**2. Methodology**

#### *2.1. Overview of Fuzzy Cognitive Maps*

FCMs are soft computing techniques that combine fuzzy logic and neural networks [31]. They were first introduced by Kosko [21,32] as fuzzy-graph structures for representing causal reasoning. They provide a more flexible and natural ability for knowledge representation and reasoning, which are essential to intelligent systems [33,34].

A set of nodes (concepts), representing the key elements of the given system, and directed arcs (links), defining the causal relationships between the nodes, form an FCM [35]. Each concept is indicated by *Ci*, *i* = 1, ... , *N* (where *N* is the number of concepts in the problem domain) and is also specified by an activation value *Ai* in [0, 1]. The links are labeled with fuzzy weights in the interval of [0, 1] or [−1, +1], which show the strength of the impact between the concepts [36]. Weights of links are associated with a weight value matrix E NxN, where each element of the matrix *wij* takes values in [−1, +1]. There are three types of weights:


Word weights like "little" or "somewhat" can be used instead of numeric values [37]. Figure 1 shows an example of a FCM with its corresponding adjacency weight matrix.

**Figure 1.** Fuzzy cognitive map (**left**) and the correspondent weight adjacency matrix (**right**), showing the positive and negative causal influences.

An FCM is not a static representation of the world; FCM's graph structure facilitates causal reasoning, where calculations can be made to assess the consequences of a specific system state. In [38], *auto-associative neural network* mechanisms were used to study the system dynamics of FCM models and produce projections for different possible scenarios.

We used a multi-step FCM development process, as shown in Figure 2.

**Figure 2.** A visual illustration of the fuzzy cognitive map (FCM) development process.

#### *2.2. Obtaining Cognitive Maps from the Participants*

This study adopted a mixed-concept design approach for obtaining cognitive maps involving open-concept design followed by closed-concept design. Expert-based FCM was obtained using open-concept design. A total of 31 national and state-level implementers identified 20 categories of main concepts and 129 sub-concepts. The visual representation of this expert-based FCM model is depicted in Figure 3, which will be further compared with the models derived from the aggregation processes in order to help this study meet its goals.

**Figure 3.** Expert-based FCM model. **Note:** SHGs federate into VO and VOs federate into CLF. These together called CBOs (community-based organisations).

We prepared a protocol/instrument based on the expert-based FCM model drawing all the 20 categories of main concepts and 129 sub-concepts on the paper.

Four different groups of women functionaries of DAY-NRLM of Jammu and Kashmir state of India—The Self-Help Groups (SHGs), the Village Organization (VOs), the Cluster Level Federations (CLFs), and the Community Resource Persons (CRPs) constructed FCMs in groups of 4–5 members. The SHGs group consists of 36 participants, the VOs have 52 participants, and the CLFs comprise 60 participants, whereas the CRPs include 31 participants. We generated a list of SHGs, VOs, and CLFs, to be interviewed for the FCM exercise, using "Microsoft Excel RAND function" from the 10 districts of Jammu and Kashmir, 5 districts from each region. In total, 179 individual fuzzy cognitive maps were collected during the FCM exercise from approximately 600 participants coming from 10 districts of the state of Jammu and Kashmir in India.

Every key concept was formed from a list of certain sub-concepts that define it well. The subconcepts were introduced by the experts and policymakers to offer a deeper understanding of the examined problem, making it clear to the participants. Table 1 illustrates all the sub-concepts for each key concept.




**Table 1.** *Cont.*


**Table 1.** *Cont.*

Meanwhile, participants of all the four groups (SHG, VO, CLF, and CRP) were asked to assign a numerical value (degree of significance) to every sub-concept on a scale of 1–10 in order to assess the impact of each sub-concept to the corresponding key concept. An overall average degree of significance was calculated for every key concept to estimate the significance of each concept in the examined FCM model. This process also helped us in the next step, with the selection of the most important concepts for policy-making for the scenario analysis.

Table 2 illustrates an example regarding the mean values of the degree of significance for the three sub-concepts of the key concept C1, from each group of the Kashmir region, along with the calculated average value (degree of significance) that corresponds to the key concept C1.

