Robust semi-quantitative fuzzy cognitive map model for complex systems and case study: mitigating the water scarcity problem in Joran

Abstract

Many contemporary real life problems are characterised by uncertainty due to human-environment interactions. Such problems are typically qualitative, participatory, complex and dynamic such that the domain knowledge (typically the perceptions of participants) can only be represented in the form of relevant factors linked to each other through imprecise cause-effect relationships and many feedback loops. A Fuzzy Cognitive Map (FCM) is able to deal with and model such problems. FCM is a qualitative soft computing approach that represents domain knowledge on a map by a way of nodes and imprecise directed connections between them to represent the factors and relationships, respectively. It incorporates uncertainty in relationships through imprecise values for connection strengths and allows feedback loops to appropriately represent systemic behaviour. An individual FCM can represent perceptions of a participant regardless of the level of their knowledge. FCM approach can combine different FCMs/perceptions into a group or social FCM/perception to obtain a comprehensive understanding of the problem. It also can simplify (condense) large FCMs that include a large number of nodes and connections to better understand the problem and gain meaningful insights. Finally, individual and group FCMs are to be analysed and simulated using what-if policy scenario simulations to reveal suggestions for solving a problem. All these aspects of FCM approach have limitations. Therefore, this thesis aims to address these aspects of the FCM approach in a systemic way and test its applicability and validity in a case study involving mitigating water scarcity in Jordan. The first part of this thesis proposes the development of a robust semi-quantitative FCM model consisting of robust methods for adequately and accurately collecting, representing and manipulating imprecise data describing a complex problem. This model uses in-depth qualitative interviews based on open-ended questions to collect qualitative data about the problem from relevant stakeholders. These data are then transformed into factors and imprecise (linguistic expressions such as 'high', 'medium', 'low’, etc. or numeric expressions) connection values among these factors to produce different stakeholder FCMs. These FCMs could be further updated based on a review of their corresponding interviews. To deal with the different FCMs expressed by different imprecise values appropriately, they are represented in a unified format using a robust representation approach called 2-tuple fuzzy linguistic representation model. With this representation, it can combine imprecise linguistic and numeric values with different granularity and/or semantic without loss of information. To condense a large FCM, this thesis uses a semi-quantitative FCM condensation method that allows multi-level condensation. In each level of condensation, groups of similar variables are subjectively condensed and the corresponding imprecise connections are computationally condensed. In this regard, the credibility weights assigned to variables based on Consensus Centrality Measure (CCM) values of these variables are used. CCM is used to reflect variables’ importance and obtained based on the most common centrality measures of a variable in a directed network – Degree, Closeness and Betweenness. To obtain a realistic group FCM, this thesis uses a quantitative fuzzy method for FCM aggregation based on the 2-tuple model and the credibility weights of FCMs assigned based on their CCM values. These credibility weights reflect the importance of different levels of knowledge of stakeholders developed these FCMs. This thesis uses graph theory indices to analyse the structure of individual and group FCMs. It also makes comparisons between theses FCMs to examine different perceptions. This could be useful for planning simulations and understanding and interpreting simulation results. For FCM simulation, Auto-associative Artificial Neural networks (AANN) are used to implement various what-if policy scenarios on condensed or non-condensed group FCMs. This thesis also uses a number of criteria to select the most effective policies before making recommendations to decision makers. To reflect the robustness and effectiveness of the proposed model, the second part of this thesis examines an application of the proposed model to a case study representing a big real-life problem - "Mitigating the Water Scarcity Problem in Jordan". In this study, 35 face to face recorded interviews were conducted in Jordan with 39 participants from 5 stakeholder groups consisting of private sector, local people, water experts, managers and farmers. A well prepared questionnaire was used in the interviews to motivate the stakeholders in identifying relevant factors and connections. This data collection part lasted about five months and produced 35 original FCMs developed by the stakeholders. The recorded interviews and FCMs were reviewed one to three times to obtain comprehensive FCMs that include all important factors and connections mentioned in the interviews. The resulting FCMs included 186 different factors as original variables in total. These FCMs were condensed in two levels of condensation and then aggregated into five group FCMs and one social FCM using the proposed FCM model. The analysis of the interviews and the structures of the FCMs revealed a high level of agreement between stakeholder and group perceptions. The stakeholders defined many similar important original variables and drew relatively similar connections between them. The stakeholder perceptions for ending or alleviating the water scarcity focused toward increasing water supply and decreasing water demand. The stakeholder group FCMs and the overall social group FCM at the higher (second) level of condensation were used to simulate different policy scenarios. According to the analysis of the results of these simulations, an investigation process was carried out at the lower levels (first level of condensation and the original FCMs) based on some novel criteria to assess the appropriateness of variables at these levels to address the problem. Accordingly, this thesis recommends the following towards mitigating water scarcity in Jordan: a) implement rainwater harvesting, Disi and Red Sea-Dead Sea Water Conveyance projects as regardless of their high cost they would greatly help alleviate the problem b) improve water treatment technologies, especially wastewater treatment, c) implement effective management strategies and policies such as integrated and reformed management, effective and deterrent laws, stable plans and policies, regular maintenance of water networks, irrigation technologies, and securing rights to shared water with Israel and Syria, and d) involve the private sector in water management.