Multi-Criteria Decision Analysis (MCDA) has emerged as a central practice within decision analysis, intended to support rational choice in contexts involving multiple, often conflicting, objectives. Despite decades of methodological proliferation, the field continues to neglect the theoretical basis that ensures logical coherence, transparency, and normative robustness. This article presents the foundations of a universal software platform, UNEDA (Universal Engine for Decision Analysis), designed to operationalise MCDA methods in alignment with classical decision-theoretic principles. Central to the approach is a formal system of desiderata derived from the axiomatic foundations of expected utility theory and multi-attribute utility theory. These desiderata define the necessary conditions for a decision method to be considered consistent with established rationality principles, such as transitivity, monotonicity, independence, and decomposability. We evaluate the Big Five most widely used MCDA methods, VIKOR, TOPSIS, PROMÉTHÉE, ÉLECTRE, and AHP, against these desiderata. By providing a theoretically grounded and computationally efficient environment for MCDA, UNEDA facilitates the development of decision tools that meet rigorous analytical standards. The software is open-source and freely available, aiming to serve academic, policy, and applied decision-making communities alike.

There are well-known issues in eliciting probabilities, utilities, and criteria weights in real-life decision analysis. In this paper, we examine automatic multi-criteria weight-generating algorithms which are seen as one remedy to some of the elicitation issues. The results show that the newer Sum Rank approaches perform better in terms of both performance and robustness than older (classical) methods, also when compared to the new and promising geometric class of methods. Additionally, as expected the cardinal surrogate models perform better than their ordinal counterparts (with one exception) due to their ability to take more information into account. Unexpectedly, though, the well-established linear programming model’s performance is worse in this respect than previously thought, despite a promising mapping between linear optimisation and surrogate weight generation which is explored in the paper.

In this article, we suggest a group decision method within an integrated computational framework for decision policy. Based on a co-creation workflow, epidemiological estimates, and socioeconomic factors, decisions are considered in a multi-stakeholder, multi-criteria context to elicit attitudes, perceptions, and preferences of relevant stakeholder groups. The complete framework has been applied in Botswana, Romania, and Jordan to assess mitigation actions related to the Covid-19 pandemic in order to mobilize better response strategies for other relevant future scenarios, and potentially more serious pandemics and other hazardous events. The framework was recommended as best practice in the EU under the European Open Science Cloud EOSC, Covid-19 Fast Track Funding.

Jordan is currently facing a serious problem of water scarcity. It is the fourth water-scarce country in the world. The sustainability of water supply in Jordan is affected not only by the depletion of water reserves but also by increasing electricity tariffs. In this paper, we present some results regarding the water-energy nexus governance in Jordan using a computer-supported co-creative approach for evaluating stakeholder preferences on criteria and possible scenarios of development for the sectors. We describe a decision support tool and a methodology for evaluating stakeholder preferences for both sectors and on possible scenarios of development for the water and energy sectors. We rank possible energy and water futures ranked under a set of sector-relevant criteria while considering entire ranges of possible alternative values and criteria weights. Using second-order probabilistic considerations, we furthermore analyse how plausible it is that a scenario outranks the others.

In decision analysis, there are several problems with the assignment of precise numbers to decision components, such as probabilities, values and weighs. These can very seldom realistically be estimated. Therefore, various alternative approaches have been suggested over the years, such as interval, capacity and ranking models. The more general of these are however problematical from several computational viewpoints and in this article, we deal with the server-side issues when converting the application from a stand-alone PC program to a server-client decision analytical software. On a server with a large number of users, space requirements become paramount as opposed to a single user on a PC. On a PC, matrices can be explicitly stored in memory, while on a server, to save space, matrices might have to be stored in an implicit (compacted) way, leading to space-time trade-offs.

In classic decision theory, it is assumed that a decision-maker can assign precise numerical values corresponding to the true value of each consequence, as well as precise numerical probabilities for their occurrences. However, in real-life situations, the ordering of alternatives from most to least preferred is often a delicate matter and an adequate mathematical representation is crucial. In attempting to address real-life problems, where uncertainty about data prevails, some kind of representation of imprecise information is important and several have been proposed. However, general methods have turned out to be insufficient and we demonstrate in this article that there is not one set of coding techniques that result in the best performing software for decision analysis.