**Table 2.** Degree of significance for the sub-concepts of C1, for Kashmir. CRP: Community Resource Persons.


#### *2.3. Coding Individual Cognitive Maps into an Adjacency Matrix*

Individual fuzzy cognitive maps were coded into separate excel sheets to form adjacency matrices [39,40]. The values were coded into the square matrix only when a connection existed between two concepts [39]. Weights given to each link were then normalised between 0 and +1 (the value 7 was normalised to 0.7) for coding into the adjacency matrix [40–42].

#### *2.4. Aggregating Individual Fuzzy Cognitive Maps from Each Group to Produce Aggregated FCMs*

All coded maps from each group were aggregated using the two aggregation methods, the weighted average, and the OWA, to make collective fuzzy cognitive maps. Two collective FCMs were created for every group of participants for each aggregation method, named as the average-FCM and OWA-FCM.

#### 2.4.1. Average Aggregation

We aggregated individual FCMs to form collective-FCM through matrix addition [39,41,43–45]. The collective-FCM represents the perception of all members of a particular stakeholder group.

Considering *n* stakeholders assign a weight value *wij*, between the nodes *Ci* and *Cj* on individual FCMs, then the aggregated weight *w*(*ave*) *ij*between the average value of the *n* weights *wij*:

$$w\_{ij}^{(\text{are})} = \frac{w\_{ij}^{(1)} + w\_{ij}^{(2)} + \dots + w\_{ij}^{(n)}}{n}.\tag{1}$$

2.4.2. OWA Aggregation

> An OWA operator [19] of dimension n is a mapping:

$$f: \mathbb{R}^n \to \mathbb{R},$$

that has an associated weighting vector *W*

$$\mathcal{W} = \begin{bmatrix} w\_1 & w\_2 & \dots \ w\_n \end{bmatrix}^T,\tag{2}$$

such that

$$
\Sigma\_i w\_i = 1; \ w\_i \in [0, 1], \tag{3}
$$

where

$$f(a\_1, \ldots, a\_n) = \sum\_{j=1}^n w\_j \, b\_j \tag{4}$$

where *bj* is the jth largest element of the collection of the aggregated objects *a*1, *a*2 ... , *an*. The function value *f*( *a*1, ... , *an*) determines the aggregated value of arguments *a*1, *a*2 ... , *an*.

A fundamental aspect of the OWA operator is the re-ordering step, in particular, an argumen<sup>t</sup> *ai* is not associated with a particular weight *wi* but rather a weight *wi* is associated with a particular ordered position *i* of the arguments. A known property of the OWA operators is that they include the *Max*, *Min*, and arithmetic mean operators for the appropriate selection of the vector *W*:

$$\begin{aligned} \text{i.} \qquad \text{For } W = \begin{bmatrix} 1 \\ 0 \\ \vdots \\ 0 \end{bmatrix}, f(\begin{bmatrix} a\_{1\prime} & \dots & a\_{n} \end{bmatrix} = \text{Max } a\_{i\prime} \\ \text{ii.} \qquad \text{For } W = \begin{bmatrix} 0 \\ 0 \\ \vdots \\ 1 \end{bmatrix}, f(\begin{bmatrix} a\_{1\prime} & \dots & a\_{n} \end{bmatrix} = \text{Min } a\_{i\prime} \\ \text{iii.} \qquad \text{For } W = \begin{bmatrix} 1/n \\ 1/n \\ \vdots \\ 1/n \end{bmatrix} \\ \text{iii.} \qquad \text{For } W = \begin{bmatrix} 1/n \\ 1/n \\ \vdots \\ 1/n \end{bmatrix}, f(\begin{bmatrix} a\_{1\prime} & \dots & a\_{n} \end{bmatrix} = \frac{1}{n} \sum\_{i=1}^{n} a\_{i} \end{aligned}$$

