Final answer:
According to utility theory, non-transitive decisions are considered irrational because they violate the necessary consistency of preferences that are complete and transitive.
Step-by-step explanation:
The statement that non-transitive decisions are irrational according to utility theory is true. In utility theory, preferences must be complete and transitive for decisions to be considered rational. A transitive preference means that if an individual prefers option A over B and B over C, then that individual must also prefer A over C. In cases where preferences are non-transitive, they violate the consistency required by the rational decision-making model of utility theory and are therefore deemed irrational.