Mathematics

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https://hdl.handle.net/20.500.14540/131

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Browsing Mathematics by Advisor "Prof. Dr. Narayan prasad Pahari"

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    A Study of Fuzzy Logic and Fuzzy Sequence with Their Application to the Real World
    (Institute of Science and Technology, 2024-06) Paudel, Gyan Prasad; Prof. Dr. Narayan prasad Pahari
    Sequence space and difference sequence spaces play an important role in many areas of analysis, such as the Schauer basis, summability, fixed point theory, non-linear analysis, and structural theory of topological vector space. Fuzzy logic is the study of uncertainty and vagueness. It is a flexible, uncertainty-based reasoning method for rational decision making that addresses vague or incomplete information and solves specific problems. The fuzzy set theory has been successfully applied in a wide range of mathematical fields. Fuzzy sequence analysis offers a robust framework for handling uncertainty and imprecision in sequence-based data, enhancing practicality and effectiveness. This dissertation deals with the fundamental topological properties of sequence space and the difference sequence spaces of fuzzy real numbers. To study the basic topological properties of the classes l_F (X,λ ̅,p ̅ ) and l_F (X,λ ̅,p ̅,L) we use the Orlicz and paranorm function. Moreover, linearity, completeness, solidity, and some inclusion properties of a class S(X,M,P,A) of difference sequence and classes F_∞ (ρ,M,p,A), F_c (ρ,M,p,A) and F_o (ρ,M,p,A) of generalized difference sequences. We also study some topological properties classes Z_F (M,λ\,ξ) where, Z_F=l_∞^F,C^F,C_o^F f double sequences of fuzzy real numbers. Additionally, this thesis also includes the generalized form of the P-bounded variation bV_p^F of fuzzy real numbers. In addition this thesis further explores the practical implementation of fuzzy real numbers in various real-world scenarios. Specifically, it examines how fuzzy sets and fuzzy logic are employed in decision-making processes, particularly in selecting the best option using the Bellmen-Zadeh max-min method. Furthermore, this thesis delves into the field of healthcare and addresses Sanchez’s medical condition, utilizing a case study to illustrate the application of fuzzy arithmetic-based methods in identifying and assessing medical issues with a case study. Moreover, the thesis extends its exploration to the domain of insurance fraud detection. It presents a fuzzy model designed to assist internal auditors in identifying potentially fraudulent claims during the claim-settlement process. Additionally, the thesis examines the utilization of machine learning techniques in the detection of cardiovascular diseases. It outlines how a fuzzy model is developed to classify and assess the risk of cardiovascular disease based on various input factors.