Browsing by Author "Priyadharshini M"

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    Operators and Measures on Cubic Intuitionistic Fuzzy Sets and their Applications in Image Processing
    (Avinashilingam, 2025-02) Priyadharshini M; Guide - Dr. D. Jayanthi
    Cubic intuitionistic fuzzy sets are efficient on handling hybrid information by combining interval-valued intuitionistic fuzzy sets with intuitionistic fuzzy sets. The primary objective of this thesis is to introduce diverse operators and measures on cubic intuitionistic fuzzy sets and applying them in multi-criteria decision-making and image processing. Several operators on the cubic intuitionistic fuzzy sets under P-order, such as the arithmetic mean (@), geometric mean ($), multiplication operator (*), necessity (□) and possibility (◇) operations, are defined. The concept of modal operators like 𝒟 ( ), ℱ ,𝛽 , 𝒢 ,𝛽 , ℋ ,𝛽 and 𝒥 ,𝛽 are introduced on cubic intuitionistic fuzzy sets. Moreover, several operators of the cubic intuitionistic fuzzy sets, such as concentration, dilation, contrast intensification, and normalization under the P-order are provided.Properties of these operators for cubic intuitionistic fuzzy sets are comprehensively studied and demonstrated. Cardinality and relative cardinality on cubic intuitionistic fuzzy sets are defined and some properties are analyzed. The axioms of cubic intuitionistic fuzzy entropy are introduced and extended several families of entropy measures from interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets to cubic intuitionistic fuzzy situations. Furthermore, new entropy measures based on distance measures are proposed. A numerical example is provided to demonstrate whether the suggested entropy measures are reasonable or not. A similarity measure on cubic intuitionistic fuzzy sets is introduced and additional similarity measures based on the geometric model, set-theoretic approach, and matching function are discussed. A numerical example illustrates the effectiveness and significance of the proposed operators and measures in solving a multi-criteria decision-making problem. Also, a comparative study is presented between intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, and cubic intuitionistic fuzzy sets. The application of cubic intuitionistic fuzzy sets in image processing is discussed, specifically focusing on contrast intensification operators in image enhancement under P-order and the use of cubic intuitionistic fuzzy similarity measures in image recognition. The proposed algorithm, implemented in MATLAB, delivers superior results compared to existing approaches. Finally, summary and conclusion are provided, along with future research directions.