Electromyography (EMG) is a widely used method for estimating muscle activity and could help in understanding how muscles interact with each other and affect human movement control. To detect muscle interactions during elbow flexion and extension, a recently developed InterCriteria Analysis (ICrA) based on the mathematical formalisms of index matrices and intuitionistic fuzzy sets is applied. ICrA has had numerous implementations in different fields, including biomedicine and quality of life; however, this is the first time the approach has been used for establishing muscle interactions. Six human upper arm large surface muscles or parts of muscles responsible for flexion and extension in shoulder and elbow joints were selected. Surface EMG signals were recorded from four one-joint (pars clavicularis and pars spinata of m. deltoideus [DELcla and DELspi, respectively], m. brachialis [BRA], and m. anconeus [ANC]) and two two-joint (m. biceps brachii [BIC] and m. triceps brachii-caput longum [TRI]) muscles. The outcomes from ten healthy subjects performing flexion and extension movements in the sagittal plane at four speeds with and without additional load are implemented in this study. When ICrA was applied to examine the two different movements, the BIC–BRA muscle interaction was distinguished during flexion. On the other hand, when the ten subjects were observed, four interacting muscle pairs, namely DELcla-DELspi, BIC-TRI, BIC-BRA, and TRI-BRA, were detected. The results obtained after the ICrA application confirmed the expectations that the investigated muscles contribute differently to the human upper arm movements when the flexion and extension velocities are changed, or a load is added.