It can be easily seen [46] that the OWA operators are aggregation operators, satisfying the commutativity, monotonicity, and idempotency properties and are bounded by the *Max* and *Min* operators, for OWA operators:

$$\lim\_{i} a\_{i} \le f(\; a\_{1}, \; \dots, \; a\_{n}) \le \max\_{i} a\_{i}. \tag{5}$$

Because this class of operators runs between the *Max* (*or*) and the *Min* (*and*), the author of [24] introduced a measure to characterise the type of aggregation being performed for a particular value of the weighting vector. This measure, called the *orness measure* of the aggregation, is defined as:

$$\text{Orness } (W) = \frac{1}{n-1} \sum\_{i=1}^{n} (n-1)w\_i. \tag{6}$$

As suggested by Kosko [24], this measure, which lies in the unit interval, characterises the degree to which the aggregation is like an *or* (*Max*) operation. It can be shown as follows:

$$\text{orness}\left(\left[1\,0\ldots0\right]^T\right) = \mathbf{1},\tag{7}$$

$$\text{mess}\left(\left[0\,0\,\dots\,1\right]^T\right) = \,0,\tag{8}$$

$$\text{orness}\left(\left[\frac{1}{n}\ \frac{1}{n}\ldots\ \frac{1}{n}\right]^T\right) = 0.5.\tag{9}$$

Therefore, the, *Min*, and arithmetic mean operators can be regarded as OWA operators with degree of orness, respectively, 1, 0, and 0.5.

#### 2.4.3. Learning OWA Operators for Aggregating FCM Weights

This study took into consideration a previously conducted preliminary research [47] about an alternative FCM aggregation method using OWA operators and made it one step further. Specifically, learning OWA operators' weights were introduced for aggregating FCM connections/links defined by multiple experts and/or stakeholders. This work focused on developing an alternative aggregation methodology for the FCM modelling, in order to fill the absence of learning OWA operators in aggregation of weights in FCMs, considering that FCMs have been proposed as a unique methodology able to aggregate diverse sources of knowledge to represent a "scaled-up" version of individuals' knowledge and beliefs [39,48]. Moreover, learning operators were used in this study for defining weights among the concepts, so that the studying of the OWA aggregation approach would be strengthened in terms of performance. This method has particularly broad applicability and had high effectiveness when a large number of participants/stakeholders were present. A complex real-life strategic decision-making problem was studied, in which the proposed methodology was applied in order to examine/validate this approach. Specifically, the studied problem dealt with the aggregation and modeling of communities' perception, as well as scenario analysis using the FCM-based simulation process implemented by the new FCMWizard tool [31].

In this study, we present an algorithm that can be used for aggregating weights assigned by experts/stakeholders' opinion in designing FCMs. The proposed algorithm learns the weights associated with a particular use of the OWA operator from a group of experts and/or stakeholders of the specific scientific domain. The OWA weights can be obtained through the following procedure:

At first, experts' opinions are considered as argumen<sup>t</sup> values (*ak*1, *ak*2 ... , *akn*).


$$\rho \mathop{\text{M}}\_{i} \mathop{\text{Max}}\_{i} a\_{i} + (1 - \rho) \mathop{\text{M}}\_{i} \mathop{\text{min}}\_{i} a\_{i} = d. \tag{10}$$


$$
\hat{d}\_k = b\_{k1} \ w\_1 + \ \ b\_{k2} \ w\_2 + \dots + \ b\_{kn} \ w\_n \tag{11}
$$

with initial values of the OWA weights *w*1 = 1/*<sup>n</sup>*.


$$
\lambda\_i(l+1) = \lambda\_i(l) - \beta w\_i(l)(b\_{ki} - \hat{d}\_k)(\hat{d}\_k - d\_k) \tag{12}
$$

with initial values λ*i* (0)=0, *i* = (1, ... , *<sup>n</sup>*), and a learning rate of β = 0.35. vii Step 7: Use λ*i*, *i* = (1, ... , *<sup>n</sup>*),, to provide a current estimate of the weights

$$w\_i = \frac{e^{\lambda\_i(l)}}{\sum\_{j=1}^n e^{\lambda\_i(l)}}, i = (l, n) \tag{13}$$

viii Step 8: Update *wi* and ˆ *dk* at each iteration until the estimates for all the λ*i* converge to, that is, Δ = | λ(*l* + 1) − λ(*l*) |, are small.

