><mo>,<\/mo><mi>q<\/mi>\n         <\/mrow>\n        <\/mrow>\n        <mrow>\n         <msub>\n          <mrow><mi> &eta; <\/mi>\n          <\/mrow>\n          <mrow><mi>q<\/mi>\n          <\/mrow>\n         <\/msub>\n        <\/mrow>\n       <\/msubsup>\n      <\/mrow>\n     <\/mtd>\n    <\/mtr>\n    <mtr>\n     <mtd>\n      <mrow>\n       <msubsup>\n        <mrow><mo> &prod; <\/mo>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n         <\/mrow>\n        <\/mrow>\n        <mrow><mi>r<\/mi>\n        <\/mrow>\n       <\/msubsup>\n       <msubsup>\n        <mrow><mi>c<\/mi>\n        <\/mrow>\n        <mrow>\n         <mrow><mi>n<\/mi><mo>,<\/mo><mn>1<\/mn><mo>,<\/mo><mi>q<\/mi>\n         <\/mrow>\n        <\/mrow>\n        <mrow>\n         <msub>\n          <mrow><mi> &eta; <\/mi>\n          <\/mrow>\n          <mrow><mi>q<\/mi>\n          <\/mrow>\n         <\/msub>\n        <\/mrow>\n       <\/msubsup>\n      <\/mrow>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd>\n      <mi>&ctdot;\n      <\/mi>\n     <\/mtd>\n     <mtd><mn>1<\/mn>\n     <\/mtd>\n    <\/mtr>\n   <\/mtable><mo form='postfix' fence='true' stretchy='true' symmetric='true' lspace='thinmathspace'>)<\/mo><mo>,<\/mo>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n<h4 class=\"subsubsection_\" id='magicparlabel-45886'>Page 150, line 7 from the bottom <\/h4>\n<div class=\"standard\" id='magicparlabel-45887'><em><b>is<\/b><\/em><\/div>\n\n<div class=\"standard\" id='magicparlabel-45888'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>w<\/mi><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n   <msub>\n    <mrow><mi>a<\/mi>\n    <\/mrow>\n    <mrow><mi>i<\/mi>\n    <\/mrow>\n   <\/msub>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n<mo>=<\/mo>\n   <msup>\n    <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n     <mrow>\n      <msubsup>\n       <mrow><mo> &prod; <\/mo>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>k<\/mi><mo>=<\/mo><mn>1<\/mn>\n        <\/mrow>\n       <\/mrow>\n       <mrow><mi>n<\/mi>\n       <\/mrow>\n      <\/msubsup>\n      <msup>\n       <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n        <mrow>\n         <msubsup>\n          <mrow><mo> &prod; <\/mo>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n           <\/mrow>\n          <\/mrow>\n          <mrow><mi>r<\/mi>\n          <\/mrow>\n         <\/msubsup>\n         <msubsup>\n          <mrow><mi>c<\/mi>\n          <\/mrow>\n          <mrow>\n           <mrow><mi>i<\/mi><mo>,<\/mo><mi>k<\/mi><mo>,<\/mo><mi>q<\/mi>\n           <\/mrow>\n          <\/mrow>\n          <mrow>\n           <msub>\n            <mrow><mi> &eta; <\/mi>\n            <\/mrow>\n            <mrow><mi>q<\/mi>\n            <\/mrow>\n           <\/msub>\n          <\/mrow>\n         <\/msubsup>\n        <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n       <\/mrow>\n       <mrow>\n        <mrow><mn>1<\/mn><mo>\/<\/mo><mi>r<\/mi>\n        <\/mrow>\n       <\/mrow>\n      <\/msup>\n     <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n    <\/mrow>\n    <mrow>\n     <mrow><mn>1<\/mn><mo>\/<\/mo><mi>n<\/mi>\n     <\/mrow>\n    <\/mrow>\n   <\/msup>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n\n<div class=\"standard\" id='magicparlabel-45889'><em><b>should be<\/b><\/em><\/div>\n\n<div class=\"standard\" id='magicparlabel-45890'><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n <mrow>\n  <mrow><mi>w<\/mi><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n   <msub>\n    <mrow><mi>a<\/mi>\n    <\/mrow>\n    <mrow><mi>i<\/mi>\n    <\/mrow>\n   <\/msub>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n<mo>=<\/mo>\n   <msup>\n    <mrow><mo form='prefix' fence='true' stretchy='true' symmetric='true'>(<\/mo>\n\n     <mrow>\n      <msubsup>\n       <mrow><mo> &prod; <\/mo>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>k<\/mi><mo>=<\/mo><mn>1<\/mn>\n        <\/mrow>\n       <\/mrow>\n       <mrow><mi>n<\/mi>\n       <\/mrow>\n      <\/msubsup>\n      <msubsup>\n       <mrow><mo> &prod; <\/mo>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>q<\/mi><mo>=<\/mo><mn>1<\/mn>\n        <\/mrow>\n       <\/mrow>\n       <mrow><mi>r<\/mi>\n       <\/mrow>\n      <\/msubsup>\n      <msubsup>\n       <mrow><mi>c<\/mi>\n       <\/mrow>\n       <mrow>\n        <mrow><mi>i<\/mi><mo>,<\/mo><mi>k<\/mi><mo>,<\/mo><mi>q<\/mi>\n        <\/mrow>\n       <\/mrow>\n       <mrow>\n        <msub>\n         <mrow><mi> &eta; <\/mi>\n         <\/mrow>\n         <mrow><mi>q<\/mi>\n         <\/mrow>\n        <\/msub>\n       <\/mrow>\n      <\/msubsup>\n     <\/mrow>\n<mo form='postfix' fence='true' stretchy='true' symmetric='true'>)<\/mo>\n\n    <\/mrow>\n    <mrow>\n     <mrow><mn>1<\/mn><mo>\/<\/mo><mi>n<\/mi>\n     <\/mrow>\n    <\/mrow>\n   <\/msup><mn>.<\/mn>\n  <\/mrow>\n <\/mrow><\/math><\/div>\n\n<div class=\"standard\" id='magicparlabel-45891'><h2 class='bibtex'>References<\/h2><div class='bibtex'><div class='bibtexentry' id='LyXCite-Kulakowski2020utahp'><span class='bibtexlabel'>1<\/span><span class='bibtexinfo'><span class=\"bib-fullnames:author\">K. Ku\u0142akowski<\/span>, <i><span class=\"bib-title\">Understanding the Analytic Hierarchy Process<\/span><\/i> (<span class=\"bib-publisher\">Chapman and Hall \/ CRC Press<\/span>, <span class=\"bib-year\">2020<\/span>).<\/span><\/div>\n<\/div><\/div>\n<\/body>\n<\/html>\n\n\n\n<p><strong>Erratum can also be downloaded as the <a href=\"\/kkulak\/wp-content\/uploads\/2025\/01\/book_erratum.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">PDF file here<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Book Erratum Understanding The Analytic Hierarchy Process Konrad Ku\u0142akowski Abstract Errors found in the book Understanding The Analytic Hierarchy Process [1] Page 40, line 3 from the top is n ij ={ 0 if i=j or { a i , a j } &isin; E 1 if i &ne; j and { a i , [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width.php","meta":{"footnotes":""},"class_list":["post-141","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/home.agh.edu.pl\/~kkulak\/wp-json\/wp\/v2\/pages\/141","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.agh.edu.pl\/~kkulak\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.agh.edu.pl\/~kkulak\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.agh.edu.pl\/~kkulak\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/home.agh.edu.pl\/~kkulak\/wp-json\/wp\/v2\/comments?post=141"}],"version-history":[{"count":4,"href":"https:\/\/home.agh.edu.pl\/~kkulak\/wp-json\/wp\/v2\/pages\/141\/revisions"}],"predecessor-version":[{"id":147,"href":"https:\/\/home.agh.edu.pl\/~kkulak\/wp-json\/wp\/v2\/pages\/141\/revisions\/147"}],"wp:attachment":[{"href":"https:\/\/home.agh.edu.pl\/~kkulak\/wp-json\/wp\/v2\/media?parent=141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}