Interval-Valued Intuitionistic Fuzzy Pattern Recognition Model for Assessment of Social Cohesion

This article is a summary of the scientific work published by Gorkhmaz Imanov, Asif Aliyev
The original source can be accessed via DOI 10.33111/nfmte.2023.133

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Social cohesion, first conceptualized by Emile Durkheim, refers to the bonds, shared values, and sense of belonging that unite members of a society. Durkheim emphasized its role in maintaining social order and collective solidarity. Contemporary definitions expand this concept to include elements such as interpersonal trust, social equality, civic participation, institutional legitimacy, and inclusive public policies that contribute to collective well-being and stability. As societies become more diverse and complex, social cohesion has evolved into a critical framework for assessing how well individuals and groups integrate and cooperate within the broader social fabric.

Academic literature typically classifies social cohesion into several interrelated domains. These include the quality and quantity of interpersonal relationships, the sense of identity and belonging within social groups, and perceptions of fairness and equality. Additionally, it involves adherence to shared norms, values, and engagement in democratic processes. The framework of social cohesion also encompasses three essential dimensions: bonding, which relates to close personal networks such as family and friends; bridging, which refers to broader social connections within communities; and linking, which reflects the level of trust and interaction between citizens and public institutions.

Moreover, effective social cohesion requires inclusive participation across all demographic groups, including marginalized populations. It is reinforced through policies that address disparities in income, access to services, and political representation. Ultimately, a high level of social cohesion supports societal resilience, enhances economic productivity, and fosters an environment where innovation and inclusive growth can thrive.

Global frameworks offer structured indicators to measure cohesion. For example, the Economic Commission for Latin America and the Caribbean (ECLAC) presents a detailed system of social cohesion indicators, as shown below:

Given the complexity and uncertainty in measuring such multifaceted constructs, this study employs advanced methods based on interval-valued intuitionistic fuzzy sets (IVIFS) and multiple-criteria decision-making (MCDM) to calculate a Social Cohesion Index (SCI). The paper outlines the problem, proposes an algorithmic approach, and provides empirical examples of SCI computation.

Social Cohesion Index Methodology Using Fuzzy Logic (Case of Azerbaijan)

A methodology is presented for calculating the Social Cohesion Index (SCI) using interval-valued intuitionistic fuzzy sets (IVIFS) within a multiple-criteria decision-making (MCDM) framework. Grounded in the United Nations’ methodology developed for Latin America, this approach is specifically designed to manage the ambiguity, subjectivity, and incompleteness often associated with social data. Unlike traditional statistical methods, IVIFS enables a deeper, more nuanced assessment of intangible and qualitative factors such as institutional trust, social inclusion, and perceived inequality—variables that are critical to understanding and improving societal resilience.

This methodology transforms conventional data into fuzzy variables by defining membership and non-membership degrees that reflect real-world uncertainty. To illustrate the process, Azerbaijan’s data for 2021 was used, encompassing a wide spectrum of socio-economic indicators. These were categorized into three primary sub-indices:

Each indicator is benchmarked against global best and worst-case values to define the upper and lower bounds of fuzzified variables. This process not only facilitates a more adaptable evaluation framework but also allows the index to account for both objective metrics and subjective perceptions—crucial in assessing national cohesion comprehensively.

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This table presents the fuzzified values of the selected indicators for Azerbaijan in 2021, forming the basis for the computation of sub-indices and the overall Social Cohesion Index.

The methodology advances through the construction of a fuzzy preference matrix, ensuring consistency via both additive and multiplicative checks. Entropy-based weighting is applied to assign significance to each indicator, ensuring that more informative criteria exert greater influence on the final result. Once all sub-indices are calculated using interval-valued intuitionistic fuzzy aggregation techniques, the overall SCI is determined and categorized through similarity analysis, mapping it onto qualitative descriptors such as “very high,” “medium,” or “low” cohesion.

This robust and scalable framework empowers governments, development agencies, and researchers to better monitor and address the drivers of social fragmentation and cohesion. For emerging economies, post-conflict states, and societies undergoing transition, the ability to accurately measure social cohesion is not just an academic exercise—it is essential for crafting informed, inclusive, and forward-looking policy.