In what follows, an explanatory paradigm considering three experts will better illustrate the proposed FCM construction approach in an environmental domain.

As mentioned above, the experts' opinions are considered as argumen<sup>t</sup> values *ak*1, *ak*2 ... , *akn*, and the weight between two concepts as a sample. Zero values for weights were not considered in the aggregation process. An FCM model consisting of 7 concepts and 14 weighted connections among concepts was selected to show how the above steps are implemented (Table 3).


**Table 3.** The explanatory paradigm for aggregating three experts' opinions on agriculture.

We calculated the aggregated values using various values for parameter ρ within ρ (0.01 ≤ ρ ≤ 0.2). For example, ρ = 0.153; 0.131; 0.181; 0.075; 0.055.

Using *min* and *max* values of ρ, the aggregated value of weight was calculated as follows.

$$(0.153(0.58) + (1 - 0.153)(0.43) = 0.45.)$$

We initialised <sup>λ</sup>*i*(0) = 0, *i* = (1, *<sup>n</sup>*), β = 0.35, and *w*1 = *w*2 = *w*3 = 0.33. The estimated values of λ*i* after 108 iterations were

 $\lambda\_1 = 0.63$ ,  $\lambda\_2 = -0.19$ ,  $\lambda\_3 = 0.82$ .

The following OWA weights were calculated considering the above λ*i*:

$$w\_1 = 0.146, \ w\_2 = 0.227, \ w\_3 = 0.626.$$

We followed the same process for parameter ρ for 0.3 <ρ< 0.5 and 0.5 <ρ< 0.7.

Table 4 depicts the calculated values for OWA aggregated weights for all interrelationships among FCM concepts, as well as the deviations between the benchmark weight Wb (average method) and the Wowa, weight produced by learning OWA operators.


**Table 4.** Weights produced by learning OWA (ordered weighted averaging) operators.

#### *2.5. Visual Interpretation of Collective FCM*

The collective FCMs were analysed using the FCMWizard software tool (www.fcmwizard.com) [31]. The tool includes modelling and visualisation capabilities for the consensus FCM models, depicting the connections among the factors and also reflecting the importance of different concepts within various asset classes [43]. The average-FCM models designed by each group (SHG, VO, CLF, CRP) and produced by the FCMWizard tool are illustrated in the figures below (Figures 4–7).

**Figure 4.** Fuzzy cognitive map of SHG group of DAY-NRLM (Jammu-Kashmir National Rural Livelihoods Mission) programme.

**Figure 5.** Fuzzy cognitive map of VO group of DAY-NRLM programme.

**Figure 6.** Fuzzy cognitive map of CLF group of DAY-NRLM programme.

**Figure 7.** Fuzzy cognitive map of CRP group of DAY-NRLM programme.

#### *2.6. FCM-Based Simulations*

Typically, an FCM of *n* concepts could be represented mathematically by an *n* × *n* weight matrix (*W*). By feeding the fuzzy cognitive map with an initial stimulus state vector *X(k)* (state vector at time (*k*)), it can model the evolution of a scenario over time by evolving forward and letting concepts interacting with one another. Each subsequent value of the concept state *X(k*+*1)* can be computed as previous state *X(k)* and weight matrix multiplication, according to Equation (14):

$$X\_i^{(\kappa+1)} = f\left(\sum\_{j=1,\ j\neq i}^n w\_{ji} \times X\_j^{\kappa}\right). \tag{14}$$

