Correlative decision preference information consistency check and comprehensive dominance representation method

Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding

“…With the compatible decision preference constraints, the Choquet integral based random generation method is proposed in reference [36], as shown in Algorithm 1. Calculate the optimal capacity, denoted as µ k , with which the Choquet integral value of chosen alternative, r, is the closest to the value r obtained through an optimization model (the objective is to minimize the distance between r and r, and the constraints include D and the boundary and monotonicity conditions).…”

“…Sketching the whole view of the dominance of the decision alternatives becomes a meaningful tool in practice. A random simulation based comprehensive decision aid algorithm is also provided in [36], see Algorithm 2.…”

“…Combarro et al [33][34][35] proposed the random node and minimum plus based capacity random generation methods, but these methods only consider the boundary and monotonicity conditions (see definition of capacity), without imposing any further preference information constraints. In order to simultaneously consider the complex decision preference constraints, Wu et al [36] provided a Choquet integral and linear programming based random generation method as well as the comprehensive decision method. However, this method involves a great many times of linear programming construction and solving.…”

“…end for each pair of decision alternatives {a, b} ⊆ A do Calculate the frequencies of dominance of a over b, b over a, a equal to b, denoted as d (a, b), d ≺ (a, b) and d ∼ (a, b). end By choosing the largest frequency dominance relationship, the most creditable dominancerelationship of all alternatives is generally found (for more detailed rules for dealing with some special cases, please see[36])…”

Capacity Random Forest for Correlative Multiple Criteria Decision Pattern Learning

“…Some reduction methods for these types of constraints can be found in [13,27]. Another potential issue for strategy (a) is that some inconsistencies may possibly exist in these hard constraints, and in this case, the inconsistency check and adjustment methods need be applied before identifying the desired capacity; more technologies about inconsistency check and adjustment strategies can be found in [25,28,31].…”