By applying this methodology to Azerbaijan’s national data, the study demonstrates its real-world relevance and flexibility, highlighting how precision tools rooted in fuzzy logic can help identify priority areas for policy intervention, improve governance outcomes, and promote more cohesive, equitable societies.

Fuzzy Analysis of National Cohesion

The final stage of the study presents the computation results of the Social Cohesion Index (SCI) for Azerbaijan in 2021, applying the full interval-valued intuitionistic fuzzy model to empirical data. To account for uncertainty and data imprecision, raw indicators were transformed into interval-valued intuitionistic fuzzy numbers—allowing the model to reflect both statistical realities and expert-informed judgments. As a demonstrative case, the indicator “Percentage of women in parliament” was fuzzified using triangular membership functions calibrated against global best and worst values, emphasizing its positive contribution to societal inclusiveness.

Following this transformation, the methodology progressed through the construction of fuzzy preference matrices for each sub-index. In particular, the Sense of Belonging sub-index, which includes indicators like government effectiveness and social capital, underwent entropy-based weight calculations. This ensured that each component's impact on the overall index was proportionally aligned with its informational value.

All three sub-indices—Distances, Inclusion-Exclusion Mechanisms, and Sense of Belonging—were then aggregated through a fuzzy weighted operator to derive the composite SCI. To interpret this composite result meaningfully, a similarity analysis was conducted, comparing the fuzzy SCI value to a pre-established linguistic scale ranging from “Very Low” to “Very High.”

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Table 6 summarizes these similarity measures, revealing that the SCI score for Azerbaijan in 2021 most closely aligns with the “Medium High” category. This rating suggests that Azerbaijan outperforms countries with low social cohesion but still trails behind the most socially cohesive nations. Importantly, this assessment goes beyond a simple classification—it highlights specific strengths and weaknesses within the sub-indices, offering a diagnostic lens for targeted policy responses.

The “Medium High” rating underscores opportunities for improvement in areas such as governance quality, social representation, civic engagement, and mechanisms of inclusion and exclusion. For policymakers, these insights are instrumental in shaping strategies that aim to bolster national unity, reduce social disparities, and enhance institutional trust. The application of a fuzzy logic framework not only improves the accuracy and reliability of cohesion assessments but also equips decision-makers with a more flexible and transparent tool for long-term social planning.

From Data to Policy: A Smarter Way to Quantify Social Cohesion

The Social Cohesion Index is one of the sub-indices (social security, social empowerment, social inclusion, and social cohesion) of the Social Quality Index. For the assessment of social sustainability, computing social cohesion is a pressing contemporary problem. The study presents an innovative approach to assessing social cohesion using an interval-valued intuitionistic fuzzy pattern recognition model. This method addresses the inherent uncertainties in social cohesion indicators by applying fuzzy logic, specifically through interval-valued intuitionistic fuzzy numbers. The methodology offers a significant improvement over traditional approaches by better handling the imprecision in data and enhancing the robustness of the Social Cohesion Index calculation.

An interval-valued intuitionistic fuzzy pattern recognition model was applied to quantify social cohesion in Azerbaijan using data from 2021. The results illustrate the model’s effectiveness in capturing the nuanced dimensions of social cohesion, particularly in relation to complex socio-economic variables. In addition, a structured framework was developed for determining the weights of individual indicators and aggregating them into a composite Social Cohesion Index, which was subsequently evaluated using a fuzzy linguistic scale.

The results of investigation for Azerbaijan’s performance in social cohesion for 2021 have led to a medium high rating, which indicates that the country performs better than many countries with low social cohesion but is still behind from leading countries. This assessment provides a comprehensive understanding of Azerbaijan’s social cohesion relative to global standards, highlighting areas for policy focus and further research. For example, the fuzzy model revealed that there is potential for improvement in governance, inclusion-exclusion mechanisms, social representation, reducing inequality and increasing social capital.

Overall, this research contributes to the broader field of social processes assessment by providing a more nuanced and flexible tool. It highlights the importance of incorporating fuzzy logic into social science methodology, especially when dealing with complex and uncertain datasets. The proposed model not only advances the analytical approach to Social Cohesion Index calculations, but also offers practical insights for policymakers aiming to evaluate and enhance social cohesion within their societies.

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