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ÖgeInternal audit decision support framework using spherical fuzzy electre(Lisansüstü Eğitim Enstitüsü, 2022) Menekşe, Akın ; Akdağ Camgöz, Hatice ; 719019 ; İşletmeInternal auditing is an independent assurance and consulting activity that improves the operations of a firm. An internal audit helps the business achieve its objectives by systematically and systematically reviewing and enhancing the effectiveness of risk management, control, and governance systems. Internal auditing is done by internal auditors who are hired by businesses. The scope of internal audit in businesses can be quite broad, but the most fundamental internal audit areas are governance, risk management, efficiency and effectiveness of operations and asset protection, financial and management reporting reliability, compliance with laws and regulations, and information technology. Internal audit is becoming increasingly crucial in assisting firms in managing and responding to risks, particularly in an age where markets and sectors rely largely on technology to succeed. Internal auditors evaluate whether the established systems protect the organization's assets and data integrity and are working effectively to achieve the organization's goals or objectives. These audits can be paired with financial statement audits or other kinds of internal auditing. Internal auditors focus on governance factors such as clearly defined roles, authority, and duties; risk appetite alignment; effective communication; values management; and accountability as part of corporate governance. In the field of internal auditing, we are currently confronted with several decision-making problems, and multi-criteria decision-making approaches can be employed as a decision support tool for aiding the solution of these problems. Scholars have been working on a variety of techniques to handle complicated and difficult decision-making problems. These methods, which have wide applications in many fields and are very popular, allow for the inclusion of multiple and complex criteria in the problem, while they can offer rational solutions. ELECTRE is an MCDM approach that compares alternatives in a pairwise manner for each evaluation criterion. This method is based on outranking relationships, i.e., concordance and discordance sets for each criterion, and each alternative is scored over these sets. In this method, the user can define the limits of concordance and discordance degrees according to the problem. Following Zadeh's introduction of fuzzy logic, It's been commonly employed in decision-making problems to model the fuzziness in numerical or linguistic data and human evaluations. Recently, many new extensions of fuzzy sets have been introduced to the literature, such as Pythagorean fuzzy sets, neutrosophic fuzzy sets, and spherical fuzzy sets. Spherical fuzzy sets have a three-dimensional spherical character and have been developed for the purpose of modeling the linguistic expressions of experts in a more comprehensive way. Essentially, spherical fuzzy sets are based on the theories of neutrosophic and Pythagorean fuzzy sets, i.e., intuitionistic fuzzy sets of type two. The concept of spherical fuzzy sets may also be thought of as an extension of picture fuzzy sets, since the geometry of spherical fuzzy sets is derived by taking the squares of each parameter of picture fuzzy sets. In this way, spherical fuzzy sets allow users to define membership, non-membership, and hesitancy degrees independently and in a wide area. On the other hand, interval-valued spherical fuzzy sets provide users an interval type of domain rather than a single point, allowing flexible modeling of membership, non-membership, and hesitancy degrees, and this significantly increases the fuzziness carrying capacity of the model. Within the scope of the thesis, the ELECTRE method is strengthened with single and interval-valued versions of spherical fuzzy sets, and uncertainty modeling capacity is integrated into the models. The models developed in this context are presented as decision support models for the internal audit field and are applied to an internal audit planning problem. In this context, the units to be audited are prioritized by the internal auditors over the components of the COSO international internal control framework. The three models developed within the scope of the framework are summarized below. The first method combines the classical ELECTRE method with single-valued spherical fuzzy sets. In this method, while constructing concordance and discordance sets, single-valued spherical fuzzy numbers are compared based on the comparison of membership, non-membership, and hesitancy parameters of single-valued spherical fuzzy numbers. In this approach, three types of outranking relations are constructed. Strong concordance sets consist of greater or equal membership degrees in pairwise comparison, and small non-membership and hesitancy degrees at the same time. On the other hand, moderate concordance sets, are composed of those with a greater or equal membership degree, a small non-membership degree, and a greater or equal hesitancy degree. Finally, weak concordance sets are composed of those whose membership and non-membership degrees are greater or equal at the same time. Discordance sets are obtained with the same idea in a mutually exclusive, collectively exhaustive manner with concordance sets. In this context, strong discordance sets have the elements with a smaller membership degree and those with greater or equal degrees of non-membership and hesitancy degrees. On the other hand, moderate discordance sets are composed of those with lower membership degrees, greater or equal non-membership degrees, and lower hesitancy at the same time. Finally, the weak discordance sets are composed of those whose membership and non-membership degrees are smaller at the same time. The second model of the framework is created by again extending the ELECTRE method with single-valued spherical fuzzy sets. Unlike the first approach, this model is developed based on single types of concordance and discordance sets rather than three separate sets of outranking relationships. The score and accuracy functions described for single-valued spherical fuzzy sets are utilized to determine these sets. This strategy appears to be pretty logical, given that the score and accuracy functions are already used for ranking fuzzy numbers. The second model, obtained in this way, contains fewer computation steps and, as a result, has a simpler structure than the first model. Unlike the previous two models, the third model in the framework benefited from spherical fuzzy sets with interval-valued characteristics. This feature allows the model to quantify the verbal expressions of decision-makers in a wider range. As in the second model, the proposed interval-valued spherical fuzzy ELECTRE is based on a collective total concordance and discordance set. In future studies, other researchers may focus on the following issues: The methods used can be integrated with other fuzzy set extensions; other multi-criteria decision-making procedures can benefit from different sorts of spherical fuzzy sets; different methods can be hybridized to take advantage of each method; machine learning algorithms can be integrated into decision support models to exploit existing data; with the method called sentiment analysis or opinion mining, criterion set selection can be made and thus a more comprehensive decision support model can be created.