Preferential knowledge for multi-criteria decision making: Stability and consistency of decision rules and weights

This study introduces the Hellinger Distance Method (HDM), a novel objective weighting approach for multi-criteria decision-making (MCDM) problems. HDM employs a dual-layered structure by simultaneously accounting for the internal variation of each criterion (via standard deviation) and the distributional dissimilarities between criteria (via the Hellinger Distance). The method was applied to assess innovation performance across seven countries using the 2024 Global Innovation Index data. Rank Reversal analysis demonstrated that HDM maintains stable alternative rankings following systematic criterion removal, indicating robust sensitivity. Further comparisons with established objective weighting methods ENTROPY, CRITIC, SD, SVP, LOPCOW, and MEREC revealed strong alignment with ENTROPY and SVP, reinforcing HDM’s reliability and methodological soundness. In addition, simulation-based analyses involving ten decision matrix scenarios confirmed the statistical homogeneity and stability of HDM-derived weights, as validated by ANOM and Levene’s tests. These findings highlight the method’s consistent performance across varied data conditions. Overall, HDM emerges as a reliable, theoretically grounded, and practically effective weighting technique, offering a valuable contribution to both the academic literature and real-world MCDM applications.

Multicriteria Decision Analysis to Support Health Technology Assessment Agencies: Benefits, Limitations, and the Way Forward

A multi-source transfer-based decision-making method with domain consistency and contributions

n modern aircraft design, increased attention is being paid to the conceptual and preliminary design phases so as to increase the odds of creating a design that will ultimately be successful at the completion of the design process. Since aerospace systems are complex systems with interacting disciplines and technologies, the decision makers dealing with such design problems are involved in balancing multiple, potentially conflicting attributes/criteria, transforming a large amount of customer supplied guidelines into a solidly defined set of requirement definitions. As a result, the criteria have to be all simultaneously taken into account and a compromise essentially becomes part of the decision making process. Various methods and techniques are available to deal with such sort of multi-criteria decision making (MCDM) problems. In the 1970’s, Saaty proposed the Analytic Hierarchy Process (AHP), which facilitates the MCDM problems that have a hierarchical structure of attributes by reducing complex decisions to a series of pair-wise comparisons. In this method, the preference information is elicited as the pair-wise comparisons between attributes or alternatives and treated using the eigenvector method. The other straightforward method to handle the MCDM problem is the Overall Evaluation Criterion (OEC) technique, presented in Ref 3. The OEC is a single metric and is obtained by summing multiple non-dimensional attribute metrics normalized by the metric values of a relevant baseline. Another commonly used MCDM technique is the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). The “best” solution chosen by TOPSIS is the alternative that is the closest to the positive ideal solution and the furthest from the negative ideal solution. The separation between each alternative solution and the ideal solution, which is determined by the weighted criteria, is rather sensitive to criterion weights, so typically several weighting scenarios are investigated to determine the final solution. Among these developed MCDM methods, different methods have different underlying assumptions, information requirements, analysis models, and decision rules that are designed for solving a certain class of decision making problems. This implies that it is critical to use the most appropriate method to solve the problem under consideration since the use of unsuitable method always leads to misleading design decisions. Consequently, bad design decisions will result in big loss to the society, such as property damage or personal injury. Thus, it is necessary to review the existing MCDM methods, discuss in depth their advantages, disadvantages, applicability, computational complexity, etc. in order to make right decision when choosing the right method for the given problem. In this paper a hybrid MCDM method is developed to deal with the problem under consideration. Relative weights of the evaluation criteria are elicited by using the eigenvector method to describe the decision maker’s preference information. The TOPSIS method is used to analyze the qualitative and quantitative data of input parameters and find the solution to the given problem. An aircraft technology selection problem is conducted as a proof of implementation to demonstrate the functionality and effectiveness of the proposed methodology.

