Fuzzy Cognitive Maps Reasoning with Words Based on Triangular Fuzzy Numbers

Abstract

A pivotal difference between Artificial Neural Networks and Fuzzy Cognitive Maps (FCMs) is that the latter allow modeling a physical system in terms of concepts and causal relations, thus equipping the network with interpretability features. However, such components are normally described by quantitative terms, which may be difficult to handle by domain experts. In this paper, we explore a reasoning mechanism for FCMs based on the Computing with Words paradigm where numerical concepts and relations are replaced with linguistic terms. More explicitly, we include triangular fuzzy numbers into the qualitative reasoning process attached to our model, thus proving further interpretability and transparency. The simulations show the potential behind the symbolic reasoning mechanism proposed in this study.

FCMpy: A Python Module for Constructing and Analyzing Fuzzy Cognitive Maps

“…To generate the fuzzy membership functions we need to decide on the geometric shape that would best represent the linguistic terms. In many applications, a triangular membership function is used [17]. The triangular membership function specifies the lower and the upper bounds of the triangle (i.e., where the meaning of the given linguistic term is represented the least) and the center of the triangle (i.e., where the meaning of the given linguistic term is fully expressed).…”

“…Each solution is an N × N connection matrix. In the evaluation step, each candidate solution in the population is evaluated based on a fitness function shown in Equation (17) and Table 5. We can observe how the fitness function is calculated on a simple example, shown in Figure 6).…”

Educational Landscapes in the Context of the Digital Educational Environment

“…В работе П. Двиведи, В. Кант и К. Бхарадваджа анализируется построение индивидуальных траекторий обучения на основе методов интеллектуального анализа данных (Dwivedi, Kant, & Bharadwaj, 2018). М. Фриас с соавторами также рассматривает нечёткие когнитивные карты в контексте интеллектуального анализа данных (Frias et al, 2018).…”

Algorithm for reasoning with words based on linguistic fuzzy cognitive map

“…In human cognition, we see the world through words. Many intelligent CWW models have been studied 3‐6 . The remainder of this paper is organized as follows: Section 2 reviews some of the main concepts of modeling with words based on hedge algebra () 7 .…”

“…Many intelligent CWW models have been studied. [3][4][5][6] The remainder of this paper is organized as follows: Section 2 reviews some of the main concepts of modeling with words based on hedge algebra (HA). 7 Moreover, it provides a revision of abstract linguistic residuated lattices (LRLs) and truth layers.…”