مقدمه‌اي بر استفاده از رياضيات فازي در باستان‌شناسي (مورد مطالعاتي: بازسازي مجازي برج طغرل با استفاده از قابليت اعتماد فازي)

An Introduction to the Use of Fuzzy Mathematics in Archeology (Case Study: Virtual Reconstruction of Togrul Tower by Using Fuzzy Reliability)

امروزه استفاده از منطق و رياضيات فازي در علوم و فنون گوناگون در حال افزايش است. باستان‌شناسي از علومي است كه كمتر به روش‌هاي منطق و رياضيات فازي توجه داشته است. اما به دليل ماهيت بسياري از اطلاعات و داده‌هاي باستان‌شناسي، استفاده از اين روش‌ها در باستان‌شناسي مي‌تواند مفيد واقع شود. فازي در لغت به معناي مبهم و نادقيق است و ازآنجايي‌كه در باستان‌شناسي داده‌هايي وجود دارند كه مبهم هستند، استفاده از رياضيات و منطق فازي مي‌تواند راهگشاي برخي تحليل‌ها باشد. در پژوهش حاضر، در آغاز منطق فازي و لزوم استفاده از آن در باستان‌شناسي توضيح داده مي‌شود. سپس شرايط و بخش‌هايي از باستان‌شناسي كه در آن‌ها، رياضيات و منطق فازي كاربرد دارد، بيان‌شده است و در انتها سازوكارهاي استفاده از رياضيات و منطق فازي در باستان‌شناسي شرح داده مي‌شود. در ادامه يكي از سازوكارها، يعني قابليت اعتماد فازي و كاربرد‌هاي آن در باستان‌شناسي، به‌ويژه استفاده از آن براي بازسازي مجازي بناهاي تخريب‌شده، بيان مي‌شود. به‌عنوان مطالعه‌ي موردي، با استفاده از قابليت اعتماد فازي، بناي نيمه تخريب‌شده‌ي برج طغرل، طي چند مرحله به‌صورت كامل بازسازي شده است. در هر مرحله بيشترين مقدار ممكن قابليت اعتماد، انتخاب‌شده و در پايان، قابليت اعتماد كل بناي بازسازي‌شده با استفاده از مقدار قابليت اعتماد هر مرحله به دست آمده است. تعيين ميزان قابليت اعتماد مراحل بر اساس نظرات كارشناسان، ويژگي‌هاي فني، معماري و جغرافيايي بوده است. اين روش براي استفاده باستان‌شناسان و مرمتگران به‌منظور پس‌بيني علمي فرم سازه‌ها و اشياي از بين‌ رفته و تحليل‌هاي منتج از پس‌بيني، كاربرد دارد.

Nowadays, the use of fuzzy mathematics and fuzzy logic are increasing in various sciences. Archaeology is one of the sciences that is less attended with the methods of fuzzy mathematics and fuzzy logic. Due to the nature of many archaeological data, however, the use of such methods in archaeology can be beneficial. In this research, it has been tried to explain applications of fuzzy logic and fuzzy mathematics in archaeology. This research have six sections. In the beginning, history of using fuzzy logic in archaeology is presented. Then, fuzzy logic is explained, and in section three, necessity of using fuzzy mathematics and fuzzy logic in archaeology are explained at first and then, situations, parts and mechanism of using fuzzy mathematics and fuzzy logic in archaeology are explained. Situations are where the use of fuzzy mathematics and fuzzy logic are useful, including: when the collected data/documentation/information are imprecise, when the relationships between the variables are imprecise and when there is disagreement between archaeologists. Parts of archaeology where fuzzy logic and fuzzy mathematics are applicable include descriptions of data and analysis of data, postdiction, and decision making. The mechanism of using fuzzy mathematics and fuzzy logic in archaeology include fuzzy reliability, designing of fuzzy inference system, and the use of fuzzy statistics. In section four, virtual reconstruction in archaeology is presented. In section five, the fuzzy reliability is explained and its applications in archaeology are described. One of the applications of fuzzy reliability is its use for the virtual reconstruction of destroyed buildings. an‎d finally in section six, to show the process of this method, as a case study, a semi-destructive structure is reconstructed by using fuzzy reliability. The Toghrul Tower, where a small part of tower is collapsed, is selected for such a case study. Of course, this method is applicable to buildings where a lot of them have been destroyed, and to complex buildings. To determine the characteristics, experts commented on technical, geographical, architectural elements of building. Reconstruction is done step by step and in each step, the reliability is calculated. The reliability of the final model is obtained by combining the reliability of the steps. To obtain reliability, two methods have been suggested: use of expert opinion or mathematical/statistical analysis. The Toghrul Tower is reconstructed in comparison with its similar buildings, as well as architectural and technical analysis. Finally, the form of Toghrul Tower was recognized with determined possibilities. This method is beneficial to the archaeologists and conservator for the scientific prediction and postdiction of the structures and objects.