Fuzzy Cognitive Maps

The academic community cannot ignore the growing opportunities offered by artificial intelligence. Especially relevant are developments in this ares against the background of growing challenges and threats arising from the use of the digital environment by actors of psychological warfare-by strategists and tactics of "color revolutions' as well as terrorist and criminal groups. The main objective of the paper is to develop efective instruments to counter the destructive psychological impact on the individual, society, and the state. As a tool in such psychological warfare, the authors see the use of hybrid intellectual systems for decision support bazed on fuzzy cognitive maps, the method of hierarchies, and artificial neural networks. The authors also state for the creation of the mathematical models of decision support in psychological warfare and discuss the need for training based on data mining, obtained from the Internet, using deep learning networks.

A literature review showed that finance is a driver of sustainability. However, to achieve sustainability through finance, it is necessary to rebuild and adapt the financial system to the specifics of sustainable development. Modern financial systems can be described as one-dimensional, focusing on ensuring the economic security of transactions. Meanwhile, the growing role of risk related to non-financial factors means that the factors referred to as ESG (environmental, social, governance) become the main source threatening the stability of financial systems. Adaptation activities toward the design of so-called three-dimensional financial systems rely on incorporating ESG risk into the financial decisions of the financial institutions that make up the financial system. This is found, among other factors, in the risk assessment methodology. The general goal of the paper is to investigate which ESG criteria are incorporated into the decision-making process of financial institutions an...

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

Strategic thinking is one of the most important capabilities which managers of today's organizations must possess. Holding companies, due to the kind of problems that they experience, are in serious need of managers capable of strategic thinking. The present research has been conducted with the aim of identifying the individual dimensions of strategic thinking in holding companies' managers in Iran. In this regard, a number of managers who have had the experience of being members of the board of directors or working as CEOs of these firms have been asked to express their opinions about strategic thinking and their views have been analyzed using fuzzy cognitive maps. Results suggest that having vision, ability to analyze, having systems thinking, ability to question, creativity, ability to make synergy and ability to create advantage are the main elements of strategic thinking in successful managers of holding companies. In addition, the relationships among these variables have been explained.

International Journal of Fuzzy Logic Systems (IJFLS) is an open access peer-reviewed journal that covers all topics in theoretical, experimental and applied fuzzy techniques and systems. It is aimed to bring together researchers and developers from both academia and industry to discuss the latest scientific and theoretical advances in this field, and to demonstrate the state-of-the-art systems. The journal solicits original technical papers that were not previously published and are not currently under review for publication elsewhere.

Nuclear weapons are seemingly permanent fixtures in international relations. Although nuclear abolitionists and actors within the Nonproliferation Treaty (NPT) and the International Atomic Energy Agency (IAEA) have taken significant steps towards designing a world without
nuclear weapons, the longstanding realist logic that suggests nuclear disarmament is unenviable has born more fruit. On the other hand, some proponents of realism have suggested global nuclear disarmament is feasible, given that certain international instabilities are stabilized and that special care is taken during diplomatic negotiations. This presents an opportunity to test these predictions using fuzzy cognitive mapping, a computational modeling technique that identifies problems, their stakeholders, and stakeholders’ components in order to determine scenarios that solve complex disputes in ways that benefit the system as a whole. This study identifies two problems regarding nuclear disarmament. First, nuclear weapon states are resistant to giving up nuclear weapons, despite agreements to disarm. This problem follows realist logic. Second, the role that the IAEA plays in safeguarding special nuclear materials while guaranteeing states’ rights to nuclear technology is contrasted by states’ interest in maintaining levels of secrecy. These two problems constitute a “mess” that this study analyzes. Synthesis between the problems requires that solving one does not make the other worse. Therefore, this study tests various scenarios and finds that, given present-day international instabilities are stabilized, nuclear disarmament is feasible if three conditions are met: First, a global disarmament agreement must not unreasonably affect states’ sovereign rights outside of the agreement. Second, states outlying the NPT must be brought into the negotiations. Finally, present states with nuclear arsenals adopt the IAEA’s Comprehensive Safeguards Agreement with the Additional Protocol as a measure of good faith. A final factor suggests states’ rights to the technology inevitably means states should have an ability to re-proliferate in the event of future international instability that threatens global security. Once these steps are taken and technological rights guaranteed, this model suggests global nuclear disarmament is possible.

