Social responsibility auditing represents an assessment of the effects of an organization's non-financial objectives which legally reflects the performance of the organization and the perspective of the stakeholders of that organization. By playing their role of social responsibility, auditors have facilitated the control and supervision of the mechanism of individual companies and allows stakeholders to evaluate a company's social performance against specific standards or expectations; and finally, it plays the role of a social accountability tool for the organization, similar to a financial audit, however, there are many criteria that affect the auditor's responsibility in the society, and in this research, the most important criteria of the auditor's social responsibility were studied. By identifying appropriate criteria in their selection, fuzzy decision making methods were used with a combination of ANP and DEMATEL (DANP). The results showed that the criterion of social factors is the most influential and the auditor is the most influential criterion, and the criterion of the auditor is the most important in the auditor's responsibility in society.