Chapter 1 This chapter introduces the background about decision making, uncertain reasoning and regression analysis under the hesitant fuzzy environment, and the recent developments of some related theory and techniques -- Chapter 2 This chapter introduces the TODIM decision making method based on the hesitant fuzzy psychological distance measure -- Chapter 3 This chapter introduces a process-oriented dynamic decision making method based on the hesitant fuzzy decision field theory -- Chapter 4 A dynamic uncertain reasoning method based on the Dynamic Hesitant Fuzzy Bayesian Network is introduced -- Chapter 5 Two regression analysis models under the hesitant fuzzy environment are introduced -- Chapter 6 A cluster algorithm with probabilistic hesitant fuzzy correlation coefficient and the concept of interval-valued probabilistic hesitant fuzzy set are introduced to improve the theory of hesitant fuzzy set.

This book mainly introduces some techniques of decision-making, uncertain reasoning and regression analysis under the hesitant fuzzy environment and expands the applications of hesitant fuzzy sets in solving practical problems. The book pursues three major objectives: (1) to introduce some techniques about decision-making, uncertain reasoning and regression analysis under the hesitant fuzzy environment, (2) to prove these techniques theoretically and (3) to apply the involved techniques to practical problems. The book is especially valuable for readers to understand how hesitant fuzzy set could be employed in decision-making, uncertain reasoning and regression analysis and motivates researchers to expand more application fields of hesitant fuzzy set.