Fuzzy Cognitive Maps for Modeling Complex Systems

PurposeThe purpose of this paper is to apply a fuzzy LinPreRa cognitive map to evaluate the interaction and importance of factors affecting the development of strategic alliance partnerships between the outlying island duty-free shops and existing collaboration firms in duty-free shops. Meanwhile, the key factors should be considered in establishing strategic alliance partnerships while analyzing and comparing the perspectives of owners for outlying island duty-free shop and partner vendors of collaborating firms along with differences of influencing key factors on partnership quality.Design/methodology/approachThis study incorporates a fuzzy linguistic preference relation analytical network process (fuzzy LinPreRa ANP) in the fuzzy cognitive map (FCM) method to formulate a fuzzy LinPreRa cognitive map to evaluate the interactions and importance of key factors and the conditions of interactive impacts during the establishment of strategic alliance partnerships. The authors use the outlying island duty-free shops in Taiwan as the empirical subject to illustrate how the fuzzy LinPreRa cognitive map is applied. In-depth, interviews and questionnaire surveys are conducted to collect and evaluate respondents concerning key factors affecting strategic alliance partnerships establishment.FindingsThe following three findings based on the results of empirical analysis: first, the administrative behavioral patterns of managers for strategic alliance partnerships encompass shared values and goal coherence, while the associative statements are located on the first layer of fuzzy LinPreRa cognitive map core associations, which illustrates that businesses attach great importance to conceptual ideas. Second, integrity and reputations of both parties are the governing mechanism of strategic alliance partnerships, influencing mutual reputation. Third, the relationship of strategic alliance partnerships refers to the profit opportunities of both parties and their ability to respond to the market, including future development, regional indicators, marketing capabilities, brand multiplicity and customer retention. However, it can be inferred that such associative factors are located in the outer layer or belong to noncore associations, which means that both parties’ abilities to respond to market reactions are weakened.Practical implicationsThis study provides valuable relationship managerial strategies to maintain long-term partnerships for outlying island duty-free shops and their alliance collaborating firms including strengthened relationships of both parties’ managers to achieve common values and consistent objectives; improved beneficial value of both parties in strategic alliance partnerships; continued close communications to enhance the quality of strategic alliance partnerships; and establishment of personnel training mechanisms and strict formulation of management rules for strategic alliance partnerships.Originality/valueThe main valuable contributions are included the fuzzy LinPreRa cognitive map by combining two different decision methods including FCM and fuzzy LinPreRa ANP is proposed to help decision makers to improve the evaluation quality and calculation efficiency for critical elements’ interaction and importance; the fuzzy LinPreRa cognitive map can clarify considering significant factors when maintaining strategic alliance partnerships and further provide valuable relationship managerial strategies to maintain long-term relationships for duty-free shop owners and their alliance collaborating firms.

Fuzzy cognitive map based approach for predicting yield in cotton crop production as a basis for decision support system in precision agriculture application

This survey makes a review of the most recent applications and trends on fuzzy cognitive maps (FCMs) over the past decade. FCMs are inference networks, using cyclic digraphs, for knowledge representation and reasoning. Over the past decade, FCMs have gained considerable research interest and are widely used to analyze causal complex systems, which have originated from the combination of fuzzy logic and neural networks. FCMs have been applied in diverse application domains, such as computer science, engineering, environmental sciences, behavioral sciences, medicine, business, information systems, and information technology. Their dynamic characteristics and learning capabilities make them essential for a number of tasks such as modeling, analysis, decision making, forecast, etc. Overall, this paper summarizes the current state of knowledge of the topic of FCMs. It creates an understanding of the topic for the reader by discussing the findings presented in recent research papers. A survey on FCM studies concentrated on FCM applications on diverse scientific areas, where the FCMs emerged with a high degree of applicability, has also been done during the past ten years.

