Fuzzy Sets and Triangular Norms

This book aims to serve as a comprehensive resource that equips readers with the knowledge and practical skills needed to navigate the intricacies of fuzzy set theory, t-norms, and their integration into decision-aided intelligent systems. It provides a comprehensive understanding of aggregation operators and their role in data fusion, risk analysis, and expert opinion aggregation.

• New aggregation operators, entropy measures, t-norm, and t-conorm structures are developed across multiple fuzzy set extensions to better model uncertainty and hesitation in decision-making.
• A wide range of real-world applications, including, tourism planning, smart cities, urban mobility, water security, smart campus automation, energy facility siting, and firefighting helicopter selection, are addressed using advanced multi-criteria decision making methods.
• The chapters collectively emphasize sustainable, data-driven, and uncertainty-aware decision support, contributing solutions in areas such as environmental protection, resource optimization, public services, and technological infrastructure.
• Innovative techniques, such as Lambert W–based aggregation operators, Choquet integral–based entropy, confidence-level aggregation, and fuzzy–machine learning hybrid models, improve the representation of interaction, ambiguity, and complexity in multi-criteria decision problems.

The text is primarily written for senior undergraduates, graduate students, and academic researchers in diverse fields including mathematics, industrial engineering, supply chain management, operations research, manufacturing engineering, production engineering, and applied mathematics.

Mehmet Ünver completed his undergraduate studies in the Department of Mathematics at Ankara University (Türkiye) in 2007, followed by his master's degree at the same institution in 2009. During his master's studies, he focused on summability theory and Korovkin-type approximation theory. He earned his PhD in Mathematics from Ankara University in 2013, continuing his research in summability theory and Korovkin-type approximation theory. He served as a research assistant at the Department of Mathematics, Ankara University, from 2009 to 2015, and later as an assistant professor from 2015 to 2017. He has held the position of Associate Professor at the Department of Mathematics, at Ankara University. He is currently working as a full time professor at the same instutition. His current research pursuits encompass fuzzy measure and fuzzy set theory, multi-criteria decision-making, Korovkin-type approximation theory, and summability theory, resulting in numerous published papers in highly cited journals on topics including summability theory and the applications of fuzzy set theory in multi-criteria decision-making, pattern recognition, aggregation operators, and classification.

Gökhan Özçelik obtained his bachelor's degree from the Department of Industrial Engineering at Gazi University (Türkiye) in 2009. He completed his master's degree in the same department in 2011 and subsequently received his PhD in Industrial Engineering from Gazi University in 2016. Presently, he serves as an Associate Professor at Karadeniz Technical University (Türkiye). His research primarily focuses on optimization, multi-criteria decision-making, and fuzzy sets and systems. He has an extensive publication record in reputable journals such as the European Journal of Operational Research, Transportation Research Part E, Expert Systems with Applications, International Journal of Production Research, and Journal of Cleaner Production, among others.