Based on the literature, two other equations were proposed for FCM inference, the modified Kosko (Equation (15)) and the rescaled Kosko (Equation (16)):

$$\mathbf{X}\_{i}^{(\kappa+1)} = f\left(\mathbf{X}\_{i}(t) + \sum\_{\substack{j=1\\j\neq i}}^{n} \mathbf{X}\_{j}(t) \cdot \boldsymbol{w}\_{j,i}\right) \tag{15}$$

$$X\_i^{(\kappa+1)} = f\left(\left(2 \times X\_i^{\kappa} - 1\right) + \sum\_{\substack{j=1,\ j \neq i}}^n w\_{ji} \times \left(2 \times X\_j^{\kappa} - 1\right)\right),\tag{16}$$

where *X*(κ+<sup>1</sup>) *i* is the value of concept *Ci* at simulation step κ + 1, *X*(κ) *j* is the value of concept *Cj* at the simulation step κ, *wji* is the weight of the interconnection between concept *Cj* and concept *Ci*, and *f*(·) is the threshold transfer function used to retain the values within the range of [0, 1] or [−1, +1]. Generally, the most commonly used transfer function is Sigmoid [49], as shown by Equation (17).

$$f(\mathbf{x}) = \frac{1}{1 + e^{-\lambda x}}\tag{17}$$

where λ is a real positive number (λ > <sup>0</sup>), which determines the steepness of the continuous function *f*, and *x* is the value *X*(κ) *i*for a given iteration.

The simulation stops when the system reaches equilibrium, that is, a limit vector is reached as *X<sup>t</sup>* = *Xt*−<sup>1</sup> or when *X<sup>t</sup>* − *Xt*−<sup>1</sup> ≤ *e*, where *e* is a residual, describing the minimum error di fference among the subsequent concepts. Its value depends on the application type and it is typically set to 0.001.

#### **3. Results and Discussion**

#### *3.1. Characteristics of the Key Concepts of the DAY-NRLM Programme*

When there are a large number of concepts that need to be studied individually, then it is necessary to keep only the most influential ones. The filtering technique of key concepts is common in scenario planning and helps linking storylines to the quantitative model, as well as to pay attention to pivotal concepts that can influence, directly or not, the outcome of the examined system, or even significantly change its balance [50]. Key concepts were mainly identified by the experts in the FCM-based scenario analysis or emerged by certain characteristics of the studied model. There were three indicators, based on the connection weights, which help researchers to recognise the important key concepts of the system—indegree (weight of inbound links), outdegree (weight of outbound links), and degree centrality. The first two indicate to what extent a concept is a transmitter (influential) or receiver (dependent). This is similar to the bi-dimensional categorisation of influence-dependence axes in cross-impact analysis [51]. Degree centrality is the relative importance of a concept within the FCM

structure, which is calculated by the sum of the corresponding absolute indegree and outdegree causal weights [52]. These calculated indices for the collective average-FCM, along with the concepts identified previously, are summarised in Table 5. Additionally, the overall specifications of the above FCM model are presented in Table 6.

**Table 5.** Finalised concepts, their description, and type with three major indices values (indegree, outdegree, and degree centrality) for the collective average-FCM.


**Table 5.** *Cont.*


**Table 6.** Specifications of the FCM model.


#### *3.2. Characteristics of the Sub-Concepts of the DAY-NRLM Programme*

Every participant was given a list of sub-concepts for each key concept (as presented in Table 1) to assign a degree of significance on the scale of 1–10, where 10 is the most significant sub-concept and 1 the least significant. This procedure was followed for two regions, Jammu and Kashmir. Table 7 includes the key concepts with the respective mean values for both regions, as well as the overall average value of the degree of significance, whereas the next figure (Figure 8) illustrates these values in a graph for better visual interpretation of the results.


**Table 7.** Mean values of significance for two regions and the average degree of significance.

**Figure 8.** Mean values of significance for the regions of Jammu and Kashmir.

Having a thorough look at the values presented in Table 8, it was observed that the concepts C1, C2, C3, C15, C17, C18, and C20 were among concepts with the highest values for both degree centrality and degree of significance. Moreover, comparing these values with the corresponding degree centrality of the aggregated and the expert-based FCM model, we can verify that the key concepts mentioned earlier can be indeed selected as the most significant ones, and will be further used in the scenario analysis.


