combine_weights: Combine Subjective and Objective Weights

In zhjx19/mathmodels: Comprehensive Mathematical Modeling Algorithms in R

Combine Subjective and Objective Weights

Description

Combines subjective and objective weights using linear, multiplicative, or game theory-based methods (geometric mean or linear system).

Usage

combine_weights(w_subj, w_obj, type = "linear", alpha = 0.5)

Arguments

w_subj	Numeric vector of subjective weights.
w_obj	Numeric vector of objective weights.
type	Character string specifying the combination method: "linear", "multiplicative", "game", or "game_linear".
alpha	Numeric value between 0 and 1, used only for the linear method to weight subjective weights. Defaults to 0.5.

Details

The function supports four methods:

• Linear: Combines weights as alpha * w_subj + (1 - alpha) * w_obj.

• Multiplicative: Combines weights as w_subj * w_obj, requiring positive weights.

• Game: Uses the geometric mean (sqrt(w_subj * w_obj)) to balance weights.

• Game_linear: Uses a game-theoretic approach by solving a linear system based on the cross-product of weights.

Value

A numeric vector of combined weights, normalized to sum to 1.

Examples

w_subj = c(0.4, 0.3, 0.2, 0.1)
w_obj = c(0.25, 0.2, 0.3, 0.25)
combine_weights(w_subj, w_obj, type = "linear", alpha = 0.6)
combine_weights(w_subj, w_obj, type = "multiplicative")
combine_weights(w_subj, w_obj, type = "game")
combine_weights(w_subj, w_obj, type = "game_linear")

zhjx19/mathmodels documentation built on June 2, 2025, 12:18 a.m.