This paper examines the use of fuzzy cognitive maps (FCMs) as a technique for modeling political and strategic issues situations and supporting the decision-making process in view of an imminent crisis. Its object domain is soft computing using as its basic elements different methods from the areas of fuzzy logic, cognitive maps, neural networks and genetic algorithms. FCMs, more specifically, use notions borrowed from artificial intelligence and combine characteristics of both fuzzy logic and neural networks, in the form of dynamic models that describe a given political setting. The present work proposes the use of the genetically evolved certainty neuron fuzzy cognitive map (GECNFCM) as an extension of certainty neuron fuzzy cognitive maps (CNFCMs) aiming at overcoming the main weaknesses of the latter, namely the recalculation of the weights corresponding to each concept every time a new strategy is adopted. This novel technique combines CNFCMs with genetic algorithms (GAs), the advantage of which lies with their ability to offer the optimal solution without a problem-solving strategy, once the requirements are defined. Using a multiple scenario analysis we demonstrate the value of such a hybrid technique in the context of a model that reflects the political and strategic complexity of the Cyprus issue, as well as the uncertainties involved in it. The issue has been treated on a purely technical level, with distances carefully kept concerning all sides involved in it.

Fuzzy cognitive maps (FCMs) can structure virtual worlds that change with time. A FCM links causal events, actors, values, goals, and trends in a fuzzy feedback dynamical system. A fuzzy rule defines a fuzzy patch in the input -output state-space of a system. It links commonsense knowledge with state-space geometry. A FCM connects the fuzzy rules or causal flow paths that relate events. It can guide actors in a virtual world as the actors move through a web of cause and effect and react to events and to other actors. Experts draw FCM causal pictures of the virtual world. Complex FCMs can give virtual worlds with ?>new ?> or chaotic equilibrium behavior. Simple FCMs give virtual worlds with periodic behavior. They map input states to limit-cycle equilibria. A FCM limit cycle repeats a sequence of events or a chain of actions and responses. Limit cycles can control the steady-state rhythms and patterns in a virtual world. In nested FCMs each causal concept can control its own FCM or fuzzy function approximator. Appendix A shows how an additive fuzzy system can uniformly approximate any continuous (or bounded measurable) function on a compact domain to any degree of accuracy. This gives levels of fuzzy systems that can choose goals and causal webs as well as move objects and guide actors in the webs. FCM matrices sum to give a combined FCM virtual world for any number of knowledge sources. Adaptive FCMs change their fuzzy causal web as causal patterns change and as actors act and experts state their causal knowledge. Neural learning laws change the causal rules and the limit cycles. Actors learn new patterns and reinforce old ones. In complex FCMs the user can choose the dynamical structure of the virtual world from a spectrum that ranges from mildly to wildly nonlinear. We use an adaptive FCM to model an undersea virtual world of dolphins, fish, and sharks.

Fuzzy cognitive strategic maps in business process performance measurement

Fuzzy Cognitive Maps (FCMs) are well-suited techniques to model the behavior of complex systems. But, since they depend on the quality of human knowledge they are prone to subjective false estimations. Moreover, even domain experts can fully describe only less complex systems which, in turn, limits the effectiveness of FCMs in real world applications. Thus, a technique is needed that, on the one hand, eases the use and, on the other hand, optimizes the formal structure of an FCM. Against that background, this article elucidates the use of different bio-inspired algorithms to optimize the application of the FCMs: Evolutionary Strategies (ES), Particle Swarm Optimization (PSO), and Big Bang-Big Crunch (BB-BC). The proposed approaches are applied to a novel valuation technique using FCMs. Besides principal feasibility, we demonstrate its potential to facilitate the use of vague and incomplete expert knowledge in the valuation of complex investment opportunities such as, but not limited to, young High-Technology Ventures.

