Cognitive support methods for multi-criteria expert decision making

In this paper, written for the session on multi-criteria decision analysis of the EURO XV–INFORMS XXXIV International Conference (Barcelona, July 1997), we present different cognitive methods for supporting an expert decision maker in her/his daily decision practice. The first part of the paper deals with the construction of a cognitive artifact of the decision problem. The second part discusses the main methodological components of our approach and the final part introduces some possible approaches as candidates for an ecological validation.     

Raising the bar: strategic multi-criteria decision analysis

This paper discusses the use of multi-criteria decision analysis for supporting strategic decision making in organisations. It begins by exploring the notions of strategic decisions and the strategic decision-making process. We suggest that structuring strategic objectives, dealing with high levels of uncertainty about the future, as well as considering the interconnectedness of strategic options and their long-term consequences are key aspects of strategic decision making support. We then consider the discursive nature of the processes within which strategic decisions are created and negotiated. Our exploration of these concepts leads us to propose a number of adaptations to the standard multi-criteria decision analysis approach, if it were to provide effective strategic decision support, particularly in strategy workshops. We make suggestions on how to implement these proposals, and illustrate their potential with examples drawn from real-world interventions in which we have provided strategic decision support.     

Evaluation of photovoltaic cells in a multi-criteria decision making process

The requirements to satisfy the energy needs of today without compromising those of future generations have forced humans to adopt rules that permit a better use of the available resources, of which the sun is an inexhaustible energy source. Amongst the energy sources that offer the possibility of exploiting the resources offered by the Earth, solar energy has acquired great strength. Photovoltaic energy has presented a major evolution and it is forecasted as being an important contributor to power generation and an alternative to other non-renewable energy sources. The high cost of solar electricity is today the main reason why electricity from photovoltaic systems has not been introduced in a more widespread way. In this context, the aim of this paper is the study and analysis of the decision criteria to be used when searching for the best photovoltaic cell, studying both the criteria that exert most influence or their manufacture (defined by quantitative and qualitative values) and the alternatives which will be the decision problem to be solved; each alternative will correspond to one type of photovoltaic cell. Thus, relevant information has been provided by three experts and the TOPSIS method has been used to aggregate all the information combined with the use of fuzzy sets which will model the use of linguistic labels in the process.     

A multi-criteria decision making model for advanced repair-to-order and disassembly-to-order system

Sensor-embedded products (SEPs) eliminate a majority of uncertainties involved in product recovery by providing item-based life-cycle information. This information includes the content of each product and component conditions, and enables the estimation of remaining useful life of the components. Once the data on the products are captured, it is possible to make optimal recovery decisions without any preliminary disassembly or inspection operations.     

Behavioural decision theory for multi-criteria decision analysis: a guided tour

Multi-criteria decision analysis (MCDA) involves asking decision makers difficult questions, and can leave them thinking that their judgements are not as coherent as they might have thought. This experience can be distressing and may even lead to rejection of the analysis. The psychology of preference sheds light both on how people naturally make choices without decision analytic assistance, and on how people think about the MCDA elicitation questions. As such, it can help the analyst to respond helpfully to difficulties which decision makers may face. In this paper, we review research from Behavioural Decision Theory relevant to MCDA. Our review follows the MCDA process, discussing research relevant to the structuring, value elicitation, and weighting phases of the analysis, outlining relevant and important findings, and open questions for research and practice.     

Integration and propagation of a multi-criteria decision making model in constraint programming

In this paper we propose a general integration scheme for a Multi-Criteria Decision Making model of the Multi-Attribute Utility Theory in Constraint Programming. We introduce the Choquet integral as a general aggregation function for multi-criteria optimization problems and define the Choquet global constraint that propagates this function during the Branch-and-Bound search. Finally the benefits of the propagation of the Choquet constraint are evaluated on the examination timetabling problem.     

On the maximum number of feasible ranking sequences in multi-criteria decision making problems

In many decision problems the focus is on ranking a set of m alternatives in terms of a number, say n, of decision criteria. Given are the performance values of the alternatives for each one of the criteria and the weights of importance of the criteria. This paper demonstrates that if one assumes that the criteria weights are changeable, then the number of all possible rankings may be significantly less than the upper limit of m!. As a matter of fact, this paper demonstrates that the number of possible rankings is a function of the number of alternatives and the number of criteria. These findings are important from a sensitivity analysis point of view or when a group decision making environment is considered.     

