Data analysis

We employed MCDA to analyse qualitative data of the FRS because the sustainability complexity and human needs are multi-dimensional concepts. MCDA is an approach to evaluate multiple conflicting criteria in decision making for future directions, and it has been used for sustainability in different disciplines (Munda 2016). Velasquez and Hester (2013) conducted a literature review and

SECTION 2.4: QUANTITATIVE APPROACHES

a b c d

a b d d

Figure 2.4: Fuzzy rating scale for sustainability profiling

analysis of common MCDA, and Antunes and Henriques (2016) discussed the most popular MCDA used in the energy sector. Both studies identified the following methods as the most common:

• Multi-Attribute Utility Theory (MAUT),

• Analytic Hierarchy Process (AHP),

• Case-Based Reasoning (CBR),

• Data Envelopment Analysis (DEA),

• Goal Programming (GP),

• Simple Multi-Attribute Rating Technique (SMART),

• ELimination Et Choix Traduisant la REalité (Elimination and Choice Expressing Reality; ELECTRE),

• Preference Ranking Organisation METHod for Enrichment Evaluation (PROMETHEE),

• Simple Additive Weighting (SAW), and

Multi-attribute utility theory

MAUT is based on the attributes (criteria) of alternatives, and it is an ordinal additive value function (Dyer 2016). The alternatives can incorporate performance and present them in the context of certainty. The main problems with MAUT are that alternatives need stronger assumptions and substantial input to make precise alternatives as well as to allow MAUT to derive ordinal judgement (Dyer 2016, Velasquez and Hester 2013).

Analytic hierarchy process

AHP, including its more generalisation extension analytic network process, is a pair-wise com- parison method and it is similar to MAUT. However, AHP has the characteristic of dependence assumptions and derives ratio judgement (Saaty 2016). Although the AHP is a structured depen- dence method and does not need intensive input, inconsistency in inherent assumptions is its main limitation (Saaty 2016, Velasquez and Hester 2013).

Case-based reasoning

The CBR approach provides a conclusion of decisions based on previous and most similar cases (Richter and Weber 2013). The CBR can be improved over time by adding more cases but if these cases are invalid, the results may be invalid because of uncertain and inconsistent data in the cases (Chen et al. 2008, Velasquez and Hester 2013).

Data envelopment analysis

DEA is a linear programming method to measure the efficiency of decision making alternatives. It requires a mix of MCDA to rate alternatives and then evaluates the efficiencies by comparing them (Cooper et al. 2004). In addition, DEA assists in uncovering relationships that remain hidden on using other methods but all input output data need to be precisely known (Velasquez and Hester 2013).

Goal programming

Similarly, GP requires a combination of MCDA to measure the weighted sums of deviations among alternatives against each other (Jones and Tamiz 2016). Although GP needs other MCDA to weight coefficients, it has the ability of producing infinite alternatives compared with other MCDA methods (Jones and Tamiz 2016).

Simple multi-attribute rating technique

SMART is the simplest form of MAUT. Rating alternatives against criteria in SMART or other weight assignment techniques produces the algebraic mean that becomes its ranking value (Ve- lasquez and Hester 2013). SMART is simple and requires less effort compared with other MCDA.

SECTION 2.4: QUANTITATIVE APPROACHES

However, the use of weight coefficients in this method is not convenient, and hence, SMART has to be combined with another MCDA to determine its coefficients (Konidari and Mavrakis 2007).

Elimination et choix traduisant la realité (elimination and choice expressing reality)

ELECTRE family consists of methods using pair-wise comparisons to rank and sort alternatives under each criterion, based on a concordance index and non-discordance analysis (Figueira et al. 2016). ELECTRE having several improved methods, such as ELECTRE I, II, III, IV and TRI, is convenient only with a large number of alternatives and a few criteria (Velasquez and Hester 2013). In addition, ELECTRE methods ignore the difference level between alternatives (Wang et al. 2009).

Preference ranking organisation method for enrichment evaluation

The PROMETHEE family is similar to ELECTRE but the former does not ignore the difference level between alternatives (Velasquez and Hester 2013). PROMETHEE consists of information between the criteria as well as within each criterion (Brans and De Smet 2016). However, rank reversal may occur under some conditions (Brans and De Smet 2016, Verly and De Smet 2013).

Simple additive weighting

SAW is a method in which each alternative value is equal to additive weighting of the criterion weight and attribute data (Antunes and Henriques 2016). SAW is simple but its result might not be logical because one criterion value largely differs from that of other criteria (Verly and De Smet 2013).

Technique for order of preference by similarity to ideal solution

TOPSIS identifies the best alternative that is nearest to an ideal solution and farthest from a negative ideal solution (Mairiza et al. 2014). The principles of TOPSIS are simple and positive ideal solutions and negative ideal solutions are formed (Mateo 2012). The benefit criteria in the positive ideal solution are maximised and the cost criteria are minimised, while the cost criteria in the negative ideal solution are maximised and the benefit criteria are minimised (Behzadian et al. 2012). Although TOPSIS is based on the preference ratio, the uncertainty assumption and vagueness of human feelings affect solutions (Wang et al. 2009).

Considering the simplicity and flexibility of use as well as the fact that it identifies both the shortest distance from the positive ideal and farthest distance from negative ideal solution, TOPSIS should be considered an important solution to analyse the positive and negative impact of sustainability. Further, to overcome imprecision or the vagueness of human feeling, TOPSIS has to be combined with FRS (see, Section 2.4.1). To analyse sustainability requirements, we utilise the FRS to collect stakeholders ranking and then analyse them through TOPSIS; see Chapter 5. For these reasons, we provide here a more detailed description of this method.

TOPSIS procedure

The following is the stepwise procedure of TOPSIS according to Behzadian et al. (2012):

Step 1: Construct a normalised decision matrix rij

rij = xij q Pm i=1x2ij , f or i = 1, · · · , m, j = 1, · · · , n (2.1)

if xij is an element of original decision matrix, x is the value in the i-th row and j-th column,

while m and n are the number of alternatives and criteria, respectively. where rij is a normalised value of xij in the decision matrix

Step 2: Construct the weighted normalised decision matrix vij

vij = wirij (2.2)

where wjis the weight for j criterion.

Step 3: Determine the positive ideal (A∗) and the negative ideal solutions (A0): Positive ideal solutions

A∗= {hmax(vij| i = 1, 2, . . . , m) | j ∈ J−i, hmin(vij| i = 1, 2, . . . , m) | j ∈ J+i} ≡ {vj∗| j = 1, 2, . . . , n},

(2.3) Negative ideal solutions

A0 = {hmin(vij| i = 1, 2, . . . , m) | j ∈ J−i, hmax(vij| i = 1, 2, . . . , m) | j ∈ J+i} ≡ {v

0

j | j = 1, 2, . . . , n},

(2.4) where,

J+= {j = 1, 2, . . . , n | j}J+= {j = 1, 2, . . . , n | j}associated with the positive criteria, and

J−= {j = 1, 2, . . . , n | j}J−= {j = 1, 2, . . . , n | j} associated with the negative criteria.

Step 4: Calculate the separation measures: The separation from positive ideal is

S∗ = v u u t n X j=1 (vij − vi∗)2, i = {1, · · · , m} (2.5)

Similarly, the separation from negative ideal is

S0 = v u u t n X j=1 (vij − v 0 i)2, i = {1, · · · , m} (2.6)