A framework for dynamic multiple-criteria decision making

doi:10.1016/j.dss.2011.05.003

Decision Support Systems

Volume 52, Issue 1, December 2011, Pages 52-60

https://doi.org/10.1016/j.dss.2011.05.003 Get rights and content

Abstract

The classic multiple-criteria decision making (MCDM) model assumes that, when taking a decision, the decision maker has defined a fixed set of criteria and is presented with a clear picture of all available alternatives. The task then reduces to computing the score of each alternative, thus producing a ranking, and choosing the one that maximizes this value.

However, most real-world decisions take place in a dynamic environment, where the final decision is only taken at the end of some exploratory process. Exploration of the problem is often beneficial, in that it may unveil previously unconsidered alternatives or criteria, as well as render some of them unnecessary.

In this paper we introduce a flexible framework for dynamic MCDM, based on the classic model, that can be applied to any dynamic decision process and which is illustrated by means of a small helicopter landing example. In addition, we outline a number of possible applications in very diverse fields, to highlight its versatility.

Research highlights

► Most real-world decision problems are highly dynamic and time-dependent ► Most multiple-criteria decision making (MCDM) models are unable to capture this dynamism ► Very few tools exist for dynamic MCDM, mostly outside of the decision making field ► We propose a versatile framework for dynamic MCDM based on the classic model ► We present a series of possible applications to highlight its versatility

Introduction

Most real-world decision problems are dynamic, in the sense that the final decision is taken only at the end of some exploratory process, during which both alternatives and criteria may vary, as the examples of Section 6.1 testify.

However, the classic multiple-criteria decision making (MCDM) model is unable to capture this dynamicity, since it assumes that, before proceeding with the ranking, the decision maker must have identified fixed sets of criteria and alternatives. While, in principle, this model could be used in a dynamic setting by considering subsequent decisions to be completely independent one from the other, doing so would constitute a gross oversimplification of the way humans think about the fine interlinking that exists among decisions in a dynamic environment, in which earlier evaluations affect later ones.

The framework we propose in this paper aims to address this problem by extending the classic MCDM model in a flexible way that enables its use in very diverse fields requiring some form of dynamic decision making.

The rest of this paper is organized as follows. In Section 2, we briefly review the classic MCDM model and present the general theory our framework is set in. Subsequently, in Section 3, we delve into the crucial issue of choosing an appropriate aggregation function for this model, and present some well-known examples from the recent literature. We then give, in Section 4, a general overview of related work, before going into the details of our proposed framework in Section 5. To better illustrate our proposal, we make use of a numerical example (Section 6) and present a number of possible applications (Section 6.1).

Section snippets

Classic MCDM model

The classic multiple-criteria decision making (MCDM) model [18], [44] prescribes ways of evaluating, prioritizing and selecting the most favorable alternative from a set of available ones that are characterized by multiple, usually conflicting, levels of achievement for a set of attributes. The final decision is made by considering both inter-attribute and intra-attribute comparisons, possibly involving trade-off mechanisms.

Mathematically, a typical MCDM problem with m alternatives and n

Aggregation functions

As we have seen in the previous section, the key component of the classic MCDM model is the aggregation function used to associate a single score to each alternative by distilling the different evaluations (one for each criterion). It is thus easy to understand that the mathematical properties of this function will have a direct impact on the produced values and, therefore, on the final ranking of alternatives.

In the rest of this section we will present well-known aggregation functions,

Overview of related work in dynamic MCDM

Having introduced the classic MCDM model as well as reviewed the most relevant aggregation functions, and before we move to our proposed extension, it is beneficial to give a brief overview of the current state of the art in the field of dynamic decision making, to allow a better understanding of where our framework finds its place.

The problem of making decisions in a dynamic environment has been the object of study in many different fields, but has received special consideration in psychology

Dynamic MCDM model

Given a (possibly infinite) set of positive time instants $T$ = {1, 2, …}, let $A_{t}$ denote the set of alternatives available at time t ∈ $T$ , C_t: $A_{t}$ → [0, 1]ⁿ the function mapping each alternative to the corresponding vector of values for the n criteria over which alternatives are evaluated, and w_t ∈ [0, 1]ⁿ, $\sum_{w \in w_{t}} w = 1, \forall t \in T$ a weight vector for expressing criteria's relative importance. The set notation we have just introduced is used instead of the more common matrix notation presented in Section 2 because of

Numerical example: helicopter landing

To better illustrate our model, let us introduce a simple numerical example in which a decision maker has to pick a site for landing an helicopter from among a set of nine possible choices.

We shall consider the following criteria:

Effort
the effort required to change route towards the site (for example, an estimate of the required amount of fuel).
Roughness
the (estimated) roughness of the terrain.
Slope
the (estimated) slope of the terrain.
Sunlight
the (estimated) availability of sunlight at the site.

For the sake of simplicity,

Potential applications

To illustrate the applicability of our model, we present in this section a number of very diverse contexts it could find use in. We are confident that, with due modifications, the model could be applied in even more situations, and are looking forward to further developments in this area.

Conclusions

In this paper we introduced a versatile model for decision making in a dynamic environment, in which both sets of alternatives and criteria undergo modifications as the problem is further explored in a number of iterations. In this context, decisions may then be taken either frequently, or just at the end of the process.

The proposed framework can be flexibly adapted to different situations by choosing a retention policy for the historical set of alternatives, i.e. a rule for selecting

Gianluca Campanella is currently pursuing his Master of Science degree in Applied Mathematics at the Universidade Nova de Lisboa, Portugal after graduating with maximum grades in Applied Computer Science at the Free University of Bolzano, Italy. He is currently working as a researcher at the CA3 research group of the research institution UNINOVA, under the supervision of Prof. Rita A. Ribeiro. His research interests span a variety of topics in operations research, fuzzy systems, decision

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E-mail [email protected].

Web page http://www.campanella.org.

Rita A. Ribeiro is Associate Professor in the Department of Electronic and Computer Engineering of the Universidade Nova de Lisboa, Portugal. She is also coordinator and senior researcher of the CA3 research group, part of the research institution UNINOVA. Her research interests include fuzzy multiple-criteria decision making, decision support systems, fuzzy inference systems, fuzzy optimization and their applications to real-world problems.

E-mail [email protected].

Web page http://www.ca3-uninova.org.

View full text

A framework for dynamic multiple-criteria decision making

Abstract

Research highlights

Introduction

Section snippets

Classic MCDM model

Aggregation functions

Overview of related work in dynamic MCDM

Dynamic MCDM model

Numerical example: helicopter landing

Potential applications

Conclusions

Decision Support Systems

Acta Psychologica

Journal of Mathematical Psychology

Decision Support Systems

Journal of Mathematical Psychology

Organizational Behavior and Human Decision Processes

Fuzzy Sets and Systems

European Journal of Operational Research

Expert Systems with Applications

Decision Support Systems

Decision Support Systems

European Journal of Operational Research

Mathematical and Computer Modelling

Trends in Cognitive Sciences

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Appropriate choice of aggregation operators in fuzzy decision support systems

IEEE Transactions on Fuzzy Systems

Aggregation Functions: A Guide for Practitioners, volume 221 of Studies in Fuzziness and Soft Computing

Aggregation Operators: New Trends and Applications, volume 97 of Studies in Fuzziness and Soft Computing

Theory of capacities

Annales de l'Institut Fourier