Behavioral multi-criteria decision analysis: the TODIM method with criteria interactions

In this paper a multi-criteria decision aiding model is developed through the use of the Choquet integral. The proposed model is an extension of the TODIM method, which is based on nonlinear Cumulative Prospect Theory. The paper starts by reviewing the first steps of behavioral decision theory. A presentation of the TODIM method follows. The basic concepts of the Choquet integral as related to multi-criteria decision aiding are reviewed. It is also shown how the measures of dominance of the TODIM method can be rewritten through the application of the Choquet integral. From the ordering of decision criteria the fuzzy measures of criteria interactions are computed, which leads to the ranking of alternatives. A case study on the forecasting of property values for rent in a Brazilian city illustrates the proposed model. Results obtained from the use of the Choquet integral are then compared against a previously made usage of the TODIM method. It is concluded that significant advantages exist derived from the use of the Choquet integral. The paper closes with recommendations for future research.     

Generalized intuitionistic fuzzy geometric aggregation operators and their application to multi-criteria decision making

In this paper, we extend the generalized weighted geometric and generalized ordered weighted geometric operators to intuitionistic fuzzy environments, that is, we develop a series of generalized intuitionistic fuzzy geometric operators to aggregate input arguments that are expressed by intuitionistic fuzzy values based on Archimedean t-conorm and t-norm. Then some desired properties of these aggregation operators are investigated. The relations between these operators and some existing intuitionistic fuzzy geometric aggregation operators are discussed in detail. Furthermore, applying these proposed operators, we develop an approach for multi-criteria decision making with intuitionistic fuzzy information. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Simulation techniques for the sensitivity analysis of multi-criteria decision models

This paper presents a simulation approach for high dimensional sensitivity analysis of the weights of multi-criteria decision models. This approach allows simultaneous changes of the weights and generates results that can easily be analyzed statistically to provide insights into multi-criteria model recommendations. In this study we consider three cases: no information, order information, and partial information regarding the weights. Our approach also allows investigation of sensitivity to the form of multi-criteria decision models. The simulation procedures we propose can also be used to aide in the actual decision process, particularly when the task is to select a subset of superior alternatives.     

Extension of VIKOR method for multi-criteria group decision making problem with linguistic information

A new method is proposed to solve multi-criteria group decision making problems in which both the criteria values and criteria weights take the form of linguistic information based on the traditional idea of VIKOR method. Firstly, the linguistic criteria weights given by all decision makers are transformed into trapezoidal fuzzy numbers, and then aggregated and defuzzified to crisp values. Secondly, the individual linguistic decision matrix given by each decision maker (DM) is transformed into 2-tuple linguistic decision matrix, and then aggregated into collective 2-tuple linguistic decision matrix by 2-tuple linguistic arithmetic mean operation. Thirdly, the 2-tuple linguistic values (_Si,_αi),$(S_i\text{,}{\alpha }_i)\text{,}$(_Ri,_αi)$(R_i\text{,}{\alpha }_i)$ and (_Qi,_αi)$(Q_i\text{,}{\alpha }_i)$ are calculated by defining the 2-tuple linguistic positive ideal solution (TL-PIS) and 2-tuple linguistic negative ideal solution (TL-NIS). Furthermore, the compromise solution can be obtained. Finally, a numerical example is used to illustrate the application of the proposed approach, and the method is verified by comparing the evaluation result with that of 2-tuple linguistic TOPSIS (TL-TOPSIS) method.     

Extending the multi-criteria decision making method DEX with numeric attributes,value distributions and relational models

Central European Journal of Operations Research - DEX is a qualitative multi-criteria decision analysis method. The method supports decision makers in making complex decisions based on multiple,...     

Transparent prioritisation,budgeting and resource allocation with multi-criteria decision analysis and decision conferencing

Managers in both for-profit and not-for-profit organisations continually face the task of allocating resources by balancing costs, benefits and risks and gaining commitment by a wide constituency of stakeholders to those decisions. This task is complex and difficult because many options are present, benefits and risks are rarely expressed as single objectives, multiple stakeholders with different agendas compete for limited resources, individually optimal resource allocations to organisational units are rarely collectively optimal, and those dissatisfied with the decisions taken may resist implementation. We first explain three current approaches to resource allocation taken from corporate finance, operational research and decision analysis, and we identify a common mistake organisations make in allocating resources. The paper then presents a technical process, multi-criteria portfolio analysis, for balancing the conflicting elements of the problem, and a social process, decision conferencing, which engages all the key players during the modelling process, ensuring their ownership of the model and the subsequent implementation. This socio-technical process improves communication within the organisation, develops shared understanding of the portfolio and generates a sense of common purpose about those projects that will best realise the organisation’s objectives. The paper concludes with lessons we have learned from actual practice. The authors want to thank Allergan and FCT (Portuguese Science Foundation) for their support.     

