Nonadditive robust ordinal regression with nonadditivity index and multiple goal linear programming

Abstract

Nonadditive robust ordinal regression (NAROR) is a widely adopted approach to analyze and reveal the dominance relationships among all decision alternatives based on nonadditive measures, called capacities. In this paper, we first investigate some advantages of the nonadditivity index as an explicit interaction index, as compared with the traditional probabilistic simultaneous interaction indices, and show that nonadditivity index can serve as an equivalent representation of a capacity. Then we enhance the NAROR method by using nonadditivity index as well as multiple‐goal linear programming, where the former is used to replace the traditional interaction index to more naturally represent the decision maker's preferences, and the latter aims to replace the 0 to 1 mixed integer programming to enhance the ability to detect and adjust contradictory and redundant preference information. The updated NAROR's steps are constructed and discussed in detail and illustrated with a practical example.

Capacity Random Forest for Correlative Multiple Criteria Decision Pattern Learning

“…• Strategy (b) basically uses the goal constraints which are soft equations and does not further concern the inconsistency among these constraints or the infeasibility issue in application; however, the strategy (a) has to face the strict constraints and carefully deals with the unavoidable contradiction among them (some inconsistency checks and adjustment strategies can be found in references [8,25,32]).…”

“…More properties of nonadditivity indices can be found in [2,22,23,25]. In brief, the Shapley nonadditivity index of a single criterion can be taken as its overall importance index to the decision problem, and the Shapley nonadditivity index of non-singleton nonempty set can be regarded as its comprehensive interaction index, which reflects the interaction kind and tensity among all criteria in it.…”

“…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].…”

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

“…Combing the boundary and monotonicity conditions of capacity with the decision preference constraints, we can get the domain of feasible capacities if those conditions and constraints are all compatible. Otherwise, we can adopt some inconsistency methods and adjustment strategies, see, e.g., [39][40][41].…”

“…Consider an example adapted from [39]. Suppose a buyer adopts five criteria to evaluate a vehicle: The selling price, the space and comfort, the safety and convenience, the engine and transmission system and the maintenance cost for five years, denoted as criteria 1-5, respectively.…”