INFLUENCE OF EPISTEMOLOGICAL BELIEFS ON ACADEMIC PERFORMANCE - A STUDY USING FUZZY RELATIONAL MAP WEIGHTED WITH TRIANGULAR AND TRAPEZOIDAL FUZZY NUMBERS

Sep 4, 2026

Fuzzy Relational Map (FRM) models knowledge as a graphical structure where nodes denote concepts and edges capture causal influence between disjoint concept sets. Uncertainty in linguistic concepts and causalities is quantified using triangular and trapezoidal fuzzy numbers. The causal influence between epistemological beliefs and academic performance attributes is derived through an inference process and a fixed-point vector. Concepts are ranked by influence using the average weight of the stable vector, and rankings from triangular and trapezoidal FRMs are compared.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages18

Reading Time45 min

AccessFree to download

Abstract

1. Introduction

2. Fuzzy Relational Map: A Neuro-Fuzzy Tool

3. Representation of Concepts and Causal Connections using TrFN and TpFN

INFLUENCE OF EPISTEMOLOGICAL BELIEFS ON ACADEMIC PERFORMANCE: A STUDY USING FUZZY RELATIONAL MAP WEIGHTED WITH TRIANGULAR AND TRAPEZOIDAL FUZZY NUMBERS S. AROKIAMARY and M. MARY MEJRULLO MERLIN Department of Mathematics Mother Gnanamma Women’s College of Arts and Science (Affiliated to Bharathidasan University) Varadarajanpet, Ariyalur -621805, Tamilnadu, India E-mail: [arokiamarysamimuthu@gmail.com](arokiamarysamimuthu@gmail.com) PG and Research Department of Mathematics Holy Cross College-Autonomous Tiruchirappalli -600002, India [E-mail: marymejrullomerlin@hcctrichy.ac.in](E-mail: marymejrullomerlin@hcctrichy.ac.in) Abstract Fuzzy Relational Map is a framework that illustrates the knowledge stored in a system with a graphical structure. The nodes represent the concepts and the edges represent the causal relationship between the disjoint set of concepts. The strength of concepts and causal relationships is represented by fuzzy numbers. Quantifying the linguistic concepts with advanced fuzzy numbers gives a better view of the problem. This dynamical structure is efficient at predicting the causal relationship between the concepts of two disjoint sets. The causal influence between the concepts is obtained from the inference process and from the fixed-point vector. The causal relationship between epistemological beliefs and the attributes of academic performance is examined in this article using fuzzy relationship maps. With this tool, triangular and trapezoidal fuzzy numbers are employed to quantify the uncertain information of conceptsand causal connections. The concepts can be ranked in the order of influence using the average weight of the stable vector and the rankings according to triangular and trapezoidal Fuzzy Relational Maps are compared. 1. Introduction Robert Axelrod (1976), a Political Scientist, introduced a formal way of representing social scientific knowledge with the help of a graphical structure called Cognitive Maps [2] . These maps reflect the visualisation of a complex problem as a human being would comprehend. The reasoning process helps to understand the behaviour and dynamics of the problem. The cognitive maps demonstrated whether or not there is influence between the concepts but did not provide any information about the level of influence. A decade later, Bart Kosko (1986) proposed a new idea to overcome this issue by considering fuzzy values for the concepts and fuzzy degrees for the causalities between the concepts [10] . This indeed enhanced the power of cognitive maps, improved their functioning and increased their applications in various fields. Vasantha Kandasamy (2000) introduced Fuzzy Relational Maps (FRM) that can represent the causal association between two disjoint sets of concepts [9] . Fuzzy Relational Map (FRM) methodology is a symbolic representation of a system and it describes the behaviour and dynamics of the system. FRM presents a complex system with a graphical structure where the accumulated knowledge of the system can be represented in terms of concepts and causalities. A concept can represent a state or characteristic of a system, whereas a causality describes the relationship between them. The concepts of FRM belong to two disjoint sets and it is assumed that there is no interaction between the concepts within a set. The FRM methodology integrates both the stored knowledge information in the systems and the expertise of the experts. This results in a conclusion that portrays the future state and behaviour of the system that is studied. The standard of educational excellence among students is influenced by several factors. Epistemological beliefs are one of the factors that can have a subtle but strong influence on motivating students to perform better in academics. Though there are differing views about the relationship between self-beliefs and academic achievement in the research arena, the general opinion is that young students are strongly influenced by

FAQs

What does a Fuzzy Relational Map (FRM) represent in this study?

An FRM represents knowledge using a signed directed graph where nodes are concepts and edges encode causal relationships between disjoint concept sets.

How are uncertainties handled in the causal analysis?

Triangular and trapezoidal fuzzy numbers are used to quantify uncertain information in linguistic concepts and in causal connections.

How are the concepts ranked by their influence?

Concepts are ranked using the average weight of the stable vector, and the rankings from triangular and trapezoidal fuzzy relational maps are compared.

Sep 4, 2026

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