<p>Multi-criteria decision making (MCDM) has been introduced to GIS about 15 years ago. Decision rules that have been implemented in the GIS environment include weighted linear combination, analytical hierarchy process, ideal point analysis, concordance-discordance analysis, and ordered weighted averaging. The spatial dimensions of MCDM include spatially distributed decision-makers and decision alternatives, decision objectives relating to geographical objects, and a non-uniform weighting across space. However, few (if any) MCDM methods incorporate spatial relationships in the decision rule itself. This presentation suggests using geographical weighting to influence the calculation of aggregated suitability scores. Inverse distance-based weights are used to adapt the suitability of locations to their neighbours’ scores. This method was implemented in the thematic mapping package CommonGIS, and applied to a site selection problem to demonstrate the usefulness of geographically weighted MCDM. Through its interactive cartography, CommonGIS supports the application of geographical weighting in conjunction with other spatial dimensions of multi-criteria analysis. </p>

<p>Multi-criteria decision making (MCDM) has been introduced to GIS about 15 years ago. Decision rules that have been implemented in the GIS environment include weighted linear combination, analytical hierarchy process, ideal point analysis, concordance-discordance analysis, and ordered weighted averaging. The spatial dimensions of MCDM include spatially distributed decision-makers and decision alternatives, decision objectives relating to geographical objects, and a non-uniform weighting across space. However, few (if any) MCDM methods incorporate spatial relationships in the decision rule itself. This presentation suggests using geographical weighting to influence the calculation of aggregated suitability scores. Inverse distance-based weights are used to adapt the suitability of locations to their neighbours’ scores. This method was implemented in the thematic mapping package CommonGIS, and applied to a site selection problem to demonstrate the usefulness of geographically weighted MCDM. Through its interactive cartography, CommonGIS supports the application of geographical weighting in conjunction with other spatial dimensions of multi-criteria analysis. </p>

<p>Multi-criteria decision making (MCDM) has been introduced to GIS about 15 years ago. Decision rules that have been implemented in the GIS environment include weighted linear combination, analytical hierarchy process, ideal point analysis, concordance-discordance analysis, and ordered weighted averaging. The spatial dimensions of MCDM include spatially distributed decision-makers and decision alternatives, decision objectives relating to geographical objects, and a non-uniform weighting across space. However, few (if any) MCDM methods incorporate spatial relationships in the decision rule itself. This presentation suggests using geographical weighting to influence the calculation of aggregated suitability scores. Inverse distance-based weights are used to adapt the suitability of locations to their neighbours’ scores. This method was implemented in the thematic mapping package CommonGIS, and applied to a site selection problem to demonstrate the usefulness of geographically weighted MCDM. Through its interactive cartography, CommonGIS supports the application of geographical weighting in conjunction with other spatial dimensions of multi-criteria analysis.</p>

<p>Multi-criteria decision making (MCDM) has been introduced to GIS about 15 years ago. Decision rules that have been implemented in the GIS environment include weighted linear combination, analytical hierarchy process, ideal point analysis, concordance-discordance analysis, and ordered weighted averaging. The spatial dimensions of MCDM include spatially distributed decision-makers and decision alternatives, decision objectives relating to geographical objects, and a non-uniform weighting across space. However, few (if any) MCDM methods incorporate spatial relationships in the decision rule itself. This presentation suggests using geographical weighting to influence the calculation of aggregated suitability scores. Inverse distance-based weights are used to adapt the suitability of locations to their neighbours’ scores. This method was implemented in the thematic mapping package CommonGIS, and applied to a site selection problem to demonstrate the usefulness of geographically weighted MCDM. Through its interactive cartography, CommonGIS supports the application of geographical weighting in conjunction with other spatial dimensions of multi-criteria analysis.</p>

The essay has a twofold objective: primarily, to present an application of voting theory as a possible evaluation method, and concurrently, to offer a pedagogic framework, based on that very application. Evaluation and certain notions of preference and value have common semantic roots. By equating preference and choice, we end up amidst social choice (SC) theory and voting methods, also manageable as joint decisions in multiple-criteria decision making (MCDM). With the aid of the Saari triangle some essential differences of pairwise and positional voting rules for up to three alternatives can be depicted. A voting or decision rule does not necessarily follow the true preferences of the actors, but may mirror the problematics of the chosen rule. The Saari triangle makes it possible to visualize some paradoxical results in the exemplary evaluations of digital websites through an imaginary case description via voting and MCDM. As candidates and voters in SC are put to stand for alternatives and criteria in MCDM, the methodological and pedagogical goals of the study are achieved.

