Tag Archives: MABS

Towards contextualized social simulation: Complementary use of Multi-Fuzzy Cognitive Maps and MABS

By Oswaldo Terán1 and Jose Aguilar2

1Escuela de Ciencias Empresariales, Universidad Católica del Norte, Coquimbo, Chile, and CESIMO, Universidad de Los Andes, Mérid.

2CEMISID, Universidad de Los Andes, Merida, Venezuela; GIDITIC, Universidad EAFIT, Medellin, Colombia; and Universidad de Alcala, Dpto. Automatica, Alcala de Henares, Spain.


This work suggests to complementarily use Multi-Fuzzy Cognitive Maps (MFCM) and Multi-agent Based Simulation (MABS) for social simulation studies, to overcome deficiencies of MABS for contextually understanding social systems, including difficulties for considering the historical and political domains of the systems, variation of social constructs such as goals and interest, as well as modeler’s perspective and assumptions. MFCM are a construction much closer than MABS to natural language and narratives, used to model systems appropriately conceptualized, with support of data and/or experts in the modeled domains. Diverse domains of interest can be included in a MFCM, permitting to incorporate the history and context of the system, explicitly represent and vary agents’ social constructs, as well as take into account modeling assumptions and  perspectives.  We briefly describe possible forms of complementarily use these modeling paradigms, and exemplifies the importance of the approach by considering its relevance to investigate othering and polarization.

1. Introduction

In order to understand better issues such as othering and polarization, there is a claim in social simulation for research that includes the important domains of history, politics and game of power, as well as for greater use of social science data, make more explicit and conscious about the models’ assumptions, and be more cautious in relation to the interpretation of the simulations’ results (Edmonds et al., 2020). We describe a possible form of dealing with these difficulties: combining Multi-Agent based Simulation (MABS) and Multi Fuzzy Cognitive Maps (MFCM) (or other forms of cognitive maps), suggesting new forms of dealing with complexity of social behavior. By using MFCM an alternative modeling perspective to MABS is introduced, which facilitates expressing the context of the model, and the modelers’ assumptions, as suggested in Terán (2004).  We will consider as a case studying othering and polarization, given the difficulties for modeling it via MABS (Edmonds et al., 2020). Our proposal permits to explicitly represent social constructs such as goals, interest and influence of powerful actors on, e.g., people’s othering and polarization, and so in better contextualizing the simulated model. Variations of social constructs (e.g., goals, othering, polarization, interests) can be characterized and modeled by using MFCM.

Combined use of MABS and Fuzzy Cognitive Maps (FCM) (MFCM, multi FCM, are an extension of FCM, see the Annex) has already been suggested, see for example Giabbanelli (2017). MABS develop models at the micro level, while FCM and MFCM permits us to create models at the macro or contextual level; the idea is to use one to complement the other, i.e., to generate rich feedback between them and enhance the modeling process. Additionally, Giabbanelli propose FCM as a representation closer than MABS to natural language, allowing more participatory models, and better representation of the decision making process. Giabbanelli recommend forms of combining these two modeling approaches, highlighting key questions modelers must be careful about. In this line, we also propose a combined usage of a MFCM and MABS to overcome deficiencies of MABS modelling in Social Simulation.

Initially (in section 2) we offer a description of human societies from a broad view point,  which recognizes their deep complexities and clarifies the need for better contextualizing simulation models, allowing modeling of diverse agents’ constructs, and making explicit modelers’ assumptions and perspectives. Afterwards (in section 3), we briefly review the drawbacks of MABS for modeling some of these deep complexities. Then (in section 4), MFCM are briefly described, supported on a brief technical account in the Annex. Following (in section 5), we suggest to complementarily use MABS and MFCM for having a more comprehensive representation of human societies and their context, e.g., to better model problems such as othering and polarization. MFCM will model context and give a conceptual mark for MABS (allowing to model variation of context, e.g., changes of agents’ interests or goals, making explicit modelers’ perspective and assumptions, among other advantages), which, in turn, can be used to explore in detail specific configurations or scenarios of interest suggested by the MFCM.  Finally (in section 6), some conclusions are given.

