This paper studies welfare criteria under an environment in which a decision maker is endowed with a nontransitive preference relation. In such an environment, the classical utilitarian welfare criterion may not identify the welfare order, and the problem of maximizing the decision maker's welfare becomes ambiguous. In order to find a sensible welfare criterion that applies to nontransitive preference relations, I propose a series of desirable properties of welfare criteria and uniquely identify a consistent rule that infers welfare orders from nontransitive preference relations. This rule, called the transitive core, is applied to a variety of nontransitive preference models, such as semiorders on a commodity space, relative discounting time preferences, justifiable preferences over ambiguous acts, regret preferences on risky prospects, and collective preference relations induced by the majority criterion. These examinations show that the proposed method provides successful inference of welfare in respective contexts.