126 The UMAP Journal 30.2(2009) 10° We apply expert system and group decision theory to determine the weights of the species in Population 2. We have a multi-attribute deci on problem, where the aim is to select the optimal solution from many lternatives or to sort the available alternatives. Assume that the finite solution set is y=fy1 ., yny, the attribute set is C=fcl,., cab, and the decision expert set is E=el,., em] Let S=[s1,.., g be a predefined set consisting of odd-chain elements Expert ek selects one element from S as the value of solution yi under attribute c; i let it be denoted as pi E S, and let p=(ping denote the judgment matrix of expert ek on all the solutions for all the attributes. The attribute weight vector in evaluating information given by ert ek is W=wi, where wf is the weight of attribute c selected by expert ek from set S, v∈S This theory can be actualized through the Analytical Hierarchy Process (AHP), first put forward by American operational researcher T.L. Saaty in the 1970s AhP is a method for decision-making analysis that combines qualitative and quantitative methods. Using this method, decision-makers126 The UMAP Journal 30.2 (2009) 12..xle 0 5 10 Figure 2. Numexical solutions for xi(t). We apply expert system and group decision theory to determine the weights of the species in Population 2. We have a multi-attribute deci￾sion problem, where the aim is to select the optimal solution from many alternatives or to sort the available alternatives. Assume that the finite solution set is Y = {yi, .. . ,y,}, the attribute set is C = {ci, . . . , cq}, and the decision expert set is E = {ei, ... , el}. Let S = {si,..., s.} be a predefined set consisting of odd-chain elements. Expert ek selects one element from S as the value of solution yi under attribute cj; let it be denoted as pikj E S, and let = (Pkj)n×q denote the judgment matrix of expert ek on all the solutions for all the attributes. The attribute weight vector in evaluating information given by expert ek is where wk is the weight of attribute cj selected by expert ek from set S, Wk ES. This theory can be actualized through the Analytical Hierarchy Process (AHP), first put forward by American operational researcher T.L. Saaty in the 1970s. AHP is a method for decision-making analysis that combines qualitative and quantitative methods. Using this method, decision-makers -X 0 ------- - --- -- - -- -- -- -- -- ----------- 4-- ------------ 48----- -- ------------------------------------------- --- L--------------------------- 6------------------------------ -------------- 24---- ------------------------------------------------------------------- /I SI I - - -I I 2------------------I----------------I---------------- I