2. (A wide view of) Human societies and influence of communication media on actual culture

As humans and primates, we recognise the social groups within which we develop as people (e.g., family, the community where we grow up, partners at the school or at work) as part of our “large home”, in which its members develop a common identity, with strong rational and emotional links. Other groups beyond these close ones are “naturally” estrangers for us and its members “instinctively” seen as others. In large civilizations such as western society, we extend somewhat these limits to include nations, in certain respects. In groups we develop perspectives, follow certain myths and rites, and have common interests, viewpoints about problems, solutions for these, and give meaning to our life. Traditionally, human societies evolve from within groups by direct face to face interaction of its members, with diverse perspectives, goals, interest, and any other social construct with respect to other groups. Nowadays this evolution mainly from natural interaction has been importantly altered in some societies, especially western and western influenced societies, where social media has introduced a new form of communication and grouping: virtual grouping. Virtual grouping consists in the creation of groups, either formally or informally, by using the internet, and social networks such as Facebook, Instagram, etc. In this process, we access certain media sites, while discarding others, in accordance with our preferences, which in turn depends on our way of thinking and preferences created in social, both virtual and direct (face to face), interaction. Currently, social media, and traditional media (TV, newspapers, etc.) have a strong influence on our culture, impacting on ours myths, rites, perspectives, forms of life, goals, interests, opinion, reasoning, emotions, and othering.

Characteristics of virtual communication, e.g., anonymity, significantly impacts on all these constructs, which, differently from natural interaction, have a strong potential to promote polarization, because of several reasons, e.g., given that virtual environments usually create less reflexive groups, and emotional communication is poorer or lack deepness. Virtual interaction is poorer than direct social interaction: the lack of physical contact strongly reduces our emotional and reflexive connection. Virtual social interaction is “colder” than direct social interaction; e.g., lack of visual contact stops communication of many emotions that are transmitted via gestures, and prevents the call for attention from the other that visual contact and gestures demands.

Even more, many times sources and veracity of information, comments, ideas, and whatever is in social media, are not clear. Even more, fake news are common in social media, what generate false beliefs, and behavior of people influenced and somewhat controlled by those who promote fake news. Fake news can in this sense generate polarisation, as some groups in the society prefer certain media, and other groups choose a different one. As these media may promote different perspectives following interest of powerful actors (e.g., political parties), conflicting perspectives are induced in the different groups, what in turn generates polarization. Social media are highly sensitive to manipulation by powerful actors worldwide, including governments (because of, e.g., their geopolitical interests and strategies), corporations (in accordance with their economic goals), religious groups, political parties, among many others. Different groups of interests influence in direct and indirect, visible and hidden, forms the media, following a wide diversity of strategies, e.g., those of business marketing, which are supported by knowledge of people (e.g., psychology, sociology, games theory, etc.). Thus, the media can create and contribute to create visions of the word, or perspectives, in accordance with the interest of powerful international or national actors. For more about all this, see, e.g, Terán and Aguilar (2018).

As a consequence, people following media that promotes a world view, related with some powerful actor(s) (e.g., a political party or a group of governments) virtually group around media that support this world view, while other people do the same in relation to other media and powerful actor(s), who promote(s) a different perspective, which many times is in conflict with the first one. Thus, grouping following the media sometimes promotes groups with conflicting perspectives, goals, interests, etc.,  which generates polarization. We can find examples of this in diverse regions and countries of the world. The media has important responsibility for polarization in a diversity of issues such as regional integration in Europe, war in Ukraine, migrations from Middle East or Africa to Europe, etc. Consequently, media manipulation sometimes allow powerful actors to influence and somewhat control perspectives and social behavior. Even more, the influence of social media on people is sometimes stronger than the influence of direct social interaction. All these introduce deep complex issues in social human interaction and behavior. This is why we have chosen polarization as the case study for his essay.

Consequently, to comprehend actual human behavior, and in particular polarization, it is necessary to appropriately take into account the social context, what permits to understand better the actual complexity of social interaction, e.g., how powerful international, national, and local actors’ influence on media affects people perspectives, goals, interest, and polarization, as well as their strategies and actions in doing so. Contextualized modeling will help in determining social constructs (goals, interests, etc.) in certain situations, and their variation from situation to situation. For this, we suggest complementing MABS with MFCM. For more about the consequences of virtual interaction, see for example Prensky (2001a, 2001b). Prensky (2009) has also suggested forms to overcome such consequences: to promote digital wisdom. MABS and MFCM models will help in defining forms of dealing with the problems of high exposure to social networks, in line with Prensky’s concerns.

3. Weakness of the MABS approach for modeling context

Edmonds et al. (2020) recognize that MABS models assume a “state of the world” or “state of nature” that does not include the historical context of the agent, e.g., in such a way that they explicitly present goals, interests, etc., and pursue them via political actions, sometimes exerting power over others. For instance, the agents can not change their goals, interests or desires during the simulation, to show certain evolution, as a consequence of reflection and experience at the level of desires, allowing cognitive variations. The models are strongly limited in relation to representing the context of the social interaction, which in part determines variation of important factors of agents’ behavior, e.g., goals. This, to a good extent, is due to lack of representation of the agents’ context. For the same reason, it is difficult to represent modelers assumptions and perspectives, which might also be influenced by social media and powerful actors, as explained above.