The study of this paper suggests on dependency problem in fuzzy computational method by using the numerical solution of Fuzzy differential equations(FDEs) in Milne's predictor-corrector method. This method is adopted to solve the dependency problem in fuzzy computation. We solve some fuzzy initial value problems to illustrate the theory. KEYWORDS Fuzzy initial value problem, Dependency problem in fuzzy computation, Milnes predictor-corrector method.

Please cite this article as: A. Nair, D. Reckien and M.F.A.M. van Maarseveen, Generalised fuzzy cognitive maps: Considering the time dynamics between a cause and an effect, Applied Soft Computing Journal (2020), doi: https://doi. Abstract Fuzzy Cognitive Maps (FCMs) have been used to quantitatively model the dynamics of complex systems and predict their behaviours. However, they are usually unable to address the issues arising from time lags between causes and effects. Accordingly, Generalized Fuzzy Cognitive Maps (GFCMs) have been introduced to overcome this problem. This article deals with a breed of GFCMs that addresses time lags between cause(s) and effect(s), demonstrated by a case-study that deals with the social, economic and technological consequences of heavy rainfall in Kampala, Uganda. The results show that the inclusion of time lags alters both, the final steady-state values of the social, economic and technological consequences of heavy rainfall and the time taken to stabilise. Thus, the inclusion of time lags increases the reliability of GFCMs as a means to quantitatively model the dynamics of complex systems.

Corporate and institutional senior executives use the information presented to them by (or through) data scientists for decision-making without an appreciation for the robust science underlying the analysis.  This paper introduces complexity science to executives and provides the background for additional study.

The increasingly complex challenges facing agricultural systems require problem-solving processes and systems analysis (SA) tools that engage multiple actors across disciplines. In this article, we employ the theory of af-fordances to unravel what tools may furnish users, and how those affordances contribute to a tool's usefulness in co-design and co-innovation processes. Affordance is defined as a function provided by an object through an interaction with a user. We first present a conceptual framework to assess the affordances of SA tools. This framework is then applied in a literature review of three SA tools used in agricultural systems research (fuzzy cognitive mapping, bio-economic whole-farm models, and role play and serious games). Through this exercise, we extend the SA tool design and implementation dialogue by illuminating (i) links between lower-level af-fordances, tool design, and heuristic functioning, and (ii) the central role of use setting and facilitation in mobilizing higher-level, productive affordances. Based on our findings, we make five propositions for how SA tool design and implementation in participatory problem-solving settings can be improved.

Sports persons’ performance evaluation is a critical issue. The parameters used for this purpose are vague and imprecise. We propose a fuzzy cognitive map based cricket player performance evaluator tool that uses fuzzy logic to perform computation keeping in view the relations among various input parameters. A very simple and effective graphical user interface is build to use the proposed model.

Fuzzy Cognitive Maps (FCMs) were developed as a tool for capturing and modelling the behaviour of qualitative system dynamics. However, several drawbacks have been identified that limit FCMs ability in simulating the behaviour of qualitative system. This paper addresses the limitations of FCMs in modelling complex qualitative system dynamics and proposes a generalised Fuzzy Cognitive Mapping (FCM) approach that is able to overcome those limitations. This approach uses fuzzy rules to represent the dynamics of concepts and relations, including time dynamics of relations and introduces a multistep simulation approach that can use several single layer perceptrons to simulate the dynamics of concepts and relations overtime. This approach also incorporates the fuzziness and ambiguity widely associated with expert knowledge when representing and simulating the dynamics of concepts and relations. In this paper, the design of the proposed generalised FCM approach is explained and demonstrated for a real-world case of the consequences of high intensity rainfall in Kampala City, Uganda. This generalised FCM approach creates a new perspective and an alternative approach to model the behaviour of complex qualitative system dynamics using FCMs.

Purpose – The aim of this paper is to present a research framework to investigate the behaviour of a Special Purpose Entity (SPE), i.e. a temporary project company, in the delivery of a megaproject, and, particularly uncover critical factors affecting the megaproject performance.

Design/methodology/approach – The framework adopts a systemic knowledge-based perspective to construct the complex network of variables of the project governing system coordinated by the SPE. Fuzzy Cognitive Maps (FCMs) are used to elicit knowledge from expert and identify concepts and relationships associated to the variables of the SPE project governing system. Several scenarios are generated by performing FCM simulation.

Originality/value –The proposed research framework allows dealing with the particular nature of uniqueness and complexity of infrastructure megaprojects by adopting a “case-based systemic” research approach to the study of the SPE and its project governing system that does not simplify, but rather preserves these project characteristics, and, in the same time, takes into account environment and context factors.