Fuzzy Cognitive Maps (FCMs) are a causal modelling technique. FCM models contain nodes (representing the concepts to be modelled) and directed weighted edges (representing the causal relations between the concepts). Data-driven FCM learning algorithms are an objective approach with the potential to discover the causal relations that are unknown to human experts. Learning FCM from data can be a difficult problem because the size of the solution space grows quadratically with the number of nodes in the FCM models. A data-driven learning algorithm based on Ant Colony Optimization (ACO) is proposed to develop Fuzzy Cognitive Maps (FCMs). The FCM models can be isomorphically represented as weight vectors. The objective function is to minimize the difference between the estimated response of the FCM model and the target response observed from the to-be-modelled system. An ACO algorithm with heuristic information is proposed to find the best FCM model. The performance of the ACO algorithm was tested on both randomly generated data and DREAM4 project data (publicly available in-silico gene expression data). The experiment results show that the ACO algorithm is able to learn FCMs with at least 40 nodes.

This paper focuses on the social function of historical public space in Turkey that has been transformed with rise of modernism. Before that, it functioned as a suburban recreational area. The increasing demand for urban lands has been led to its transformation and its function as an urban component. The historical pattern of urban space can be conserved to protect and strengthen social interactions as the key issue of urban social sustainability. With a focus on the urban design through literature review, the aim is to identify the role of social interactions on social sustainability of historical urban street in Turkey. A field survey study was conducted to observe and in-depth interviews to locally evaluate the socio-spatial design principles in Bagdat street, as a research case. Fuzzy Cognitive Map (FCM) and Cognitive Spatial Map (CSM) were used to investigate the spatial experiences of the respondents. Results indicated that the historical continuity of socio-spatial activities through the time in respect to the socio-cultural values and user satisfaction has led to enhance the sense of belongings for citizens. As a conclusion, all data were integrated to propose a socio-spatial framework for designing and developing of Turkish public street, to enhance the urban social sustainability in future communities.

The evaluation of the teaching-learning process is a conduct that poses great challenges from a modeling perspective. Tutor modules form part of intelligent systems that are applied to education, and should assess: when to interrupt, how to teach a given topic, and what to teach in a given moment. By considering the different types of errors, a good evaluation of the teaching-learning process allows the systems to adapt in an optimum form to different users. This paper proposes a design technique to model the conduct of an expert that evaluates the results of the teaching-learning process within a reactive learning environment. To achieve this, a fuzzy cognitive map, which is a representation recently proposed to model the conduct and operation of complex systems, is used. Bart Kosko introduced this type of maps in 1986 with the aim of describing the behavior of a system in terms of concepts and causal relations between concepts. Since then, their use has been extended to diverse real-world situations that span from the analysis of investment in stock to supervisory system control. Missing conceptions, which provide a basis to assemble the didactic tactics, are imputed to this representation. Starting from the mental model of the expert in the learning domain, a conceptual genetic graph is established to orientate the fuzzy cognitive map. Finally, this paper presents a concrete example.

Fuzzy cognitive maps (FCMs) are widely used for modeling complex systems and supporting explainable AI. However, traditional FCMs cannot effectively represent indeterminacy that arises from incomplete or conflicting information. Neutrosophic cognitive maps (NCMs) extended FCMs to handle such uncertainty, but their use of a single indeterminate symbol (I) limits their ability to model complex, real-world interactions. This paper introduces Refined neutrosophic cognitive maps (RNCMs), a novel framework that combines single-valued neutrosophic sets (SVNSs) for representing concept states with a new refined dual neutrosophic set (RDNS) for modeling causal relationships. RNCMs capture five distinct causal relationships—positive to positive, positive to negative, negative to positive, negative to negative, and indeterminate to indeterminate—allowing a richer and more precise modeling of dual and uncertain relationships than FCMs or NCMs. A case study on students’ academic performance demonstrates that RNCMs reproduce the outputs of FCMs and NCMs while uncovering additional causal nuances, such as polarity shifts and the distinction between genuine indeterminacy and measurable influence. RNCMs also reveal when positive states in certain factors lead to negative outcomes—insights that earlier models fail to capture. Although the model requires higher computational effort, it remains robust across thresholds and provides better explainability and interpretability. Overall, RNCMs advance cognitive map modeling by integrating refined uncertainty handling with dual causal relationships, making them a powerful and explainable tool for complex decision-making systems.

