This chapter describes a fuzzy restriction that acts as an elastic constraint on the values that may be assigned to a variable, and introduces possibility measures and necessity measures. A theory that is based on possibility and necessity measures is usually called a possibility theory. The chapter discusses the possibility theory and its relation to the probability theory. It presents the reasons for the inadequacy of probability theory to deal with uncertainty and imprecision. Mathematics is an abstract language that has its own rules and principles. What makes this language important is the use of mathematics to describe the world. Probability and possibility theories are mathematical tools that are used to describe the world. The chapter provides information on the unexpected application of possibility theory using statistical models such as Neyman–Pearson–Fisher model and general linear model.