Εvaluation of Measures for Combating Water Shortage Based on Beneficial and Constraining Criteria

Abstract

Water Scarcity encompasses both permanent and occasional water resources shortages. Measures to combat water scarcity are of different nature dependent on whether they intend to withstand permanent or occasional water deficiency. It is the aim of this paper to discuss and propose a systematic framework for the evaluation of measures of the Contingency Plan of a drought affected area, so that the measures are compatible and complementary to the long term Strategic Plans. For this reason the establishment of two sets of criteria is proposed, the beneficial and the constraining criteria. The beneficial criteria are those representing the short term good performance, whilst the constraining criteria express the incompatibility with the long term Strategic Plans and the long term negative impacts to the environment and the society. The beneficial criteria are aggregated by applying the widely-used multicriteria method of the weighted Euclidean Distance. The compatibility of the constraining criteria with the beneficial criteria is expressed by the use of suitable fuzzy implications. Finally a simple weighted sum is used in order to take into account both the beneficial criteria and the compatibility between the beneficial and constraining criteria. Based on this approach the selection and prioritisation of measures is enhanced leading to a more balanced and realistic defence against drought and water shortage. A numerical application is presented for illustrating the proposed methodology taking the city of Heraklion (Crete) as a case study.

Appendix

Proposition

If we express the negative influence of the constraining criteria by using the crisp complement (α′ = 1−α), then the use of the S-implication with respect to α′ and f ^* leads to a corresponding fuzzy intersection with respect of α and f ^* .

Proof

Let J a S-implication and let the crisp complement, α′ = 1−α = N(α), then according to definition of the S-implications it holds (Eq. 5):

$$ 1-J\left({f}^{*},a^{\prime}\right)=1-J\left({f}^{*},\;1-a\right)=1-\left(S\left(1-{f}^{*},1-a\right)\right) $$

(A1)

In fuzzy logic the De Morgan laws hold for a selected combination of the fuzzy union, S, fuzzy intersection, T, with respect to a fuzzy complement (here the crisp negation). Therefore for a dual choice of both the fuzzy intersection and fuzzy union it holds:

$$ 1-\left(S\left(1-{f}^{*},1-a\right)\right)=T\left({f}^{*},a\right) $$

(A2)

It should be mentioned that only some combinations of fuzzy unions, fuzzy intersections, and fuzzy complements can satisfy the De Morgan laws (Klir and Yuan 1995). In this case, a combination that can satisfy both the two laws of the conventional logic (which are widely known as De Morgan Laws) could be selected.