Practical implications – The simulation output has showed that the contractor(s) technical capability, the SPE project management and planning capability and the SPE technical capability are important variables of the SPE governing system which influence project performance. Because of its flexibility, the framework can be used to model the project governing system coordinated by the SPE at different stages of the megaproject lifecycle, thus identifying the more important features and functions of the different SPE configurations.

In this paper, we consider cognitive maps as an additional tool for
building a knowledge base of the DSS. Here we present the problem of choosing the optimal scenario of the impact between nodes in the cognitive maps based on of the introduced criteria for the optimality of the impact. Two criteria for the optimality of the impact, which are called the force of impact and the speed of implementation of the scenario, are considered. To obtain a unique solution of the problem, a multi-criterial assessment of the received scenarios using the Pareto principle was applied. Based on the criteria of a force of impact and the speed of implementation of the scenario, the choice of the optimal scenario of
impact was justified. The results and advantages of the proposed approach in comparison with the Kosko model are presented. Also we calculate rank distribution of nodes according to the degree of their impact on each other to reveal key and the most influential components of the cognitive map that corresponds some subject domain.

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters.

Keywords: Eventology, event, probability, probability theory, Kolmogorov’s axiomatics, experience, chance, cause, consequence, co∼event, set of co∼events, bra-event, set of bra-events, ket-event, set of ket-events, believability, certainty, believability theory, certainty theory, theory of co∼events, theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.

A literature review showed that finance is a driver of sustainability. However, to achieve sustainability through finance, it is necessary to rebuild and adapt the financial system to the specifics of sustainable development. Modern financial systems can be described as one-dimensional, focusing on ensuring the economic security of transactions. Meanwhile, the growing role of risk related to non-financial factors means that the factors referred to as ESG (environmental, social, governance) become the main source threatening the stability of financial systems. Adaptation activities toward the design of so-called three-dimensional financial systems rely on incorporating ESG risk into the financial decisions of the financial institutions that make up the financial system. This is found, among other factors, in the risk assessment methodology. The general goal of the paper is to investigate which ESG criteria are incorporated into the decision-making process of financial institutions and to verify the level of sustainability of financial systems in selected OECD (Organization for Economic Cooperation and Development) countries. The main research hypothesis assumes that incorporating ESG factors into the decision-making process of financial institutions makes financial systems more sustainable. A two-stage research procedure was used to achieve the research goal. In the first stage, to determine the ESG factors that affect the level of sustainability of financial systems and identify dependencies between ESG factors incorporated by financial institutions into the decision-making process, a fuzzy cognitive map (FCM) was used. The collective map elaborating on the basis of the opinions of experts participating in the study was built using the software FCMapper_bugfix_27.1.2016. In the second stage, based on multiple-criteria decision analysis (MCDA) using the PROMETHEE method (Preference Ranking Organization Method of Enrichment Evaluation), 23 OECD countries that respect the Equator Principles were ranked according to seven groups of criteria defined for financial system assessment (financial depth, development, vulnerability, soundness, fragility, stability, and sustainability), based on a literature review. The ranking confirmed the strong position of Scandinavian countries for assuring best sustainability practices in financial institutions and in the economy. The added value of this paper can be considered at two levels: theoretical and empirical. From the theoretical point of view, it should be noted that it is the first of this kind of analysis which prioritizes ESG factors in financial decisions and ranks financial systems according to fulfilling sustainability criteria. The original empirical approach based on the two-stage research procedure provided analysis of 62 factors, of which 21 represented the environmental scope, 25 the social scope, and 16 the governance scope, which is the main advantage of the empirical study presented in the paper.

New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of the well-known Sclar's theorem on copulas (1959). The Kopulas of doublets and triplets of events are given, as well as of some N-sets of events. For further development of this topic, see my later works: https://www.academia.edu/34390291/, https://www.academia.edu/34373279/, https://www.academia.edu/34357251/

Keywords: eventology, probability, Kolmogorov event, event, set of events, Kopula (eventological copula), Kopula characterizing a set of events.

If you are interested in my work, and you have the opportunity to provide financial support for the publication of my book "Theory of experience and of chance as a theory of being," I ask you to use my PayPal account: paypal.me/EventologyTheory

This paper takes as its starting point a definition of islands that goes beyond geographical isolation to consider islands as social constructs insofar as they reflect feelings of isolation, separateness, distinctiveness and otherness. Nowhere is this truer than in the case of the ‘dry’ island, an island that although once surrounded by water has long since lost its physical isolation due to changes in sea level and drainage patterns. Taking the Isle of Ely in the fens of East Anglia in the United Kingdom between AD 1200-1600 as a case study, and utilising archaeological evidence for diet and for the local Ely ware pottery, it is possible to reconstruct a cognitive mappa, which describes the perception of islandness amongst the island’s medieval inhabitants.

