Keywords

1 Introduction

Multi-Criteria Decision Analysis (MCDA) is a technique to assist with decision making in the presence of differing criteria [57]. According to Kenney [32], it is an approach that applies common logic to make decisions in the presence of multiple criteria. MCDA techniques are applied to real-world problems related to various socio-economic sectors, such as the  water sector, agriculture, tourism, energy, environment, biodiversity and forestry [59].

MCDA is a well-known area of Decision Theory [61] in which decisions are made to reach the final objective under a set of decision-making options [21, 58]. Hipel [28] divided decision problems into Multiple Participant-Single Criterion (MPSC) and Single Participant-Multiple Criteria (SPMC) types. Most problems in the real-world context can be categorized as multi-criteria decision problems, as a single criterion is judged to be unsatisfactory to help in decision making for complex real-world problems [40]. A comparison of MPSC and SPMC is presented in Table 1.

Table 1 Comparison of MPSC and SPMC Decision Making
Full size table

Doumpos and Zopounidis [17] divided decision-making problems into two groups: discrete and continuous. A discrete set of alternatives is associated with discrete problems in which each alternative is described in terms of attributes. During decision making, these attributes work as evaluation criteria. In continuous problems, infinite alternatives are possible. In decision making, one can only outline the feasible region where the alternatives remain [17].

The process that is followed in making a final decision by applying MCDA is called a problematic. In a discrete decision-making challenge, there are four main kinds of problematics: (i) choice, (ii) sorting, (iii) ranking and (ii) description [17]. See Fig. 1.

Fig. 1
figure 1

Source Adapted and modified from [17] with permission

Decision-making problematics with definitions.

Full size image

MCDA has become a specialized subject in the field of Operations Research (OR), which was initiated by the British Royal Air Force around 1937 to study the network of radar operators and how the judgments they made influenced the results of their radar operations [63]. MCDA is also one of the prominent fields of Management Science [34]. MCDA techniques have been exhaustively described and reviewed by many authors (e.g., [4, 17, 24]. The detailed theoretical underpinnings of different MCDA techniques can be found in Belton and Stewart [4].

1.1 MCDA Procedures

At present, many software programs have been developed to carry out MCDA analysis. In short, the MCDA technique usually takes a four-step procedure. The objectives are defined in the first step. In the second step, the decision criteria are selected based on the objectives to specify the alternative decisions. After deciding on the criteria and the alternatives, in the third step, the units of the criteria are normalized and weights are given to the criteria to reflect their relative value in decision making. The last step is to select and apply a mathematical algorithm to rank each alternative [25]. Table 2 gives more detail about each step.

Table 2 Steps in MCDA techniques
Full size table

1.2 Strengths and Weaknesses of MCDA

Belton and Stewart [4] presented the strengths and weaknesses of various MCDA techniques. MCDA leads to sensible, justifiable and explainable decisions. It helps to rank different options and find the most desirable outcome [16]. MCDA techniques are capable of considering a broad variety of conflicting but associated criteria [4, 70]. The strengths and weaknesses of MCDA from expert and stakeholder/participant perspectives are presented in Table 3.

Table 3 Strengths and weaknesses of MCDA techniques
Full size table

1.3 Classification of MCDA Techniques

MCDA techniques come from various “axiomatic groups” and “schools of thought” (Herath and Prato [25]:5) and have been classified in a number of ways [8, 9, 17, 23, 25, 42]. According to Hajkowicz et al. [23], MCDA techniques are either continuous or discrete. Commonly, MCDA techniques are classified into (i) Multi-Objective Decision Making (MODM) and (ii) Multi-Attribute Decision Making (MADM). MODM deals with the decision problems in a continuous decision space, whereas MADM is suitable when all objectives of a decision problem need to be satisfied. In the literature, experts have classified MCDA techniques into many groups. Examples of the classification schemes of MCDA techniques by different experts are presented in Table 4.

Table 4 Classification schemes of MCDA techniques
Full size table

1.4 Why Choose MCDA for Sustainability Assessment?

Sustainability assessment must integrate issues of economic, social and environmental interaction into decision making [14, 20, 58], and conflicting dimensions of economic, environmental, social, technical, human and physical issues are involved. Sustainability assessment aims to improve decision making in complex projects by involving the public and experts [19]. This is why MCDA is increasingly being applied to issues related to sustainability [25, 13, 58].

The assessment of sustainability is the key to ensuring sustainable development. For sustainability assessment of any development activities or any socioeconomic system, various information as well as stakeholders’ perspectives must be considered and integrated. Therefore, the assessment of sustainability can be considered a decision-making problem [55, 58] that requires a technique that is capable of integrating data from the three pillars of sustainability, following a transparent process, doing robust analysis and taking into consideration stakeholders’ opinions of sustainability criteria. MCDA techniques have this capacity as they follow a transparent structural process, are able to break  down complex decision problems, can trigger discussion among stakeholders, can incorporate stakeholders’ opinions on criteria and their weight and present the result visually [2, 39, 40, 58, 62, 69]. Therefore, MCDA techniques are applicable for sustainability assessment.

1.5 Selection of MCDA Techniques for Sustainability Assessment

All MCDA techniques come with pros and cons in terms of their ability to handle diverse information and weighting of the criteria. Specific techniques are suitable for specific situations [58]. For example, MAUT has the advantage of obtaining robust results and PROMETHEE has the advantage in ranking [11, 58]. Here, examples are presented of using MAUT and PROMETHEE to assess agricultural sustainability in light of these methods’ capacity. These two methods were selected on the basis of prerequisites (see Table 5) of the nature and scope of the study, available information, selected criteria and stakeholder opinion. Brief descriptions of MAUT and PROMETHEE are given below in Sects. 6.1 and 6.2.

