An interval version of PROMETHEE for the comparison of building products' design with ill-defined data on environmental quality

doi:10.1016/S0377-2217(98)00074-5

European Journal of Operational Research

Volume 109, Issue 2, 1 September 1998, Pages 522-529

https://doi.org/10.1016/S0377-2217(98)00074-5 Get rights and content

Abstract

Life Cycle Assessment (LCA) is a powerful technique used to calculate total input and output flows of materials and energy from and to the environment during every step of a product life. A measure of a product Environmental Quality (EQ) can then be derived and help in the selection and in the design of more environmentally friendly design alternatives. EQ is a multicriteria measurement. In the construction field, LCA flows cannot be known with precision without loss of realism. Hence intervals have been introduced to model them. Thus, different designs are characterized by interval multicriteria measures. Manipulation of such environmental performances calls for a MCDA method which (1) does not allow for trade-offs between criteria, (2) preserves as much information as possible and (3) is simple enough to be understood by non-specialist users. PROMETHEE was identified as a suitable method according to the previous criteria, but it is not able to handle interval performances so far. We discuss the necessary changes to devise an interval version, called “PROMETHEE I”.

Section snippets

On the environmental quality of building products

There is a growing claim from consumers, manufacturers, and various governmental bodies, for an assessment of the environmental quality of products. This claim is becoming stronger in the construction field as well. Architects want to know how environmentally friendly a given product is, manufacturers want to improve their products' designs for marketing needs, and users are getting very sensitive to indoor air quality issues.

Life Cycle Analysis (LCA) is a very powerful technique to calculate

Environmental quality and the utility theory

According to some (SETAC, 1994), EQ should be aggregated into a single index, thus providing a very convenient way to assess an individual product's EQ and to compare alternative products or designs on a single scale.

However, most single index methods are derived from a weighted average, thus allowing for clean air to compensate for dirty water. We consider that it is against what environmental management should lead to. While trade-offs between criteria are the essence of decision, we consider

Environmental quality and outranking

Outranking methods are an attractive alternative to the “utility” approach. It seems, however, that very little applications related to LCA have been published. ELECTRE (I and III) has been used in France in connection with LCA (Rousseaux, 1993). The basic principle of outranking is that, providing that alternative a performs better than alternative b on a majority of criteria and that there is no criterion such that b is strongly better than a, then a will be preferred over b (democratic

The current framework

The following briefly describes the general PROMETHEE framework. Let A be a set of alternative products or designs to rank or choose from. Assuming k criteria have been considered, for each alternative a ∈ A, f_j(a) is the value of criteria j for alternative a. A ranking is performed in three steps:

Step 1. A preference function P_j is associated with each criterion j. P_j(a,b) is calculated for each pair of actions. It varies from 0 to 1, starting at 0 if f_j(a)=f_j(b) and increasing with f_j(a) − f_j(b),

Ranking alternatives

Now, ranking alternatives amounts to ranking interval values of leaving, entering and net flows, rather than crisp ones. It can be done providing that new preorders are defined, but relevance can be questioned as interval enlarge and get more “similar” one from the other. Hence another approach must be looked for. This new approach should ideally (i) allow for a better differentiation between intervals, and (ii) be usable with existing PROMETHEE preorders.

Numerical application

The goal of this small study is to compare four alternative designs for the fabrication of 100 m² plaster wallboards. The data are real but outdated. They were calculated from an EPA study dating back to 1974 (EPA, 1977). In addition, the following results are incomplete. Hence they are not relevant to the contemporary European gypsum industry but they are sufficient to illustrate the method proposed in Section 5.

The four alternatives combine open pit/underground mining of the gypsum ore and

Concluding remarks

An extension of the PROMETHEE framework called “PROMETHEE I” has been introduced to cope with interval criteria introduced for the evaluation of the environmental quality of building products through LCA. Of course, this procedure can be applied to any situation where the decision matrix is an interval matrix.

Leaving, entering and net flows can be calculated using simple interval arithmetic and further sampled in two average cases. The resulting continuous fuzzy flow is defuzzyfied using a

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