Experimental Materials for "Multi-Criteria Decision Making through the Fusion of Quantitative and Qualitative Information: A Triadic Information Fusion Model and an Innovative Approach in AHP"

C-AHP and C-AHP++ are two improved versions of the AHP method. In this repository, you will find experimental results of these new methods and their application to a real problem such as "Car Selection".

Kartal, Hakan Emre hek@nula.com.tr 0000-0002-3952-7235 DOI: 10.36227/techrxiv.176115768.87188579/v1

C-AHP and C-AHP++

Contextual and Enhanced-Contextual Analytic Hierarchy Process
(Extensions of the classical AHP framework)

Feature	Classical AHP	C-AHP	C-AHP++
Decision Basis	Pairwise subjective judgments only	Fusion of subjective judgments with global context	Fusion of subjective judgments with alternative-specific context
Input Requirements	Pairwise judgments only	Judgments + global alternative ($\alpha_i$) and criteria ($\omega_j$) weights	Judgments + alternative-specific contextual weights ($\alpha_i$, $\omega_{ij}$)
Subjectivity Issue	Vulnerable (“Super Subjectivity Paradox”: all weights entirely subjective)	Resolved via global subjective–objective fusion	Resolved via contextualized reweighting (alternative-specific)
Flexibility	Static (no context awareness)	Moderate (global context-aware)	High (alternative-specific context-aware)
Contextual Weight Structure	None	Global vector ($\omega_j$): one weight vector shared across all alternatives	Alternative-specific matrix ($\omega_{ij}$): contextualized per alternative and criterion
Main Limitation	Risk of detachment from reality	Uniform evaluation across alternatives	Requires larger data and stronger domain expertise to parameterize $\omega_{ij}$
Gradient-Based Learning	❌ No	✅ Yes †	✅ Yes †
Differentiability	❌ No	⚠️ Partially differentiable (piecewise due to $\max$)	⚠️ Partially differentiable (piecewise due to $\max$)
Entropy Control ($\tau$)	❌ No	✅ Yes (temperature parameter $\tau$ tunes subjectivity–objectivity balance)	✅ Yes (same as C-AHP, extended to contextual weights)

† End-to-end gradient learning is possible provided the $\max$-based decision topology remains constant during training.

Files

• C-AHP_Experiments_v1.zip: Package containing the problem to which the proposed methods are applied, the applied methods, all solution steps, data, results, result graphs, and outputs.
  • Car_Selection_Decision.ods: Open Office Calc (or Excel) file containing the step-by-step solution and formulations of the car selection problem using AHP, C-AHP, and C-AHP++ methods.
  • Car_Selection_Decision_All_Results_Comparison_With_Graphs.pdf: Output file comparing all method outputs with data and schematics.
  • Car_Selection_Decision_C-AHP(Tau=0.5).pdf: Output file containing all data sets and results for the $\tau = 0.5$ parameter of the C-AHP method.
  • Car_Selection_Decision_C-AHP(Tau=1.0).pdf: Output file containing all datasets and results for the $\tau = 1.0$ parameter of the C-AHP method.
  • Car_Selection_Decision_C-AHP(Tau=2.0).pdf: Output file containing all datasets and results for the $\tau = 2.0$ parameter of the C-AHP method.
  • Car_Selection_Decision_C-AHP++(Tau=0.5).pdf: Output file containing all datasets and results for the $\tau = 0.5$ parameter of the C-AHP++ method.
  • Car_Selection_Decision_C-AHP++(Tau=1.0).pdf: Output file containing all datasets and results for the $\tau = 1.0$ parameter of the C-AHP++ method.
  • Car_Selection_Decision_C-AHP++(Tau=2.0).pdf: Output file containing all datasets and results for the $\tau = 2.0$ parameter of the C-AHP++ method.
  • C-AHP_Simple_Exams.zip: A package containing all datasets, solutions, results, and result graphs for the example problems solved in the article.
    • Choosing_A-Laptop_(Tau=0.5).pdf: Output file containing all datasets and results for the $\tau = 0.5$ parameter of the laptop choice problem.
    • Choosing_A-Laptop_(Tau=1.0).pdf: Output file containing all datasets and results for the $\tau = 1.0$ parameter of the laptop choice problem.
    • Choosing_A-Laptop_(Tau=2.0).pdf: Output file containing all datasets and results for the $\tau = 2.0$ parameter of the laptop choice problem.
    • Technology-Company-Investment-Decision_(Tau=0.5).pdf: Output file containing all data sets and results for the technology company investment decision problem for $\tau = 0.5$.
    • Technology-Company-Investment-Decision_(Tau=1.0).pdf: Output file containing all data sets and results for the technology company investment decision problem for $\tau = 1.0$.
    • Technology-Company-Investment-Decision_(Tau=2.0).pdf: Output file containing all data sets and results for the technology company investment decision problem for $\tau = 2.0$.

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