**Table 8.** The average degree of significance and degree centrality values for all key concepts.

#### *3.3. Aggregation Results*

In this section, the results produced from the application of the two aggregation methods on the FCM models are presented. The FCM models constructed by every participant group (SHG, VO, CLF, and CRP) were aggregated using the two aggregation methods, the average, and the OWA. A collective FCM was produced from each of these methods. The aggregation process was delivered with the help of the OWA tool that was developed for this purpose.

From the comparative analysis that was conducted among the aggregated average-FCM, OWA-FCM, and experts-based FCM, it was observed that the minimum mean deviation value (= 0.12) was located between the OWA-FCM and the experts-based FCM. This means that the OWA-FCM model resembles the structure of the Expert-based FCM and consequently can present a similar performance to the model constructed by the experts.

#### *3.4. Scenario Results*

#### 3.4.1. Scenario Development

For the scenario analysis, the researchers identified the most important concepts (called decision concepts) that a ffected the status of the system being examined. During the FCM exercise, we also recorded the degree of significance of every key concept on the basis of the perception of over 600 participants of SHGs, VOs, CLFs, and CRPs. During the FCM exercise, the participants also identified the most significant concepts in the system. On the basis of the FCM models prepared by the participants, we can infer that social harmony (C20), women's socio-economic empowerment (C16 and C17), and personal well-being and personality development (C18) were the most significant concepts, which are likely to have considerable impacts on the system. The results for the same analysis are presented in Figure 9. The first established approach in scenario planning was the selection of the most important concepts. The seven concepts that were selected are C1—"Building strong CBOs", C2—"Governance of CBOs", C3—"Capacity building", C5—"Access to formal credit", C15—"Political empowerment", C16—"Social empowerment", and C17—"Economic empowerment". These concepts, assigned by the programme participants and implementers, were selected properly as they were among concepts with the highest degree centrality, having both in/out-degree values, whereas their degree of significance was the highest among all key concepts (see Table 8). Thus, they could significantly influence the dynamics of the system. The selected scenarios with their concepts are briefly presented in the following Table 9.

**Figure 9.** Most significant concepts of the DAY-NRLM (*Deendayal Antyodaya Yojana*-National Rural Livelihoods Mission) programme.



#### 3.4.2. FCM-Based Simulations/Scenario Analysis

FCM-based simulations can offer a deeper understanding of the concepts' behavior and their relations in terms of how one concept affects others. The researchers conducted FCM-based simulations/scenario analyses for the respective case study. The simulation process was performed by "clamping" the initial values of the key concepts one-by-one (Equation (14)). This outcome was compared against a baseline scenario where the system (output vector) reached the steady-state through clamping all the initial values to zero. Exploring the dynamic change of concepts' values between the baseline steady-state and outcome of the clamping procedure enabled quantitative interpretation of the impact of the key concepts on the system. The simulation process entailed the application of a sigmoid function with lambda = 1 as a threshold function on the adjacency matrix after it was multiplied with the input vector. The process was iterated until the system reached a steady-state. The FCMWizard, a web-based software tool, was used for the simulation purposes, as it has the unique ability to construct an FCM using data that come from experts or stakeholders' knowledge and can perform simulations for different possible scenarios, in different scientific domains, using a very intuitive graphical user interface [31]. The impact of the conducted scenarios on the selected decision concepts was examined, further identifying which key concepts affect the final deliverables of the program.

The scenario analysis performed simulations for the selected nine scenarios (Table 9). For example, scenario 1 (S1) was devoted to increasing the concept C1—"Building strong CBOs by "clamping" it to one, whereas scenarios 2 (S2) and 3 (S3) studied the effects of the concepts C2—"Governance of CBOs" and C3—"Capacity building" by clamping the values of these concepts to one. The nine scenarios were conducted with the two aggregated collective FCMs, average-FCM and OWA-FCM. The expert-based FCM, which was constructed by the experts, was considered as the benchmark model that would help the researchers to further investigate the usefulness, importance, and superiority of the proposed OWA aggregation method against the average aggregation method. The results for scenario analysis for the two aggregated groups, for both average-FCM and OWA-FCM, as well as the expert-based FCM, were illustrated in the following figures. The scenario results for the expert-based FCM model, along with the corresponding scenario results for the OWA aggregated FCM, are illustrated in Table A1 in Appendix A.