To be useful in reality, decision analytical tools must be able to handle imprecise information. This paper presents the algorithmic software design against a background of an evaluation method for analysing decision situations under semi-strong uncertainty. The design is built on a relaxation of the requirement for precise utilities, probabilities, and weights. To handle this, the calculations involved become computationally intensive to match an interactive work flow and the approach required implementation of new algorithms. We describe some particularly interesting implementation aspects of these and show how these computations can be tractable.

This paper presents a web-application supporting structured decision modelling and analysis. The application allows for decision modelling with respect to different preferences and views, allowing for numerically imprecise and vague background probabilities, values, and criteria weights, which further can be adjusted in an interactive fashion when considering calculated decision outcomes. The web-application is based on a decision tool that has been used in a large number of different domains over the last 15 years, ranging from investment decision analysis for companies to public decision support for local governments.

Multi-criteria decision analysis can be a useful tool in routing out and ranking different alternatives. However, many such analyses involve imprecise information, including estimates of utilities, outcome probabilities and criteria weights. This paper presents a general multi-criteria approach, allowing the modelling of multi-criteria and probabilistic problems in the same tree form, which includes a decision tree evaluation method integrated with a framework for analyzing decision situations under risk with a criteria hierarchy. The general method of probabilistic multi-criteria analysis extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise and uncertain facts. Thus, it relaxes the requirement for precise numerical estimates of utilities, probabilities, and weights. The evaluation is done relative to a set of decision rules, generalizing the concept of admissibility and computationally handled through the optimization of aggregated utility functions. The approach required design and development of computationally intensive algorithms for which there was no template

In attempting to address real-life decision problems, where uncertainty about data prevails, some kind of representation of imprecise information is important and several have been proposed. In particular, first-order representations, such as sets of probability measures, upper and lower probabilities, and interval probabilities and utilities of various kinds, have been suggested for enabling a better representation of the input sentences for a subsequent decision analysis. However, sometimes second-order approaches are better suited for modelling incomplete knowledge and we demonstrate how such can add important information when handling aggregations of imprecise representations, as is the case in decision trees or probabilistic networks. Based on this, we suggest a measure of belief density for such intervals. We also demonstrate important properties when operating on general distributions. The results equally apply to approaches which do not explicitly deal with second-order distributions, instead using only first-order concepts such as upper and lower bounds. While the discussion focuses on probabilistic decision trees, the results apply to other formalisms involving products of probabilities, such as probabilistic networks, and to formalisms dealing with products of interval entities such as interval weight trees in multi-criteria decision making.

We present a decision tree evaluation method for analyzing multi-attribute decisions under risk, where information is numerically imprecise. The approach extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise statements, relaxing requirements for precise estimates of decision parameters. Information is modeled in convex sets of utility and probability measures restricted by closed intervals. Evaluation is done relative to a set of rules, generalizing the concept of admissibility, computationally handled through optimization of aggregated utility functions. Pros and cons of two approaches, and tradeoffs in selecting a utility function, are discussed.

We describe how machine learning and decision theory is combined in an application that supports control room operators of a combined heating and power plant to cope with the overwhelming complexity of situations when severe plant disturbances occur. The application is designed as an assistant, rather than as an automatic system that intervenes directly in the operator/plant loop. The application is required to handle vague and numerically imprecise background information in the construction of classifier committees. A classifier committee (or ensemble) is a classifier created by combining the predictions of multiple sub-classifiers. The presented method combines classifiers into a committee by using computational methods for decision analysis that are designed to work when the information at hand is imprecise. The application evaluates and make priorities between classified alarms according to credibilities that depend on the current context. Machine learning techniques are used to construct classifiers that recognize various malfunctions in a process, determine whether a situation is normal or not, and make priorities among alarms.

We present a theory and a tool for the treatment of problems arising when a decision making agent faces a situation involving a choice between a finite set of strategies, having access to a finite set of autonomous agents reporting their opinions. Each of these agents may itself be a decision making agent, and the theory is independent of whether there is a specific coordinating agent or not. Any decision making agent is allowed to assign different credibilities to the statements made by the other autonomous agents. The theory admits the representation of vague and numerically imprecise information, and the evaluation results in a set of admissible strategies by using criteria conforming to classical statistical decision theory. The admissible strategies can be further investigated with respect to strength and also with respect to the range of values that makes them admissible.