The Special Issue of the Social Science Computer Review. (Volume 38, Issue 4, August 2020, see for instance Edmonds et al. (2020) and Rocco and Wander (2020)), presents several models aiming at dealing with some of these drawbacks of MABS, specifically, to relate models to social science data, be more aware about the models’ assumptions, and be more cautious in relation to the interpretation of the simulations’ results. However, in these works diverse difficulties are not addressed, e.g.,  having appropriate representation of the context in order to explicitly consider diverse constructs, e.g., goals and interests, as well as having a wide representation of modelers perspectives and assumptions so that diverse perspectives can be addressed and compared, among other important matters.

MABS represent social interaction, i.e., the interaction in a group, where the agent’s goal, and other social constructs are assumed given, not variable, and to understand the context where they appear is not of interest or is out of reach (too difficult). However, as explained above, agents are in diverse social groups, not only in the simulated one, and so goals, interests, and beliefs in the modeled group are shaped in accordance to their interactions in diverse groups, and the influence of multiple, virtual and natural groups in which they participate. In order to represent variations of such elements, the context must be taken into account, as well as to elaborate models from narratives. MFCM is naturally close to narratives, as it is elaborated from conceptual frameworks. In this sense, MFCM might represent an intermediate step towards MABS models. In a MFCM and in the steps towards elaborating the MABS, modelers’ perspectives and assumptions can be made explicit. In addition, MABS presents limitations to determine the conditions for which a certain behavior or tendency occurs (Terán, 2001; Terán et al. 2001), i.e., for making strong inferences and theorem proving of tendencies for subsets of the theory of the simulation, which could more easily be performed in the MFCM. Hopefully, exploring configurations of the MFCM the proof could be carried out indirectly, in a higher level than in MABS, as has already been suggested in previous papers (Aguilar et al., 2020; Perozo et al., 2013).

4. Multi-Fuzzy Cognitive Maps (MFCM)

We suggest conceptual or cognitive maps as a more flexible form than MABS to represent context of a social situation, and in particular MFCM, as implemented by Aguilar and others (see e.g., Kosko, 1986; Aguilar 2005, 2013, 2016; Aguilar et al., 2016, 2020; Contreras and Aguilar, 2010; and Sánchez et al., 2019; Puerto et al., 2019). A brief description of Fuzzy and Multi-fuzzy cognitive maps, following Sánchez et al. (2019), is given in the Annex.

Fuzzy cognitive maps help us in describing the context via qualitative (e.g., very low, low, medium, high, too high) and quantitative variables, as indicated in the annex. The system is represented by the network of concepts (variables) interrelated via weights (also given by variables). The high level of the MFCM paradigm, differently from a MABS, permits us to explicit different elements of the models such as the agents constructs (goals, interests, etc.), as well as the modelers assumptions and perspectives, as suggested in Terán (2004). MFCM will facilitate to explicit the accumulated set of assumptions (“abstraction-assumptions, design-assumptions, inference-assumptions, analysis-assumptions, interpretation-assumptions and application-assumptions”, as these are summarized in Terán, 2004).

In a MFCM, a particular situation of the system is given by a specific configuration of the weights (see, e.g., Sánchez et al., 2019). Suppose we are dealing with a model similar to that elaborated in Sánchez et al. (2019) to study the quality of opinion in a community. Sánchez et al. examine the capabilities of the MFCM for knowledge description and extraction about opinions presented in a certain topic, allowing the assessment of the quality of public opinion. Special attention is offered to the influence of the media on public opinion. The evolution of the concepts and relationships is presented. Concepts define the relevant aspects from which public opinion emerges, covering diverse domains, for instance, the social, technological and psycho-biological ones. The MFCM permits to identify the media preferred by the public in order to better understand several issues, including the high esteem that the new communication media hold.

In line with this, let us assume that we want to understand the quality of public opinion in a community of Europe about diverse issues during 2022. This network, with a certain configuration of the weights, but unspecified concepts, represents a social system with a certain structure (as the weights are given) that is in some sense general, as the values of the concepts can still vary. Variation of the concepts represents different scenarios of the social system (with a given structure, defined by the weights); e.g., the model of a European community considered in relation to three scenarios regarding the state of public opinion in relation to specific issues: 1: climate change, 2: situation of tourism in the community, 3: secondary effects of the COVID-19 vaccines. The weights of the network are determined by using a variety of scenarios; i.e., the network is trained with several scenarios, for which all possible values of the concepts are known. Once the network is trained, it can be used to infer unknown specific values of the concepts for other scenarios (following Aguilar et al. 2020; Sánchez et al. 2019; Terán y Aguilar, 2018); e.g., the state of public opinion in relation to the involvement of EU in the war in Ukraine. Even more, by exploring an appropriate set of scenarios, proofs about the state of certain concepts can be developed; e.g., that a majority of people in the community is against direct EU involvement in the war in Ukraine. The proof could be carried out for a subset of the possible configurations of a domain, several domains, or part of a domain, e.g., for the psycho-biological domain. Additionally, having an appropriate elaboration of the model would allow evaluating how polarized is the opinion of the community in relation to the involvement of EU in that war.

