Combining grey clustering and fuzzy grey cognitive maps: an approach to group decision-making on cause-and-effect relationships

Abstract

Fuzzy grey cognitive maps (FGCMs) have been widely adopted to support cause-and-effect decision-making under uncertainty. However, capturing the information for the initial state vector and the relationship matrix from various specialists can be cumbersome, which may affect the convergence of FGCMs or cause them to reach a chaotic state. To address this issue, this paper presents a novel group decision approach based on the combination of grey clustering (GC) and fuzzy grey cognitive maps for assessing causal relationships in uncertain environments. The main contribution consists in applying GC as a mean to obtain the initial state vector from the relationship matrix data. This halves the required inputs to the users, reducing uncertainty in the computational model. Also, the proposition brings a method for aggregating the linguistic judgements of multiple decision-makers when assessing causal relationships. The proposition also differs from others in the literature by providing results with lower imprecision levels, named greyness, and lower number of required iterations for the FGCM-based system to converge. A real application was conducted in a technology start-up to test the approach to practical implications. Results allowed the identification of important elements regarding the company's profile and performance, aiding prioritization and enabling the development of action plans. This paper also includes a comparison of other representative models with the proposed approach, which led to more accurate results. Hence, this study addresses the need for new alternatives to improve the reliability and convergence of FGCM-based systems. Finally, suggestions for future applications are proposed.

Use of AHP and grey fixed weight clustering to assess the maturity level of strategic communication management in Brazilian startups

“…In case the grey numbers are not yet normalized, it becomes essential to normalize the matrix α(⊗)=[⊗truea˙ij] by following Equations (3), (4) and (5), where ⊗—truea~ij represents the normalized lower limit of grey number ⊗truea~ij while ⊗¯truea~ij corresponds to its normalized upper limit, as in Zanon and Carpinetti (2021).…”

“…a ij by following Equations ( 3), ( 4) and ( 5), where ⊗ -e a ij represents the normalized lower limit of grey number ⊗ e a ij while ⊗ e a ij corresponds to its normalized upper limit, as in Zanon and Carpinetti (2021).…”

“…Furthermore, Grey Fixed Weight Clustering stands out by offering an exceptional level of model interpretability, a pivotal attribute for stakeholders and decision-makers seeking to gain meaningful insights into the underlying structure of their data (Zanon and Carpinetti, 2021). In contrast, other methodologies such as DBSCAN may yield cluster geometries that are challenging to interpret, while Fuzzy Clustering introduces the concept of partial memberships, which may necessitate prior domain knowledge for effective interpretation.…”

Research on the Resilience Enhancement Path of Technology-Based SMEs Using Dynamic Fuzzy Cognitive Maps—Organizational Context and the Employee Loyalty Perspective

“…A dynamic fuzzy cognitive map (DFCM) is constructed by using a random neural network model to replace symbolic deduction with many computational processes, ultimately facilitating reasoning. This approach has been continuously deepened and extended by scholars from various countries, mainly in the forms of intuitionistic fuzzy cognitive maps [51], rough cognitive maps [52], fuzzy cognitive maps based on automatic control in time [53], dynamic grain cognitive maps [54], higher-order intuitionistic fuzzy cognitive maps based on variational pattern decomposition [55], and fuzzy gray cognitive maps based on gray clustering [56], which have been widely used in the social sciences [57], economics [58], energy science [59], ecology [60], healthcare [61], risk management [62], expert systems [63], education [64], and other fields.…”