Table 5 Prerequisites of MCDA techniques for sustainability assessment
Full size table

1.6 Multi-attribute Utility Theory (MAUT)

MAUT is widely applied in multi-criteria-based assessment [11] and is an important theory behind the procedure of MCDA [44]. In MAUT, the criteria can be assessed by integrating criterion values and relative or trade-off weighting [11]. A normalization process is applied to bring the criteria into a common dimension that is without unit [51, 58]. All the values of all the alternative criteria are combined and a single value score is generated, which enables comparison of the multiple preferences [12, 58]. Attributes of all criteria are used to evaluate the criteria. The relative importance of each attribute is reflected by weighting [45, 58]. MAUT can be applied to assess sustainability using the following formula:

$$v\left( x \right)\, = \,\sum\limits_{i = 1}^{n} {w_{i} v_{i} \left( x \right)}$$

where

v(x):

is equivalent to the overall value of an alternative

n:

is equivalent to the number of criteria,

wi:

is equivalent to the weight of criteria i, and

vi(x):

is equivalent to the rating of an alternative x with respect to a criteria i.

Here, the vi(x) is normalized in a range of 0–1 and the relative importance (wi) is given to the attribute i. Relative importance is assigned for each attribute/criterion by the values of worst to best [30]. MAUT structures the problem (value tree), making a reference model and finally conducting analyses [41].

1.7 Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE)

PROMETHEE, proposed by Brans et al. [5], is an outranking technique which is applicable for doing pair-wise comparison of the criteria to make a decision [66]. By considering quantitative and qualitative information of the criteria, it can generate a full ranking of the decisions from best to worst. This method is suitable where stakeholders’ participation is required for decision making Hermans et al. [26, 33, 62]. Weighting of the criteria is an important aspect of PROMETHEE and depends on the decision makers’ expertise. In this method, the preference function can be any of (i) strict, (ii) threshold, (iii) linear with threshold, (iv) linear over range and (v) stair step (level criterion). A narrative of these preference functions can be found in USACE and CDM [63]. The preference function values range from 0 to 1 [7]. The results of PROMETHEE can be visualised using Geometric Analysis for Interactive Aid (GAIA) software [4]. Figure 2 shows the steps for applying PROMETHEE to assess sustainability.

Fig. 2
figure 2

Source Behzadian et al. [3], PROMETHEE 1.4 Manual [49], Talukder and Hipel [60] with permission

Steps in PROMETHEE analysis.

Full size image

Both MAUT and PROMETHEE offer advantages and disadvantages depending on the decision-making criteria. A comparison of both techniques is presented in Table 6.

Table 6 Comparison of MAUT and PROMETHEE
Full size table

1.8 Application of MAUT and PROMETHEE for Agricultural Sustainability Assessment

Examples of the application of MAUT and PROMETHEE for agricultural sustainability assessment are drawn from Talukder et al. [57] and Talukder and Hipel [60]. In both papers, the agricultural sustainability of five types of agricultural systems is assessed: Bagda (shrimp)-based agricultural systems (S); Bagda-rice-based agricultural systems (SR); Rice-based agricultural systems (R); Galda (shrimp)-rice-vegetable-based integrated agricultural systems (I) and Traditional practices-based agricultural systems (T). Fifteen composite indicators (CI) drawn from six sustainability categories were used in the assessment: (i) Productivity (CI: Productivity); (ii) Stability (CI: Landscape stability, Soil health/stability, Water quality); (iii) Efficiency (CI: Monetary efficiency, Energy efficiency); (iv) Durability (CI: Resistance to pest stress, Resistance to economic stress, Resistance to climate change); (v) Compatibility (CI: Human compatibility, Biophysical compatibility); and (vi) Equity (CI: Education, Economic, Health, Gender). Overall assessment results of the two MCDA techniques are presented in Figs. 3 and 4.

Fig. 3
figure 3

Overall ranking of sustainability of agricultural systems using MAUT [57], with permission

Full size image
Fig. 4
figure 4

Overall ranking of sustainability of agricultural systems using PROMETHEE [60]

Full size image

A comparison of the merits and drawbacks associated with MAUT and PROMETHEE shows that both techniques are capable of assessing agricultural sustainability by considering a variety of data in different forms. Both techniques have the capacity to consider stakeholders’ opinion and values in sustainability assessment to generate complementary information. The capacity to consider stakeholder opinion and weighting for criteria for sustainability assessment is an advantage of both techniques since most sustainability assessment techniques cannot take stakeholder perspectives into consideration [58].

Overall, both case studies feature MAUT and PROMETHEE as useful, systematic, analytical tools for sustainability assessment. The step-by-step methodologies proved to be useful and suitable for assessing and ranking sustainability. MAUT can break down complex problems, structure them in a transparent way, enable participation of the stakeholders and create a space for discussion, incorporate stakeholders’ perspectives and present results visually and structurally [2, 39, 58]. Though it has some drawbacks, PROMETHEE’s holistic approach makes it useful to assess and compare the aspects of sustainability [58].

2 Conclusion

The cases in Sect. 6.1 demonstrate the applicability of MCDA techniques for sustainability assessment. More research is required to make the MCDA technique a commonly used approach to assess sustainability in different sectors. However, MCDA requires substantial mathematical knowledge for computation, which may make it less user-friendly. These challenges should motivate researchers to refine these techniques to assess sustainability.