A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making

A fuzzy-set-based approach is presented to describe linguistic information in multi-criteria decision making. After having introduced concepts of determinacy and consistency of linguistic terms, the understandable degree and consistence degree of linguistic terms are illustrated by these two concepts. A case study is demonstrated for the proposed decision-making model with an analytical conclusion of both advantages and disadvantages.     

Methodological aspects of multi-criteria decision analysis for policy support: A case study on pharmaceutical removal from hospital wastewater

Decision making in public and political contexts can be complex. Multi-attribute value/utility theory (MAVT/MAUT) can support such decision processes by providing a transparent framework that helps focusing on objectives and corresponding degrees of achievement by different alternatives.     

A new decision support model in multi-criteria decision making with intuitionistic fuzzy sets based on risk preferences and criteria reduction

In this paper, we propose a new model for decision support to address the ‘large decision table’ (eg, many criteria) challenge in intuitionistic fuzzy sets (IFSs) multi-criteria decision-making (MCDM) problems. This new model involves risk preferences of decision makers (DMs) based on the prospect theory and criteria reduction. First, we build three relationship models based on different types of DMs’ risk preferences. By building different discernibility matrices according to relationship models, we find useful criteria for IFS MCDM problems. Second, we propose a technique to obtain weights through discernibility matrix. Third, we also propose a new method to rank and select the most desirable choice(s) according to weighted combinatorial advantage values of alternatives. Finally, we use a realistic voting example to demonstrate the practicality and effectiveness of the proposed method and construct a new decision support model for IFS MCDM problems.     

Research on AHP with interval-valued intuitionistic fuzzy sets and its application in multi-criteria decision making problems

This paper investigates an approach for multi-criterion decision making (MCDM) problems with interval-valued intuitionistic fuzzy preference relations (IVIFPRs). Based on the novel interval score function, some extended concepts associated with IVIFPRs are defined, including the score matrix, the approximate optimal transfer matrix and the possibility degree matrix. By using these new matrixes, a prioritization method for IVIFPRs is proposed. Then, we investigate an interval-valued intuitionistic fuzzy AHP method for multi-criteria decision making (MCDM) problems. In the end, a numerical example is provided to illustrate the application of the proposed approach.     

Spatial fuzzy consumer's decision making: A multicriteria analysis

This paper is devoted to a multicriteria analysis of the consumer's behavior when the decision maker is acting in a fuzzy space and manifesting an imprecise attitude. At first, the process of decision making is described with the help of three relationships between the set of goods which are supplied in several locations, the set of their characteristics and the set of the consumer's a priori possible behaviors. All these relations are fuzzy. The model applies the theory of fuzzy relations equations. Then, the stages of the decision process are analyzed. Often fuzzy behavior relations are like ‘black boxes’. The mathematical solution of the model indicates in which conditions their valuations are possible. The main interest of this method is not to use additive operations on subjective items and to use operators which are coherent with the fuzzy nature of the variables.     

Convergence properties and practical estimation of the probability of rank reversal in pairwise comparisons for multi-criteria decision making problems

In this paper, we address the impact of uncertainty introduced when the experts complete pairwise comparison matrices, in the context of multi-criteria decision making. We first discuss how uncertainty can be quantified and modeled and then show how the probability of rank reversal scales with the number of experts. We consider the impact of various aspects which may affect the estimation of probability of rank reversal in the context of pairwise comparisons, such as the uncertainty level, alternative preference scales and different weight estimation methods. We also consider the case where the comparisons are carried out in a fuzzy manner. It is shown that in most circumstances, augmenting the size of the expert group beyond 15 produces a small change in the probability of rank reversal. We next address the issue of how this probability can be estimated in practice, from information gathered simply from the comparison matrices of a single expert group. We propose and validate a scheme which yields an estimate for the probability of rank reversal and test the applicability of this scheme under various conditions. The framework discussed in the paper can allow decision makers to correctly choose the number of experts participating in a pairwise comparison and obtain an estimate of the credibility of the outcome.