Fuzzy cognitive maps (FCM) is a powerful framework for representing structured human knowledge and causal inference. This paper presents a new and effective approach to analyzing causal inference mechanism of FCM. We focus on binary concept states proposed originally by Kosko (1986). Given initial conditions, FCM is able to reach only certain states in its state space. The problem of finding whether a state is reachable in the FCM is NP hard. In order to effectively carry out the design of fuzzy cognitive maps we propose to divide an FCM into basic FCM modules. This paper also presents a recursive formula for the calculation of FCM inference patterns in terms of key vertices.

Fuzzy cognitive maps (FCMs) represent the decision process in the form of a graph that is usually easy to interpret and, therefore, can be applied as a convenient decision-support tool. In the first part of this chapter, we explain the motivations for the research on FCMs and provide a review of the research in this area. Then, as stated in the title of the chapter, we concentrate our attention on the comparative study of adaptive and evolutionary FCMs. The terms adaptive and evolutionary refer to the type of learning applied to obtain a particular FCM. Despite many existing works on FCMs, most of them concentrate on one type of learning method. The purpose of our research is to learn FCMs using diverse methods on the basis of the same dataset and apply them to the same prediction problem. We assume the effectiveness of prediction to be one of the quality measures used to evaluate the trained FCMs. The contribution of this chapter is the theoretical and experimental comparison of adaptive and evolutionary FCMs. The final goal of our research is to determine which of the analyzed learning methods should be recommended for use with respect to the considered prediction problem. To illustrate the predictive capabilities of FCMs, we present an example of their application to the prediction of weather conditions.

Fuzzy cognitive map (FCM) is an important approach for modeling the behavior of dynamic systems. FCM’s ability to represent casual relationships between the concepts (factors, attributes, etc.) has attracted the interest of researchers from different disciplines. The construction process of FCMs is mostly initialized with expert knowledge because FCMs can conveniently incorporate available information and expertise in the determination of vital parameters and relations of the system. However, their higher dependence on expert knowledge may significantly influence the reliability of the model due to the increase in subjectivity. In order to avoid weaknesses depending on expert knowledge, learning algorithms that search for the appropriate relationships between the concepts have been used with FCM studies. In this paper, a FCM analysis was performed for tobacco use to understand the cause–effect relationships between demographic characteristics of people (such as gender, age range, and residence type) and likelihood to tobacco use. In order to reduce the impact of external interventions (from experts), a multi-stage learning procedure was applied by integrating two different learning algorithms (nonlinear Hebbian learning algorithm and extended Great Deluge algorithm). The results showed that the multi-stage learning procedure increased the accuracy of the model and provided more reliable maps for the studied system. They also proved that the multi-stage learning procedures can help to reduce the dependency to expert knowledge and improve the robustness of the study.

In this study, the effect of practical courses (especially robotics) on students' success is evaluated using fuzzy cognitive maps. This study particularly focuses on how practical courses increase the learning achievements in vocational schools. For this purpose, students and academicians were chosen as stakeholders for this study. Student were selected from departments of machine, electronic and computer. In total views of 30 students were taken and evaluated using fuzzy cognitive maps before the study. Students were studied on three projects within this study. These projects are autonomous cleaning robot, chameleon robot and sumo wrestler robot. Each robot was developed by a group consisting of ten students. Three main outputs determined to be gained by students in the robot development process as sensor calibration, improvement of mechanical systems and software optimization. These outputs are also among the output concepts of the fuzzy cognitive map. Sensor calibration, improvement of the mechanical systems and optimization of the software are the critical tasks respectively for the student groups of electronics, machine and computer. Each student group shared students of their departments homogeneously. Academicians were selected as one from each department. Fuzzy cognitive maps' survey applied to 15 academicians. After the design and development processes of robots, students and academicians views re-evaluated. It was observed clearly from the comparison of the results that, learning achievement, desire to learn, desire to interdisciplinary collaboration, self-confidence, interest in robotic technologies, satisfaction and desire to give priority to practical training in other subjects are increased by %45, %63, %42, %74, %85, %88 and %76 respectively.