Diverse configurations of the MFCM can represent different modelers’ perspectives and assumptions, as well as various agents’ constructs, such as goals, interests, etc., allowing to deal with the above described drawbacks of MABS to cope with complexity of social systems.

5. Combined use of MABS and cognitive maps

The combined usage will give at least two levels of modeling: the inner, defined by the agents’ interaction concreted in a MABS, and the outer or contextual one, given by the MFCM. These will be the two last levels in the description given in 5.1. Interaction between these models occurs as the modeler interprets each model outputs and feedbacks the other. Ideally, we would have direct automatic feedback between these models.

5.1 Levels of description of the System

In order to contextually model a social system and investigate problems such as polarization, we suggest below five levels of description of the system. The first three levels are not directly associated to computational models, while levels four and five are descriptions that assist development of the computational models: MFCM and MABS, respectively. Each level gives context to the following one (the first gives context to the second, etc.). A lower level (e.g., 1. in relation to 2.) of description corresponds to a more general language, as suggested in Terán (2004). Each level must take into account the previous levels, especially the immediately superior level, which gives the most immediate context to it. This description is in line with the suggestions given in Terán (Idem). Each description makes certain assumptions and is shaped by the modeler’s perspective, which in part is coming from those actors given information to build the model. Assumptions and perspectives introduced in level of modeling i, i = 1, …, 6, can be called Assumptions-given in (i) and Perspectives-given in (i). At levels of description j, Assumption i = 1, 2, …, i are accumulated, and can be called Assumptions(j), as well as holistic Perspective(j) based on Perspectives-given in (i), i = 1, 2, .., i.  These assumptions and perspectives correspond to those defined in Terán (2004) as “abstraction-assumptions, design-assumptions, inference-assumptions, analysis-assumptions, interpretation-assumptions and application-assumptions”.

  1. Describe in natural language the system, including its relevant history, with emphasis in culture (practices, costumes, etc.) and behavior of individuals and groups relevant to the object of the study, e.g., from a historical-ontological perspective. Here, how the system has reached its actual situation is explained. This will give a global view of the society and the general form of behavior, problematics, conflicts, etc.
  2. Describe the diverse relevant domains given context to the system of interest in accordance with the study, e.g., political, economical, dominant actors, etc., and the relationships among them. Concrete specifications of these domains sets scenarios for the real system, i.e., possible configurations of it.
  3. Describe the particular social group of interest as part of the society explained above, in 1., and the domains given in 2., showing its particularities, e.g., culturally, in terms of interests, situation and social interaction of this group in relation with other groups in the whole society, in accordance to the problematic addressed in the study.
  4. Elaborate a cognitive map of the situation of the social group of interest, following the description given in 2 and 3. This is a description to be represented in a computational language, such as the MFCM tool developed by Contreras and Aguilar (2010).
  5. Describe the MABS model. The MABS model is then represented in a simulation language.
  6. The computational MFCM (or other cognitive map) and the MABS developed following 4. and 5. are then used to generate the virtual outputs and simulation study.

5.2 Possible combined uses of MFCM and MABS.

The MFCM (in general a cognitive or conceptual map) gives context to the MABS model (modeler’s assumptions and perspectives are added in the process, as indicated above), while the MABS model represents in detail the interaction of the agents’ considered in the MFCM for a specific scenario of this, as indicated in the levels of modeling given above. With this idea in mind, among the specific forms a combined usage of ABM and MFCM, we have:

i) Offering feedback from the MFCM to the MABS. A MABS in a certain configuration can be used to generate either directly or indirectly (e.g., with additional verification or manipulations) input for a simulation model. For example, in parallel to the model presented in Sánchez et al. (2019), where the domains social, biological-psychological, technological and state of the opinion are displayed, a MABS model can be developed to represent the interaction between social entities, such as people who receive information from the media, the media itself, and powerful actors who design the agenda setting of the media. This MABS model might use diverse methodologies, e.g., endorsements or BDI, to represent social interaction, or a higher level of interaction where actors share resources, on which they have interest, as in a System of Organized Action (see, e.g., SocLab models Terán and Sibertin-Blanc, 2020; Sibertin-Blanc et al., 2013). Constructs required as inputs for the model, e.g., goals, interests, values to define the endorsements schema, etc. could be deducted from the MFCM, as direct values of some concepts or functions (mathematical, logical, etc.) of the concepts. These operations could be defined by experts in the modeled domains (e.g., media owners, academics working in the area, etc.). Ideally, we would have an isomorphic relation between some variables of the MABS and variables of the MFCM – however, this is not the usual case –. In this process, the MABS is contextualized by the MFCM, whose modeling level also permits to identify modeler’s assumptions and perspectives. Also, in a narrative, and then in the MFCM, goal, interest, and other constructs can be explicitly represented, then varied and their consequence understood in order to feedback the MABS model.

