Optimization is crucial in decision-making across diverse engineering, economics, supply chain management, and healthcare domains. However, many real-world optimization problems involve uncertainty, imprecise data, and vagueness, which cannot be effectively addressed using classical mathematical approaches. Fuzzy optimization, an extension of classical optimization techniques, uses fuzzy set theory to address ambiguity of information through degrees of membership instead of just binary belonging or non-belonging to sets. This chapter discusses the concepts, applications, and details of fuzzy optimization and offers readers a fully integrated view of its tools and industrial practicality. The chapter begins with an introduction to fuzzy set theory, covering key concepts such as fuzzy numbers, membership functions, and linguistic variables. It then delves into various fuzzy optimization techniques, including linear programming, multi-objective optimization, and fuzzy goal programming. These methods enable decision-makers to model and solve problems where objectives, constraints, or parameters exhibit inherent vagueness. Additionally, the chapter discusses hybrid approaches, integrating fuzzy optimization with artificial intelligence techniques such as genetic algorithms, neural networks, and swarm intelligence to enhance computational efficiency. Considerable attention is given to the applications of fuzzy optimisation in areas such as supply chain management, financial modelling, healthcare decision-making, and industrial engineering. Real-world case studies and examples demonstrate the application of fuzzy optimization models to problem solving and decision-making in uncertain environments. The chapter also discusses recent developments, major challenges and future works. The goal of this chapter is to make an effort to contribute researchers, academicians, and practitioners of fuzzy optimization with both baseline and applied methodologies. Implementation of fuzzy logic in optimizer still appears to be a potent method for facing the challenges in complex, uncertain and dynamic decision making issues.