Abstract
An important problem in Multi-Criteria Decision Analysis arises when one must select at least two alternatives at the same time. This can be denoted as a multiple choice problem. In other words, instead of evaluating each of the alternatives separately, they must be combined into groups of n alternatives, where n = 2. When the multiple choice problem must be solved under multiple criteria, the result is a multi-criteria, multiple choice problem. In this paper, it is shown through examples how this problemcan be tackled on a bipolar scale. The Choquet integral is used in this paper to take care of interactions between criteria. A numerical application example is conducted using data from SEBRAE-RJ, a non-profit private organization that has the mission of promoting competitiveness, sustainable developmentand entrepreneurship in the state of Rio de Janeiro, Brazil. The paper closes with suggestions for future research.
Highlights
The project portfolio management process involves different stages of decision making
We have concluded that the bipolar Choquet integral is adequate for solving multiple choice problems
P3 − P5 sustainable development of the region; 10 and 10 10 and 10 10 and 10 mean = 10 mean = 10 mean = 10 high capacity to interact with other sectors of the economy; high capacity to generate employment and income high capacity to contribute to the
Summary
The project portfolio management process involves different stages of decision making. Selecting a portfolio of projects is a problem that has been approached using Multi-Criteria Decision Analysis (Vetschera & Almeida, 2012; Anagnostopoulos & Mamanis, 2010; Carazo et al, 2010). The objective of this paper is to show how the bipolar Choquet integral can be used for determining two or three combinations of choices for projects to be performed at the same time under multiple criteria, given that there are interactions between criteria. A numerical application example is conducted using the data from Gomes et al (2009). The Choquet integral makes use of fuzzy measures. Those measures are very important for problems that require reliability (in a sense that an element belongs to a set) and plausibility which is dual to reliability.
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