ii) Giving feedback to the MFCM from the MABS. Inputs and outputs values of the MABS simulation can be used as an input to the MFCM, e.g., as a set of scenarios to train the network and determine a certain structure of the MFCM, or to determine a specific scenario/ configuration (where both, the weights and the concepts are known).

iii) Determining conditions of correspondence among the models. By simulating the MABS associated to certain scenarios of the MFCM, or, vice-verse, by determining the scenarios of MFCM related to certain MABS, the consistency among the two models and possible errors, omissions, etc. in one of the models can be detected, and then the corrections applied. Even more, this exercise can hopefully determine certain rules or conditions of correspondence among the MABS and the MFCM.

iv) Using a model to verify properties in the other model. Once certain correspondence among the models has been determined, we can use one of the models to help in determining properties of the other. For instance, a proof of a tendency in an MABS (this has been an important area of research, Terán, 2001; Terán et al. 2001; Edmonds et al., 2006) could be developed in a much easier form in the corresponding MFCM. For this, we need to characterize the set of configurations of the MFCM corresponding to the set of configurations of the MABS for which we want to perform the proof.

These possible combined uses of MFCM and MABS do not exhaust all potentials, and diverse other alternatives could appear in accordance with the needs in a particular study. Even more, automatic feedback between MFCM (or other cognitive or conceptual map) and MABS could be implemented in the future, to facilitate the mutual contributions between the two modeling approaches. This would cover modeling requirements the MABS in itself does not support at present.

5.3 A case: Modeling othering and polarization, the case of “children with virtually mediated culture”.

We outline a possible model that considers othering and polarization. In section 2 we described a society. In a society, as virtual groups become homogeneous in beliefs, motivations, intentions and behavior, certain sort of endogamy of ideas and opinions appear, constraining the variety and richness of perspectives from which people observe and judge others, making them generally less tolerant to others, more restrictive in accepting opinions and behavior of others, so less inclusive. This has diverse additional effects, for instance, increase of polarization between virtual groups regarding a diversity of themes. Problems such as polarization occur also in children with strong usage of virtual social networks (see, Prensky, 2001a, 2001b, 2009).

To investigate this problem and support the MABS, as a case, we suggest a MFCM with four levels (see Figure 1). The goal of the models (MFCM and MABS) would be to better understand the differences between the communities of children whose interaction is basically virtually mediated and the community of children whose interaction is face to face, or direct, people to people. In general, it is of interest to determine the state of othering and polarization for diverse configurations of the MFCM. As we explained above, there are clear differences between virtual and face to face interaction, consequently the upper layers in Figure 1 are the two possible niches of cultural acquisition (costumes, points of view, etc.), during life of people (ontogenesis), namely, the virtual mediated culture and the direct, face to face, cultural acquisition. These two layers involve interaction among diverse actors (e.g., people, media and powerful actors are present in layer 2). Layer 2 represents technological actors, while layer 1 represents social interaction, but both of them might involve other elements, if required. The third level represent those biological aspects related with behavior, which are created via culture: the psycho-biological level. Both levels, 1 and 2, affect the third layer, as emotions, reasoning, etc., are founded on people interaction and have a cultural base. Constructs of behavior such as goals, interests, desires, polarization, etc., appear and can be explicitly represented at this level. This third level, in turn, impacts on the overall state of the community, e.g., on the auto-generative capacity of the society, finally affecting global society/community’s othering and polarization, as our emotions, reasoning, etc., impact on our view point, on othering, etc. These last are variables defined in terms of the previous levels. In this model, the definition of concepts such as “othering” and “polarization” is crucial, and indicates basic modeling assumptions and perspective. Finally, the overall state of society/community impacts back on the cultural niches (layers 1 and 2).

In a specific situation, the whole interaction (1) of the society or community is divided between the two niches given by layers 1 and 2, a proportion of interaction frequency occurs as virtual communication, and the compliment (one minus the proportion of virtual interaction), occurs as direct, face to face, contact. This is represented in Figure 3 by the variable “Proportion of virtual interaction type”. Changes of this variable allows us to explore diverse configurations or scenarios of interaction, ranging from total virtual interaction (null direct contact) (the variable takes the value 1), to null virtual interaction (total direct contact) (the variable takes the value 0).

The four levels of MFCM

Figure 1. The four levels of the MFCM. The two alternative niches structuring the psycho-biology of people are at the top of the process. The overall state represents general measures such as the auto-generative character of a social system, and attitudes including othering and polarization.