Figure 10 illustrates all three FCMs (average, OWA, and expert-based), the deviation from the steady-state for all concepts after the nine scenarios had been conducted. The following figures (Figures 11 and 12) illustrate the outcomes regarding the percentage of change for certain key concepts, for all performed scenarios, with respect to FCMs.

**Figure 10.** Scenario analysis considering deviations from the steady state for all FCMs considering confidences and links. (AVE is the abbreviation of Average, EB is the abbreviation of Expert-based).

**Figure 11.** Percentage of change for decision concepts (**a**) C16, (**b**) C18, and (**c**) C17 when all scenario concepts were clamped to one for the expert-based FCM (AVE is the abbreviation of Average, EB is the abbreviation of Expert-based).

Figure 13 depicts the corresponding results of the deviation from the steady-state when FCMs were used in the scenario analysis. Figures 14 and 15 illustrate the outcomes regarding the percentage of change for decision concepts when the concepts for each scenario were clamped to one.

**Figure 12.** Decision concept C20 (social harmony) percentage of change when the key concepts of each devoted scenario were clamped to one. (AVE is the abbreviation of Average, EB is the abbreviation of Expert-based).

**Figure 13.** Scenario Analysis for all FCMs (average, OWA, expert) considering links. (AVE is the abbreviation of Average, EB is the abbreviation of Expert-based).

The following table (Table 10) briefly presents the impact that the examined scenarios had on the four decision concepts of the system.


**Table 10.** Scenarios mainly affecting decision concepts.

**Figure 14.** Percentage of change for decision concepts (**a**) C16, (**b**) C18, and (**c**) C17 when all scenario concepts were clamped to one, compared to the initial steady state (baseline scenario), considering links. (AVE is the abbreviation of Average, EB is the abbreviation of Expert-based).

**Figure 15.** Decision concept C20 (social harmony) percentage of change when the key concepts of each devoted scenario were clamped to one. (AVE is the abbreviation of Average, EB is the abbreviation of Expert-based).

The observations that were drawn from the above figures and tables focus on the following two main points:

	- i The decision concept C16—"Social empowerment" was solely affected by C15—"Political empowerment" for all FCMs (average, OWA, and expert). Moreover, women's personal well-being and personality development (decision concept C18) increased when more political and social empowerment (decision concepts C15 and C16) were offered to them.
	- ii Furthermore, it was observed that the key concept C2 (Governance of CBOs), as well as the combinations C2 (Governance of CBOs) and C3 (Capacity building), and C3 (Capacity building) and C5 (Access to formal credit), had the highest impact in the decision concept C17—"Economic empowerment" for all collective FCMs, showing a significant increase in C17, particularly when the OWA aggregation method was applied.
	- iii It also emerged from the above figures and Table 10, that the increase of social harmony (C20) was directly connected to the increase of the following key concepts: C2—"Governance of CBOs", the combination of C2—"Governance of CBOs" and C3—"Capacity building", as well as the concepts C15—" Political empowerment", C16—"Social empowerment" and C17—"Economic empowerment". Results of FCM-based simulations revealed that impacts of the DAY-NRLM programme could be realised better if strong institutions are built.
	- iv Overall, the concepts C2, C3, C5, C15, C16, and C17 had a significant impact in the policy-making and strategic planning of socio-economic sustainability of poor rural communities because they presented considerably higher deviations from the steady-state than the rest of the concepts (see Figures 10 and 13). To further check the validity of the outcomes, a sensitivity analysis regarding the impact that these key concepts had on decision concept C20, for all three FCMs (average, OWA, and expert-based), was conducted, and the corresponding results are presented in Appendix B (Figures A1–A3). There seemed to be an influence from the absence of political, social, and economic empowerment, as well as from the lack of governance of CBOs, which corresponded to the concepts C2, C15, C16, and C17, affecting the community's social harmony (C20).

