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Cognitive Maps are a vital tool that can be used for knowledge representation and reasoning. Fuzzy Cognitive Maps (FCMs) are popular soft computing techniques used to model large and complex systems, and they can aid in explainable AI. FCMs, however, cannot model the indeterminacy that arises in a system due to various uncertainties. Neutrosophic Cognitive Maps (NCMs), upgraded FCMs that could model indeterminacy, was introduced to address this issue. NCMs are a generalization of FCMs, a field of cognitive science firmly based on neural networks. NCMs have been used to solve a wide range of problems. NCMs were introduced in 2002, and even after 20 years, NCMs do not have any supportive software or package, toolbox, or visualization software like FCMs. The main reason for the absence of dedicated software is due to the indeterminacy concept ‘I’ and how it has to be handled. This paper presents the dedicated Python package created for handling the functioning of NCMs. The modelling software presented in this paper aids in visualizing the NCMs as a signed digraph with indeterminacy that is directed signed neutrosophic graph. This package implements a sample case study using NCMs.
Fuzzy Cognitive Maps (FCM) constitute cognitive models in the form of fuzzy directed graphs consisting of two basic elements: the nodes, which basically correspond to “concepts” bearing different states of activation depending on the knowledge they represent, and the “edges” denoting the causal effects that each source node exercises on the receiving concept expressed through weights. Weights take values in the interval [-1,1], which denotes the positive, negative or neutral causal relationship between two concepts. An FCM can be typically obtained through linguistic terms, inherent to fuzzy systems, but with a structure similar to the neural networks, which facilitates data processing, and has capabilities for training and adaptation. During the last 10 years, an exponential growth of published papers in FCMs was followed showing great impact potential. Different FCM structures and learning schemes have been developed, while numerous studies report their use in many contexts with highly successful modeling results. The aim of this book is to fill the existing gap in the literature concerning fundamentals, models, extensions and learning algorithms for FCMs in knowledge engineering. It comprehensively covers the state-of-the-art FCM modeling and learning methods, with algorithms, codes and software tools, and provides a set of applications that demonstrate their various usages in applied sciences and engineering.
Likert scale is the most widely used psychometric scale for obtaining feedback. The major disadvantage of Likert scale is information distortion and information loss problem that arise due to its ordinal nature and closed format. Real-world responses are mostly inconsistent, imprecise and indeterminate depending on the customers’ emotions. To capture the responses realistically, the concept of neutrosophy (study of neutralities and indeterminacy) is used. Indeterminate Likert scale based on neutrosophy is introduced in this paper. Clustering according to customer feedback is an effectiveway of classifying customers and targeting them accordingly. Clustering algorithm for feedback obtained using indeterminate Likert scaling is proposed in this paper. While dealing real-world scenarios, indeterminate Likert scaling is better in capturing the responses accurately.
This important edited volume is the first such book ever published on fuzzy cognitive maps (FCMs). Professor Michael Glykas has done an exceptional job in bringing together and editing its seventeen chapters. The volume appears nearly a quarter century after my original article “Fuzzy Cognitive Maps” appeared in the International Journal of Man-Machine Studies in 1986. The volume accordingly reflects many years of research effort in the development of FCM theory and applications—and portends many more decades of FCM research and applications to come. FCMs are fuzzy feedback models of causality. They combine aspects of fuzzy logic, neural networks, semantic networks, expert systems, and nonlinear dynamical systems. That rich structure endows FCMs with their own complexity and lets them apply to a wide range of problems in engineering and in the soft and hard sciences. Their partial edge connections allow a user to directly represent causality as a matter of degree and to learn new edge strengths from training data. Their directed graph structure allows forward or what-if inferencing. FCM cycles or feedback paths allow for complex nonlinear dynamics. Control of FCM nonlinear dynamics can in many cases let the user encode and decode concept patterns as fixed-point attractors or limit cycles or perhaps as more exotic dynamical equilibria. These global equilibrium patterns are often “hidden” in the nonlinear dynamics. The user will not likely see these global patterns by simply inspecting the local causal edges or nodes of large FCMs.
In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.
Cognitive Illusions investigates a wide range of fascinating psychological effects in the way we think, judge and remember in our everyday lives. At the beginning of each chapter, leading researchers in the field introduce the background to phenomena such as illusions of control, overconfidence and hindsight bias. This is followed by an explanation of the experimental context in which these illusions can be investigated and a theoretical discussion drawing conclusions about the wider implications of these fallacy and bias effects. Written with researchers and instructors in mind, this tightly edited, reader-friendly text provides both an overview of research in the area and many lively pedagogic features such as chapter summaries, further reading lists and suggestions for classroom demonstrations.
An account that analyzes the dynamic reasoning processes implicated in a fundamental problem of creativity in science: how does genuine novelty emerge from existing representations? How do novel scientific concepts arise? In Creating Scientific Concepts, Nancy Nersessian seeks to answer this central but virtually unasked question in the problem of conceptual change. She argues that the popular image of novel concepts and profound insight bursting forth in a blinding flash of inspiration is mistaken. Instead, novel concepts are shown to arise out of the interplay of three factors: an attempt to solve specific problems; the use of conceptual, analytical, and material resources provided by the cognitive-social-cultural context of the problem; and dynamic processes of reasoning that extend ordinary cognition. Focusing on the third factor, Nersessian draws on cognitive science research and historical accounts of scientific practices to show how scientific and ordinary cognition lie on a continuum, and how problem-solving practices in one illuminate practices in the other. Her investigations of scientific practices show conceptual change as deriving from the use of analogies, imagistic representations, and thought experiments, integrated with experimental investigations and mathematical analyses. She presents a view of constructed models as hybrid objects, serving as intermediaries between targets and analogical sources in bootstrapping processes. Extending these results, she argues that these complex cognitive operations and structures are not mere aids to discovery, but that together they constitute a powerful form of reasoning—model-based reasoning—that generates novelty. This new approach to mental modeling and analogy, together with Nersessian's cognitive-historical approach, make Creating Scientific Concepts equally valuable to cognitive science and philosophy of science.
This paper introduces Single Valued Refined Neutrosophic Set (SVRNS) which is a generalized version of the neutrosophic set. It consists of six membership functions based on imaginary and indeterminate aspect and hence, is more sensitive to real-world problems.