1. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Bisection method eLearning resources / MCDA team Director prof. Raimo P. Hämäläinen Helsinki University of Technology Systems Analysis Laboratory http://www.eLearning.sal.hut.fi

2. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Bisection method 1) Identify the least and the most preferred attribute levels x min and x max and set: 2) Define the bisection point m 1, for which 3) The value at m 1 is: 4) Define the bisection point m 2 between x min and m 1 and the bisection point m 3 between m 1 and x max, such that 5) Repeat the steps 2-4 recursively until the value scale is defined with sufficient accuracy v(x min ) = 0 v(x max ) = 1 v(m 1 ) - v(x min ) = v(x max ) - v(m 1 ) v(m 1 ) = 0.5·v(x min ) + 0.5 · v(x max ) = 0.5 v(m 2 ) = 0.5·v(x min ) + 0.5·v(m 1 ) = 0.25 v(m 3 ) = 0.5·v(m 1 ) + 0.5·v(x max ) = 0.75

3. eLearning / MCDA Systems Analysis Laboratory Helsinki University of Technology Bisection method  See the animationanimation  To the “Assessing the form of value function” slideAssessing the form of value function x max x min v(x min ) = 0v(x max ) = 1 m1m1 v(m 1 ) = 1/2 m2m2 v(m 2 ) = 1/4v(m 3 ) = 3/4 m3m3