Concerning the performance of the two examined aggregation methods, the following important observations were extracted in particular after a careful analysis of the tables and figures above.


Some limitations of the proposed methodology that need to be considered are (i) the lack of imprecision of human perception in fuzzy form in FCM representation, as this approach cannot deal with aggregating fuzzy values of multiple FCMs into a collective FCM, and (ii) the weakness in coping with complex FCMs where a large number of concepts and weights are assigned by many participants. In this case, it is di fficult to accurately define the learning parameters in OWA and handle the aggregated weighted connections.

#### *3.5. Discussion on Scenario Results*

The scenarios 1 to 6 examine how certain key concepts of the DAY-NRLM programme such as strong CBOs, good governance within CBOs, better capacity building of communities and CBOs, as well as access to formal credit, would help to achieve the final objectives of the programme, that is, alleviation of socio-economic poverty and better quality of life. In particular, increased access to formal credit and good governance would empower the SHG women economically, politically, and socially, as well as increase social harmony in the community. Consequently, income and savings would increase, and that would lead to an increase in consumption expenditure, livelihood diversification, and enterprise development. Higher-income will lead to better access to education for women and their children, consequently developing their personality, personal well-being, and overall socio-economic status.

Scenarios 7 to 9 highlight the e ffects of political (C15), social (C16), and economic (C17) empowerment of women, respectively. These empowerments represent political inclusion, political justice, participation in various village-level committees, savings, financial self-su fficiency, universal social mobilization, and social inclusion, among others. These scenarios also show an increase in income and savings, which would further lead to a rise in consumption expenditure, livelihood diversification, and enterprise development. Increased income will lead to better access to education for SHG women and their children; it would consequently develop the personality and personal well-being of SHG women. Better education will improve their intra-household bargaining power and health, hygiene, and sanitation. However, the result showed that empowerment alone is inadequate, and hence building strong CBOs and better access to formal credit are essential.

The outcomes of the scenario analysis highlight the importance of the simultaneous implementation of multiple concepts for the development of SHG members. Enhancing the capacities of SHG members, good governance within the CBOs and micro-finance through high-quality CBOs comprise the main aspects that should be taken into consideration in the examined case. Access to micro-finance and higher income will help community members to diversify their livelihood options and develop small enterprises. As a result, women empowerment and social safety nets will emerge, and women will improve their education, health, and develop their personality. All of the above factors will help poor rural communities and their members to alleviate socio-economic poverty while improving social resilience and promoting economic stability.

However, there is a need to incorporate resource e fficiency in local and collective businesses, which can reduce pressures and impacts on the environment while contributing to socio-economic development and human well-being [10,11]. A shift towards the circular economy could translate into significant changes in people's lives [14]. Worldwide, small and medium enterprises are trying to move towards circular business models and solutions; however, the lack of consumer interest and awareness along with the lack of support from demand networks prevent the implementation of green innovations and act as the main obstacle for a transition towards the circular economy [14].

Several concepts identified in this study have the potential to incorporate the circular economy approach. The characteristics of those concepts that can influence communities' perceptions and attitudes towards circular solutions could include (C8) consumption—encouraging a non-materialistic environment among households and communities, supporting decisions to buy refurbished products over new ones, and increasing longevity of purchased products; (C9) enterprise development—building green enterprises, reusing/repairing/recycling resources at various levels, and more focus on product quality and service o ffering; (C10) livelihood diversification—a shift towards green livelihoods, and building farm and non-farm livelihood portfolios; (C12) natural assets—sustainable use and managemen<sup>t</sup> of water and land resources, soil nutrient managemen<sup>t</sup> through organic fertilisers, composting, and mulching, among others, and sustainable livestock management; and (C13) health, hygiene, and sanitation—changing consumer behavior, waste managemen<sup>t</sup> at various levels, that is, households and industries, through reduction, reusing, and recycling, and wastewater treatment.
