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Waste treatment: an environmental, economic and social analysis with a new group fuzzy PROMETHEE approach

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Abstract

Most complex decisions involve several stakeholders and therefore need to be solved using a group multi-criteria decision method. However, stakeholders or decision-makers often have divergent views, especially in the environmental sector. In order to integrate this divergence, a new group fuzzy PROMETHEE approach is introduced to combine the traditional environmental criteria of life cycle assessments with social and economic criteria. The modelling of uncertainty within the group of decision-makers using a fuzzy approach makes this method unique. The proposed fuzzy approach differs significantly from the standard one. The decision-makers express their judgments in crisp forms. In order to take into account the intrinsic dispersion of judgments within the group, a posteriori fuzzification procedure is applied. The crisp values are not simply aggregated; they are converted into a triangular fuzzy number based on the given evaluations. As a consequence, the definition of fuzzy membership functions, as required in standard fuzzy logic, is not required, which simplifies the process and makes it more reliable. The new approach is illustrated with a real case study concerning the selection of the best waste treatment solution in a natural park from among a traditional incinerator and an innovative integrated plant.

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Abbreviations

I :

Number of alternatives

M :

Number of decision-makers

J :

Number of leave criteria

R :

Number of criteria

J O :

Set of quantitative (i.e. objective) leave criteria

J S :

Set of qualitative (i.e. subjective) leave criteria

J :

Set of leave criteria where \( J = J^{\text{O}} \cup J^{\text{S}} \), with \( J^{\text{O}} \cap J^{\text{S}} = \emptyset \)

a i :

Alternative, where \( i = 1, \ldots ,I \)

d m :

Decision-maker, where \( m = 1, \ldots ,M \)

c j :

Leave criterion, where \( j = 1, \ldots ,J \)

l j :

Level of c j in the hierarchy, where \( j = 1, \ldots ,J \)

c r :

Criterion, where \( r = 1, \ldots ,R \)

\( \Gamma\left( {c_{r} } \right) \) :

\( \left\{ {{\text{sub - criteria of}} c_{r} } \right\} \), where r = 1,…,R

w m,r :

Weight assigned to c r by d m , where \( r = 1, \ldots ,R \) and \( m = 1, \ldots ,M \)

w m,j :

Weight assigned to c j by d m , where \( j = 1, \ldots ,J \) and \( m = 1, \ldots ,M \)

x i,j :

Value of alternative a i for the criterion c j , where \( i = 1, \ldots ,I \) and \({c_{j}} {\in} {J^{\text{O}}}\)

x i,m,j :

Value of alternative a i for the criterion c j given by decision-maker d m , where \( i = 1, \ldots ,I \), \( c_{j} \in J^{\text{S}} \), and \( m = 1, \ldots ,M \)

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Acknowledgments

This research was partly funded by the EU as part of the project LIFE08 ENV/IT/000388 RELS—Innovative chain for energy recovery from waste in natural parks (for more details see www.life-rels.eu).

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Authors and Affiliations

  1. Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Via Amendola 2, Padiglione Morselli, 42122, Reggio Emilia, Italy

    Francesco Lolli, Rita Gamberini, Bianca Rimini, Anna Maria Ferrari & Roberto Savazza

  2. Centre for Operational Research and Logistics, Portsmouth Business School, University of Portsmouth, Portland Street – Richmond Building, Portsmouth, PO1 3DE, UK

    Alessio Ishizaka

  3. Department of Civil Buildings Engineering and Architecture, Università Politecnica delle Marche, Via Brecce Bianche 12, 60131, Ancona, Italy

    Simona Marinelli

Authors
  1. Francesco Lolli
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  2. Alessio Ishizaka
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  3. Rita Gamberini
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  4. Bianca Rimini
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  5. Anna Maria Ferrari
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  6. Simona Marinelli
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  7. Roberto Savazza
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Corresponding author

Correspondence to Alessio Ishizaka.

Appendix

Appendix

See Table 8

Table 8 The fuzzy decision matrix
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Lolli, F., Ishizaka, A., Gamberini, R. et al. Waste treatment: an environmental, economic and social analysis with a new group fuzzy PROMETHEE approach. Clean Techn Environ Policy 18, 1317–1332 (2016). https://doi.org/10.1007/s10098-015-1087-6

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