Within large integrative scenario studies, it is often problematic to fully link narrative storylines and quantitative models. This paper demonstrates the potential use of a highly participatory scenario development framework that involves a mix of qualitative, semi-quantitative and quantitative methods. The assumption is that the use of semi-quantitative methods will structure the participatory output, which provides a solid base for quantification. It should further facilitate the communication between stakeholders and modellers. Fuzzy Cognitive Maps is the main semi-quantitative method and has a central place in the proposed framework. The paper provides a detailed description of its implementation in participatory workshops, also because of a lack of documented testing of its implementation. We tested Fuzzy Cognitive Maps as part of the framework in two training sessions; both gave encouraging results. Results show that the tool provides a structured, semi-quantitative understanding of the system perceptions of a group of participants. Participants perceived the method as easy to understand and easy to use in a short period of time. This supports the hypothesis that Fuzzy Cognitive Maps can be used as part of a scenario development framework and that the new framework can help to bridge the gap between storylines and models.

Eventology of multivariate statistics
Eventology and mathematical eventology
Philosophical eventology and philosophy of probability
Practical eventology
Eventology of safety
Eventological economics and psychology
Mathematics in the humanities, socio-economic and natural sciences
Financial and actuarial mathematics
Multivariate statistical analysis
Multivariate complex analysis
Decision-making under risk and uncertainty
Risk measurement and risk models
Theory of fuzzy events and generalized theory of uncertainty
System analysis and events management

EEC'2016 ~ workshop on axiomatizing experience and chance, and Hilbert's sixth problem

With topics from quantum physics, probability and believability to economics, sociology and psychology, the workshop will be intended for an interdisciplinary discussion on mathematical theories of experience and chance. Topics of discussion include the results, thoughts and ideas on axiomatization of the eventological theory of experience and chance in the framework of the decision of Hilbert sixth problem.
Eventology of experience and chance
Beleivability theory and statistics of experience
Probability theory and statistics of chance
Axiomatizing experience and chance

International Journal of Fuzzy Logic Systems (IJFLS) is an open access peer-reviewed journal that covers all topics in theoretical, experimental and applied fuzzy techniques and systems. It is aimed to bring together researchers and developers from both academia and industry to discuss the latest scientific and theoretical advances in this field, and to demonstrate the state-of-the-art systems. The journal solicits original technical papers that were not previously published and are not currently under review for publication elsewhere.

In this paper, we devoted study the existence and controllability for the nonlinear fuzzy neutral integrodifferential equations with control system in E_N. Moreover we study the fuzzy solution for the normal, convex, upper semicontinuous and compactly supported interval fuzzy number. The results are obtained by using the contraction principle theorem. An example to illustrate the theory.

This paper presents a new machinery of compositional rule of inference called fractional fuzzy inference system (FFIS). An FFIS is a fuzzy inference system (FIS) in which consequent parts of a rule base consist of a new type of membership functions called fractional membership functions. Fractional membership functions are characterized using fractional indices. There are two types of fractional indices. Each type can be either constant or dynamic. An FFIS intelligently considers not only the truth degrees of information included in membership functions, but also the volume of the information in the process of making a conclusion. In other words, the volume of information extracted from a membership function depends on the truth degree of information. Concretely, the higher the truth degree, the larger the volume of information that is involved in the process of making a conclusion. It is shown that typical FISs, e.g. Mamdani’s or Larsen’s FISs, are special cases of FFISs. Specifically, as the fractional indices approach one, the FFIS approaches a typical FIS. In addition, using two theorems proved in this paper, it is demonstrated that, independent of the problem in question, a typical FIS never leads to results which are more satisfactory than those obtained by the FFIS corresponding to the typical FIS provided that a particular set of fractional indices is taken into account. Put another way, it seems sound to expect that applying FFIS always leads to more satisfactory results than applying its corresponding FIS. It is also shown that FFIS grants a special dynamic to FIS which can be also customized according to a new concept called reaction trajectories map (RTM). Particularly, the RTM enables decision makers to select an FFIS more suitable for their purpose. Some more concepts such as the left and right orders of an FFIS and the fracture index are also introduced in this paper.