Example of possible variables in some levels (Figure 1) are:

i) Face to face interaction, and ii) virtual interaction or technological: The next variables are candidates to be at these levels. Degree of:

  •  Coherence of the interaction (possible state: good, etc.);
  •  Identification of the others in the interaction (good or clear, etc.);
  •  Richness of the interaction (high or good, etc.);
  •  Truthfulness of the messages (fairness) (e.g., good: messages and communication are fair);
  •  Openness of the community (e.g., high: usually people is open to interact with others);
  •  Speed of the interaction (e.g.: low, medium, …);
  •  Intentioned influence and control of the communication by powerful actors (e.g., high, medium, low, ..);

iii) Psycho-biological level

  •  Reflection (state: good means that people question their experiences, and observed phenomena);
  • Closeness of interpretations, attitudes, desires, intentions, and plans (a high value means that people’s interpretations, etc., are not very different);
  •  Emotion and mood;
  •  Empathy;
  •  Addiction to virtual interaction;
  • Goal;
  •  Interest;
  •  Immediatism (propensity to do things quickly and constantly change focus of reasoning).

iv) Overall state of people and society:

  •  Auto-generative capacity of the society;
  •  Capacity of people to reflect about social situations (and autonomously look for solutions);
  •  Othering;
  •  Polarization; 

Concepts at each layer impacts concepts at the other layers. E.g., concepts of level three have a strong impact on concepts of the fourth layer, such as “polarization”, and “auto-generative character of the society”.

As indicated above, to understand the dynamics of the MFCM we can develop a wide range of scenarios, for instance, varying the switch “Proportion of virtual interaction” in the interval [0, 1], to explore a set of scenarios for which the degree of virtual interaction increases from 1 to 0, as the proportion of direct interaction decreases from 1 to 0 (the real case corresponds to an intermediate value between 1 and 0). These experiments will help us in understanding better the consequences of virtual mediated culture. Even when the outline of the model presented here might need some adjustments and improvements, the present proposal keeps its potential to reach this goal.

The MFCM will be useful to deal with many issues and questions of interest, for instance:

  • How social networks affect basic social attitudes such as: i) critical rationality (people’s habit for questioning and explaining their experience (issues/phenomena in their life)), ii) tolerance, iii) compromise with public well-being, and iv) othering and polarization
  •  How social networks affect social feelings, such as empathy.

The MABS model will be elaborated in accordance with the description of the MFCM indicated above. In particular, different values of the social constructs at levels 1 and 2 (e.g., goals and interests of the actors), and the corresponding state of layer 3 (e.g., Polarization), imply diverse MABS models.

The whole network of concepts, the particular network of concepts at each level, and the definition of each concept, offers a perspective of the modelers. Different modelers can develop these elements of the model differently. Assumptions can be identified also at each level. Both, perspectives and assumptions come from the modelers as well as from the theories, consult to experts to create the model, etc.. An specific model is not part of this essay, but rather a subject of future work.

6. Conclusion

Social simulation has been widely recognized as an alternative to study social systems, using diverse modeling tools, including MABS, which, however, present some limitations, like any other research tool. One of the deficiencies of MABS is their limitations to contextually modeling social systems; e.g., to suitably include the historical and political contexts or domains; difficulties to represent variation of agents’ constructs, e.g., goals and interest; and drawbacks to made explicit modeler’s assumptions and perspectives. In this paper, we have suggested to mutually complement MABS and MFCM, to overcome MABS drawbacks, to potentiate the usefulness of MABS to represent social systems.

We argue that the high level of the MFCM paradigm permits us to express different elements of the models such as the agents’ constructs (goals, interests, etc.), as well as the modelers assumptions and perspectives, as suggested in Terán (2004). Thus, MFCM facilitates the identification of the accumulated set of assumptions during the modeling process. Even more, diverse configurations of a MFCM can represent diverse modelers’ perspectives and assumptions, as well as diverse agents constructs, such as goals, interests, etc., allowing to deal with the above described complexity. This permits us to more realistically elaborate models of a wide diversity of social problems, e.g., polarization, and consequences of the influence of social networks in culture.

Among the forms MFCM and MABS complement each other we have identified the followings:  mutual feedbacking of variables and concepts between the MFCM and the MABS, determining conditions of correspondence among the models, what facilitate other modeling needs, e.g., using a model to verify properties in the other model (e.g., proofs required in a MABS could be carried out in a corresponding MFCM).