<p>Multi-criteria decision analysis (MCDA) is a family of decision support methods that allow analysts to structure a decision problem through the selection and evaluation of multiple and often conflicting criteria, using established techniques to standardize, weight, and combine these criteria. Through a case study of an area-based deprivation index for the city of Toronto’s 140 neighbourhoods, we examine the variability of MCDA results under different decision models. We use interactive cartographic visualization to explore the impact of criterion weighting and three decision rules: weighted linear combination, locally weighted linear combination, and ordered weighted averaging. The modelling of socioeconomic deprivation using these different decision rules and their parameters yielded different spatial patterns of deprivation for the same set of variables and weights. The results highlight the importance of examining multiple decision models before making policy recommendations.</p> <p><br></p> <p> </p> <p>Keywords: analytic hierarchy process, area-based composite index, locally weighted linear combination, multi-criteria decision analysis, ordered weighted averaging, socio-economic deprivation</p>

<p>Multi-criteria decision analysis (MCDA) is a family of decision support methods that allow analysts to structure a decision problem through the selection and evaluation of multiple and often conflicting criteria, using established techniques to standardize, weight, and combine these criteria. Through a case study of an area-based deprivation index for the city of Toronto’s 140 neighbourhoods, we examine the variability of MCDA results under different decision models. We use interactive cartographic visualization to explore the impact of criterion weighting and three decision rules: weighted linear combination, locally weighted linear combination, and ordered weighted averaging. The modelling of socioeconomic deprivation using these different decision rules and their parameters yielded different spatial patterns of deprivation for the same set of variables and weights. The results highlight the importance of examining multiple decision models before making policy recommendations.</p> <p><br></p> <p> </p> <p>Keywords: analytic hierarchy process, area-based composite index, locally weighted linear combination, multi-criteria decision analysis, ordered weighted averaging, socio-economic deprivation</p>

The supplier appraisal process is one of the most important decision problems for companies focused on improving supply chain costs. Supplier selection is typically a multi-criteria decision making (MCDM) issue, as there is a lot of uncertain information. In order to overcome this issue, The Pythagorean Fuzzy Set is applied to handle the uncertainties involved in comparing the alternatives, criteria and opinions of decision makers. At the same time, a potential of Dimensional Analysis is a technique which deploys an association of the criteria capturing the interrelationship normally present in MCDM. In this sense, the purpose of this paper is to evaluate the suppliers in a supply chain cycle using Pythagorean Fuzzy Set and Dimensional Analysis. Finally, the applicability of the proposed method is illustrated through numerical examples, and a validation via Spearman correlation and Cronbach’s alpha.

In two volumes, this new edition presents the state of the art in Multiple Criteria Decision Analysis (MCDA). Reflecting the explosive growth in the field seen during the last several years, the editors not only present surveys of the foundations of MCDA, but look as well at many new areas and new applications. Individual chapter authors are among the most prestigious names in MCDA research, and combined their chapters bring the field completely up to date. Part I of the book considers the history and current state of MCDA, with surveys that cover the early history of MCDA and an overview that discusses the “pre-theoretical” assumptions of MCDA. Part II then presents the foundations of MCDA, with individual chapters that provide a very exhaustive review of preference modeling, along with a chapter devoted to the axiomatic basis of the different models that multiple criteria preferences. Part III looks at outranking methods, with three chapters that consider the ELECTRE methods, PROMETHEE methods, and a look at the rich literature of other outranking methods. Part IV, on Multiattribute Utility and Value Theories (MAUT), presents chapters on the fundamentals of this approach, the very well known UTA methods, the Analytic Hierarchy Process (AHP) and its more recent extension, the Analytic Network Process (ANP), as well as a chapter on MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique). Part V looks at Non-Classical MCDA Approaches, with chapters on risk and uncertainty in MCDA, the decision rule approach to MCDA, the fuzzy integral approach, the verbal decision methods, and a tentative assessment of the role of fuzzy sets in decision analysis. Part VI, on Multiobjective Optimization, contains chapters on recent developments of vector and set optimization, the state of the art in continuous multiobjective programming, multiobjective combinatorial optimization, fuzzy multicriteria optimization, a review of the field of goal programming, interactive methods for solving multiobjective optimization problems, and relationships between MCDA and evolutionary multiobjective optimization (EMO). Part VII, on Applications, selects some of the most significant areas, including contributions of MCDA in finance, energy planning problems, telecommunication network planning and design, sustainable development, and portfolio analysis. Finally, Part VIII, on MCDM software, presents well known MCDA software packages.

This article gives an overview of multi-criteria decision analysis (MCDA) and the advantages of using it to structure decision problems. It includes a description of the use of MCDA for a personal decision problem. The analysis was carried out informally on the job offers available to S. The decision problem was then modelled using Analytic a, Bayesian updating and sensitivity analysis. The results modelled the decision maker's opinions exactly. This resulted in him being able to negotiate much better working conditions, due to an increased understanding of his situation and what was important to him.

A linguistic distribution behavioral multi-criteria group decision making model integrating extended generalized TODIM and quantum decision theory