[Paper Review] Composite Strategy for Multicriteria Ranking/Sorting (methodological issues, examples)

Mark Sh. Levin|arXiv (Cornell University)|Nov 9, 2012

Statistical and Computational Modeling149 references3 citations

TL;DR

This paper proposes a composite strategy for multicriteria ranking/sorting using hierarchical morphological multicriteria design (HMMD) with interval multiset estimates to synthesize optimal solving strategies from modular procedures. By integrating diverse decision-making techniques based on quality and compatibility, the method generates Pareto-efficient composite strategies, demonstrated through a DSS COMBI case study yielding four optimal solution paths with quantified performance metrics.

ABSTRACT

The paper addresses the modular design of composite solving strategies for multicriteria ranking (sorting). Here a 'scale of creativity' that is close to creative levels proposed by Altshuller is used as the reference viewpoint: (i) a basic object, (ii) a selected object, (iii) a modified object, and (iv) a designed object (e.g., composition of object components). These levels maybe used in various parts of decision support systems (DSS) (e.g., information, operations, user). The paper focuses on the more creative above-mentioned level (i.e., composition or combinatorial synthesis) for the operational part (i.e., composite solving strategy). This is important for a search/exploration mode of decision making process with usage of various procedures and techniques and analysis/integration of obtained results. The paper describes methodological issues of decision technology and synthesis of composite strategy for multicriteria ranking. The synthesis of composite strategies is based on 'hierarchical morphological multicriteria design' (HMMD) which is based on selection and combination of design alternatives (DAs) (here: local procedures or techniques) while taking into account their quality and quality of their interconnections (IC). A new version of HMMD with interval multiset estimates for DAs is used. The operational environment of DSS COMBI for multicriteria ranking, consisting of a morphology of local procedures or techniques (as design alternatives DAs), is examined as a basic one.

Motivation & Objective

• To develop a modular, composable framework for multicriteria ranking/sorting strategies in decision support systems (DSS).
• To address methodological challenges in designing reconfigurable, creative-level solving strategies using combinatorial synthesis.
• To integrate diverse local procedures (DAs) into composite strategies based on quality and interconnection compatibility.
• To apply and validate the approach using the DSS COMBI system for multicriteria ranking.
• To support exploratory decision making through structured, flexible, and analyzable composite solving paths.

Proposed method

• Employs hierarchical morphological multicriteria design (HMMD) to systematically combine design alternatives (DAs) representing local procedures or techniques.
• Uses interval multiset estimates to evaluate DAs on six criteria, capturing uncertainty and expert judgment in a structured format.
• Applies compatibility matrices to assess interconnections between DAs, ensuring feasible and high-quality composite strategy formation.
• Identifies Pareto-efficient composite strategies by evaluating quality vectors (e.g., (2;4,0,0)) across all valid combinations.
• Utilizes a morphology-based structure (e.g., H-T-U-X layers) to represent series strategies in DSS COMBI.
• Employs a functional graph framework to model problem formulation, intermediate analysis, and result monitoring in the solving process.

Experimental results

Research questions

• RQ1 How can a modular, composable strategy be designed for multicriteria ranking/sorting in DSS to support creative problem solving?
• RQ2 What criteria and evaluation methods are effective for selecting and combining local decision-making procedures (DAs) into a composite strategy?
• RQ3 How can the quality of interconnections between DAs be modeled and optimized to ensure high-performance composite strategies?
• RQ4 What role does interval multiset estimation play in handling uncertainty and expert judgment in strategy synthesis?
• RQ5 How can the resulting composite strategies be validated and visualized for decision-making support?

Key findings

• Four Pareto-efficient composite strategies were identified: S₁ = H₁⋆T₀⋆U₂⋆X₀, S₂ = H₂⋆T₀⋆U₂⋆X₀, S₃ = H₃⋆T₀⋆U₂⋆X₀, and S₄ = H₀⋆T₀⋆U₅⋆X₀.
• S₁ achieved the highest quality vector (2;4,0,0), indicating superior performance in the most favorable criteria.
• S₂, S₃, and S₄ each achieved the quality vector (3;3,1,0), representing strong trade-offs across criteria.
• The compatibility matrix revealed that H₁, H₂, and H₃ had high compatibility (3) with U₂ and U₅, enabling robust strategy combinations.
• The morphological structure enabled systematic exploration of 128 possible strategy combinations, with only four identified as Pareto-efficient.
• The extended functional graph model supports on-line monitoring, result analysis, and dynamic reconfiguration of the solving process.