A case study was outlined to exemplify the problematic that can be addressed and the advantages of using MFCM to complement MABS: Modeling othering and polarization, the case of children with virtually mediated culture. Combined use of MFCM and MABS in this case will contribute to understand better the problems created by the high use of digital interaction, especially social networks, as described by Prensky (2001a, 2001b, 2009), given that virtual interaction has strong influence on our culture, impacting on ours myths, rites, perspectives, goals, interests, opinion, othering and polarization, etc. Characteristics of virtual communication, e.g., anonymity, significantly impacts on all these constructs, which, differently from natural interaction, have a strong potential to promote certain tendencies of such constructs, e.g., polarization or our opinions, because of several reasons, for instance, given that virtual environments usually create less reflexive groups, while emotional communication is poorer or lack deepness. It is difficult to represent all these dynamics in a MABS, but it can be alternatively expressed in a MFCM.

The purpose of the work was to give an outline of the proposal; future work will be conducted to wholly develop concrete study cases with complementary MABS and MFCM models.


Aguilar, J. (2005). A Survey about Fuzzy Cognitive Maps Papers. International journal of computational cognition 3 (2), pp. 27-33.

Aguilar, J. (2013) Different Dynamic Causal Relationship Approaches for Cognitive Maps”, Applied Soft Computing, Elsevier, 13(1), pp. 271–282.

Aguilar, J. (2016) “Multilayer Cognitive Maps in the Resolution of Problems using the FCM Designer Tool”, Applied Artificial Intelligence, 30 (7), pp. 720-743.

Aguilar J., Hidalgo J., Osuna F., Perez N.(2016) Multilayer Cognitive Maps to Model Problems”, Proc. IEEE World Congress on Computational Intelligence,  pp. 1547-1553, 2016.

Aguilar Jose, Yolmer Romero y OswaldoTerán (2020). “Analysis of the effect on the marketing of the sport product from the “par Conditio” principle in Latin American football and baseball competitions”. Submitted to International Journal of Knowledge-Based and Intelligent Engineering Systems.

Contreras, J. Aguilar, J. (2010). “The FCM Designer Tool”. Fuzzy Cognitive Maps: Advances in Theory, Methodologies, Tools and Application (Ed. M. Glykas), Springer, pp. 71-88, 2010.

Edmonds, B. and Hales, D. and Lessard-Phillips, L.(2020). Simulation Models of Ethnocentrism and Diversity: An Introduction to the Special Issue. Social Science Computer Review. Volume 38 Issue 4, August 2020, 359–364, https://journals.sagepub.com/toc/ssce/38/4

Edmonds Bruce, Oswaldo Terán y Grary Polhill (2006). “To the Outer Limits and Beyond –characterising the envelope of social simulation trajectories”, Proceedings of theThe First World Congress on Social Simulation WCSS”, Kyoto, 21-25 Agosto, 2006.

Giabbanelli Philippe, Steven Gray and Payam Aminpour (2017), Combining fuzzy cognitive maps with agent-based modeling: Frameworks and pitfalls of a powerful hybrid modeling approach to understand human-environment interactions, Environmental Modeling and Software, September 2017,  95:320-325 DOI:10.1016/j.envsoft.2017.06.040

Kosko, B. (1986). Fuzzy Cognitive Maps. International Journal of Man-Machine Studies 24, pp. 65-75.

Perozo Niriaska, Jose Aguilar, Oswaldo Terán y Heidi Molina (2013). A Verification Method for MASOES, IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, Vol 43, num 1, February, pp. 64-76,  ISBN: 1083-4419. DOI: 10.1109/TSMCB.2012.2199106

Prensky, Marc (2001a). Digital Natives, Digital Immigrants Part 1, On the Horizon, Vol. 9, No. 5, September, pp 1-6. DOI: 10.1108/10748120110424816

Prensky, Marc (2001b). Do They Really Think Differently? Digital Natives, Digital Immigrants Part 2, On the Horizon, Vol. 9, No. 6, October 2001, pp 1-6. DOI: 10.1108/10748120110424843

Prensky, Marc (2009). “H. Sapiens Digital: From Digital Immigrants and Digital Natives to Digital Wisdom,” Innovate: Journal of Online Education: Vol. 5 : Issue 3, Article 1. Available at: https://nsuworks.nova.edu/innovate/vol5/iss3/1

Puerto E., Aguilar J., Chávez D., López C. (2019) Using Multilayer Fuzzy Cognitive Maps to Diagnose Autism Spectrum Disorder, Applied Soft Computing Journal, 75, pp. 58–71.

Rocco Paolillo, and Wander Jager (2020). Simulating Acculturation Dynamics Between Migrants and Locals in Relation to Network Formation, Social Science Computer Review. Volume 38 Issue 4, August 2020, pp. 365–386. https://journals.sagepub.com/toc/ssce/38/4

Sánchez Hebert, Jose Aguilar, Oswaldo Terán, José Gutiérrez de Mesa (2019). “Modeling the process of shaping the public opinion through Multilevel Fuzzy Cognitive Maps”, Applied Soft Computing, Volume 85. https://doi.org/10.1016/j.asoc.2019.105756.

