Chapter 1This 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 2This chapter introduces the TODIM decision making method based on the hesitant fuzzy psychological distance measure. Chapter 3This chapter introduces a process-oriented dynamic decision making method based on the hesitant fuzzy decision field theory.Chapter 4A dynamic uncertain reasoning method based on the Dynamic Hesitant Fuzzy Bayesian Network is introduced.Chapter 5Two regression analysis models under the hesitant fuzzy environment are introduced.Chapter 6A 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.