Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set

Provides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets This book examines fuzzy and intuitionistic fuzzy mathematics and unifies the latest existing works in literature. It enables readers to fully understand the mathematics of both fuzzy set and intuitionistic fuzzy se t so that they can use either one in their applications. Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh’s extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measures; examines matrices and determinants of a fuzzy matrix; and teaches about fuzzy linear equations. Readers will also learn about fuzzy subgroups. The second to last chapter examines the application of fuzzy and intuitionistic fuzzy mathematics in image enhancement, segmentation, and retrieval. Finally, the book concludes with coverage the extension of fuzzy sets. This book: Covers both fuzzy and intuitionistic fuzzy sets and includes examples and practical applications Discusses intuitionistic fuzzy integrals and recent aggregation operators using Choquet integral, with examples Includes a chapter on applications in image processing using fuzzy and intuitionistic fuzzy sets Explains fuzzy matrix operations and features examples Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set is an ideal text for graduate and research students, as well as professionals, in image processing, decision-making, pattern recognition, and control system design. 提供模糊集理论基本原理的详细数学阐述，包括直觉模糊集 本书考察了模糊和直觉模糊数学，并统一了文献中最新的现有作品。它使读者能够完全理解模糊集和直觉模糊集的数学，以便他们可以在他们的应用程序中使用任何一个。 模糊集及其扩展的每一章：直觉模糊集从一个引言，理论和几个例子开始，引导读者。第一个是从模糊/直觉模糊集，模糊对冲和模糊关系奠定基础。接下来介绍模糊数字并解释Zadeh的扩展原理。然后是章节看模糊算子;模糊相似度量和模糊度量;模糊/直觉模糊测度和模糊积分。本书还讨论了模糊测度的定义和性质;检查模糊矩阵的矩阵和行列式;并教导模糊线性方程。读者还将了解模糊子群。倒数第二章考察了模糊和直觉模糊数学在图像增强，分割和检索中的应用。最后，本书总结了模糊集的扩展。这本书： 涵盖模糊和直觉模糊集，包括示例和实际应用 讨论了使用Choquet积分的直觉模糊积分和最近的聚合算子，并举例说明 包括使用模糊和直觉模糊集在图像处理中应用的章节 解释模糊矩阵运算和特征示例 模糊集及其扩展：直觉模糊集是研究生和研究生以及专业人员在图像处理，决策，模式识别和控制系统设计中的理想文本。 t so that they can use either one in their applications. Each chapter of Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set begins with an introduction, theory, and several examples to guide readers along. The first one starts by laying the groundwork of fuzzy/intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. The next covers fuzzy numbers and explains Zadeh’s extension principle. Then comes chapters looking at fuzzy operators; fuzzy similarity measures and measures of fuzziness; and fuzzy/intuitionistic fuzzy measures and fuzzy integrals. The book also: discusses the definition and properties of fuzzy measures; examines matrices and determinants of a fuzzy matrix; and teaches about fuzzy linear equations. Readers will also learn about fuzzy subgroups. The second to last chapter examines the application of fuzzy and intuitionistic fuzzy mathematics in image enhancement, segmentation, and retrieval. Finally, the book concludes with coverage the extension of fuzzy sets. This book: Covers both fuzzy and intuitionistic fuzzy sets and includes examples and practical applications Discusses intuitionistic fuzzy integrals and recent aggregation operators using Choquet integral, with examples Includes a chapter on applications in image processing using fuzzy and intuitionistic fuzzy sets Explains fuzzy matrix operations and features examples Fuzzy Set and Its Extension: The Intuitionistic Fuzzy Set is an ideal text for graduate and research students, as well as professionals, in image processing, decision-making, pattern recognition, and control system design. 提供模糊集理论基本原理的详细数学阐述，包括直觉模糊集 本书考察了模糊和直觉模糊数学，并统一了文献中最新的现有作品。它使读者能够完全理解模糊集和直觉模糊集的数学，以便他们可以在他们的应用程序中使用任何一个。 模糊集及其扩展的每一章：直觉模糊集从一个引言，理论和几个例子开始，引导读者。第一个是从模糊/直觉模糊集，模糊对冲和模糊关系奠定基础。接下来介绍模糊数字并解释Zadeh的扩展原理。然后是章节看模糊算子;模糊相似度量和模糊度量;模糊/直觉模糊测度和模糊积分。本书还讨论了模糊测度的定义和性质;检查模糊矩阵的矩阵和行列式;并教导模糊线性方程。读者还将了解模糊子群。倒数第二章考察了模糊和直觉模糊数学在图像增强，分割和检索中的应用。最后，本书总结了模糊集的扩展。这本书： 涵盖模糊和直觉模糊集，包括示例和实际应用 讨论了使用Choquet积分的直觉模糊积分和最近的聚合算子，并举例说明 包括使用模糊和直觉模糊集在图像处理中应用的章节 解释模糊矩阵运算和特征示例 模糊集及其扩展：直觉模糊集是研究生和研究生以及专业人员在图像处理，决策，模式识别和控制系统设计中的理想文本。