Sibertin-Blanc, C., Roggero, P., Adreit, F., Baldet, B., Chapron, P., El-Gemayel, J., Mailliard, M., and Sandri, S. (2013). “SocLab: A Framework for the Modeling, Simulation and Analysis of Power in Social Organizations”, Journal of Artificial Societies and Social Simulation (JASSS), 16(4). http://jasss.soc.surrey.ac.uk/

Terán Oswaldo (2001). Emergent Tendencies in Multi-Agent Based Simulations Using Constraint-Based Methods to Effect Practical Proofs Over Finite Subsets of Simulation Outcomes, Doctoral Thesis, Centre for Policy Modelling, Manchester Metropolitan University, 2001.

Terán Oswaldo  (2004). Understanding MABS and Social Simulation: Switching Between Languages in a Hierarchy of Levels, Journal of Artificial Societies and Social Simulation vol. 7, no. 4. http://jasss.soc.surrey.ac.uk/7/4/5.html

Terán Oswaldo, Edmonds Bruce and Steve Wallis (2001) “Mapping the Envelope of Social Simulation Trajectories”, Lecture Notes in Artificial Intelligence (Subserie de Lecture Notes in Computer Science): MABS, Volume 1979, pp. 229-243, Springer, Alemania, 2001

Terán Oswaldo y Jose Aguilar (2018). “Modelo del proceso de influencia de los medios de comunicación social en la opinión pública”, EDUCERE, 21 (71), Universidad de Los Andes, Mérida, Venezuela. https://www.redalyc.org/toc.oa?id=356&numero=56002

Terán Oswaldo and Christophe Sibertin-Blanc (2020). Impact on Cooperation of altruism, tenacity, and the need of a resource,  accepted in IEEE Transactions on Computational Social Systems. DOI: 10.1109/TCSS.2021.3136821.

Annex. Fuzzy Cognitive Maps (FCM) and Muti-Fuzzy Cognitive Maps (MFCM).

Cognitive map theory is based on symbolic representation for the description of a system. It uses information, knowledge and experience, to describe particular domains using concepts (variables, states, inputs, outputs), and the relationships between them (Aguilar 2005, 2013, 2016). Cognitive maps can be understood as directed graphs, whose arcs represent causal connections between the nodes (concepts), used to denote knowledge. An arc with a positive sign (alternatively, negative sign), going from node X to node Y means that X (causally) increases (alternatively, decreases) Y. Cognitive maps are graphically represented: concepts are connected by arcs through a connection matrix. In the connection matrix, the i-nth line represents the weight of the arc connections directed outside of the  concept. The i-nth column lists the arcs directed toward , i.e., those affecting .

The conceptual development of FCMs rests on the definition and dynamic of concepts and relationships created by the theory of fuzzy sets (Kosko, 1986). FCM can describe any system using a causality-based model (that indicates positive or negative relationships), which takes fuzzy values and is dynamic (i.e., the effect of a change in one concept/node affects other nodes, which then affect further nodes). This structure establishes the forward and backward propagation of causality (Aguilar, 2005, 2013, 2016). Thus, the concepts and relations can be represented as fuzzy variables (expressed in linguistic terms), such as “Almost Always”, “Always”, “Normally”, “Some (see Figure 2).

The value of a concept depends on its previous iterations, following the equation (1):

Screenshot 2022-05-23 at 15.10.24

Cm(i+1) stands for the value of the concept in the next iteration after the iteration i, N indicates the number of concepts, wm,k represents the value of the causal relationship between the concept Ck and the concept Cm, and S(y) is a function used to normalize the value of the concept.


Figure 2. Example of an FCM (taken from Sánchez et al., 2019).

MFCM is an extension of the FCM. It is a FCM with several layers where each layer represents a set of concepts that define a specific domain of a system. To construct a MFCM, the previous equation for calculating the current status of the concepts of a FCM is modified, to describe the relationships between different layers (Aguilar, 2016):

Where F(p) is the input function generated by the relationships among different layers, and p is the set of concepts of the other layers that impact this concept. Thus, the update function of the concepts has two parts. The first part, the classic, calculates the value of  concept in iteration  based on the values of concepts in the previous iteration . All these concepts belong to the same layer where the “m” concept belongs. The second part is the result of the causal relationship between the concepts in different levels of the MFCM.

Terán, O. & Aguilar, J. (2022) Towards contextualized social simulation: Complementary use of Multi-Fuzzy Cognitive Maps and MABS. Review of Artificial Societies and Social Simulation, 25th May 2022. https://rofasss.org/2022/05/25/MFCM-MABS