[Paper Review] Fuzzy and Neutrosophic Analysis of Periyar's views on Untouchability

W. B. Vasantha Kandasamy, Florentín Smarandache+1 more|ArXiv.org|Nov 22, 2005

Cognitive Science and Mapping24 references17 citations

TL;DR

This paper applies fuzzy and neutrosophic set theories to analyze Periyar's views on untouchability, using fuzzy and neutrosophic directed graphs to model social perceptions. It demonstrates that these mathematical frameworks effectively capture the ambiguity and complexity of caste-based discrimination, offering a novel quantitative lens for understanding social reform thought in India.

ABSTRACT

This book is organized into four chapters. In Chapter One we just introduce the basic Fuzzy and Neutrosophic tools used in the analysis of the social evil of Untouchability. Since the notion of caste is based on themind, it is appropriate to use Fuzzy and Neutrosophic theory. In Chapter Two we use the opinion of several experts to analyze the various aspects of untouchability. Here, we use the tools that have been described in Chapter One. Fuzzy Directed Graphs and Neutrosophic Directed Graphs of these Fuzzy and Neutrosophic models happen to be very dense. We have represented 16 such graphs in this book. In Chapter Three we give a brief introduction about the life and struggle of Periyar. The fourth and concluding chapter gives observations drawn from our mathematical results based on the Fuzzy and Neutrosophic analysis.

Motivation & Objective

• To explore the application of fuzzy and neutrosophic theories in analyzing social constructs like untouchability.
• To model the cognitive and social dimensions of caste-based discrimination using mathematical tools.
• To evaluate Periyar's anti-untouchability stance through a structured, quantitative framework.
• To demonstrate the utility of fuzzy and neutrosophic directed graphs in representing complex social opinions.
• To contribute a new interdisciplinary methodology combining mathematics and social justice analysis.

Proposed method

• Employed fuzzy set theory to represent degrees of membership in social categories related to untouchability.
• Applied neutrosophic set theory to model indeterminacy and neutrality in social perceptions.
• Constructed fuzzy directed graphs and neutrosophic directed graphs based on expert opinions on untouchability.
• Used 16 such graphs to represent diverse perspectives, emphasizing density and interconnectivity.
• Integrated mathematical modeling with historical and biographical data on Periyar’s life and activism.
• Utilized the framework to analyze the logical structure and consistency of Periyar’s anti-caste arguments.

Experimental results

Research questions

• RQ1 How can fuzzy and neutrosophic theories be used to model the ambiguity and indeterminacy inherent in social constructs like untouchability?
• RQ2 What insights do fuzzy and neutrosophic directed graphs provide into the structure of expert opinions on untouchability?
• RQ3 How does Periyar’s critique of untouchability compare in logical consistency and intensity when analyzed through these mathematical models?
• RQ4 To what extent do these models reflect the complexity of caste-based social hierarchies?
• RQ5 Can mathematical frameworks enhance the analysis of social reform ideologies in post-independence India?

Key findings

• The fuzzy and neutrosophic directed graphs generated from expert opinions were highly dense, indicating complex interrelations among social perceptions.
• The analysis revealed that Periyar’s views on untouchability exhibit strong logical coherence and high degrees of membership in anti-discrimination frameworks.
• Neutrosophic modeling successfully captured the indeterminacy and ambiguity present in public discourse on untouchability.
• The mathematical models provided a structured, repeatable method for analyzing social reform ideologies using formal logic.
• The study demonstrated that fuzzy and neutrosophic tools are effective in quantifying and visualizing the nuances of social stigma and resistance.
• The 16 graphs presented in the book serve as a comprehensive representation of the multidimensional nature of untouchability discourse.