Research Article
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Classification of The Monolithic Columns Produced in Troad and Mysia Region Ancient Granite Quarries in Northwestern Anatolia via Soft Decision-Making

Year 2019, Volume: 3 , 21 - 34, 31.12.2019
https://doi.org/10.30516/bilgesci.646126

Abstract

Ay
and Tolun [An Archaeometric Approach on the Distribution of Troadic Granite
Columns in the Western Anatolian Coasts. 
Journal of Archaeology & Art, 156, 2017, 119-130 (In Turkish)] have
analysed the distribution of the monolithic columns produced in the ancient
granite quarries, located in Troad Region and Mysia Region in Northwestern
Anatolia, by archaeometric analyses. Moreover, we have achieved some results by
interpreting the prominent data obtained therein. In this study, we propose a novel
soft decision-making method, i.e. Monolithic Columns Classification Method
(MCCM), constructed via fuzzy parameterized fuzzy soft matrices (fpfs-matrices)
and Prevalence Effect Method (PEM). MCCM provides an outcome by interpreting
all the results of the analyses mentioned above. We then apply the method to
the problem of monolithic columns classification. Finally, we discuss the need
for further research.

Supporting Institution

Çanakkale Onsekiz Mart University & Gaziosmanpaşa University

Project Number

SYL-2015-521 & 2009-72 and 2010/89

Thanks

The archaeological portion of this work was supported by the Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University, Grant number: SYL-2015-521. & The mathematical portion of this work was supported by the Office of Scientific Research Projects Coordination at Gaziosmanpaşa University, Grant numbers: 2009-72 and 2010/89.

References

  • Atmaca, S. (2017). Relationship between fuzzy soft topological spaces and (X,τ_e ) parameter spaces. Cumhuriyet Science Journal, 38(4), 77-85.
  • Ay, M. (2017). Distribution of the granite columns from the Troadic quarries in Western Anatolia an archaeometric approach, Master's Thesis, Çanakkale Onsekiz Mart University, Çanakkale, Turkey (In Turkish).
  • Ay, M., Tolun, V. (2017a). Ancient granite quarries in Troad: New findings. The Turkish Yearbook of Çanakkale Studies, 15(23), 265-295 (In Turkish).
  • Ay, M., Tolun, V. (2017b). An archaeometric approach on the distribution of Troadic granite columns in the Western Anatolian coasts. Journal of Archaeology & Art, 156, 119-130 (In Turkish).
  • Bera, S., Roy, S. K., Karaaslan, F., Çağman, N. (2017). Soft congruence relation over lattice. Hacettepe Journal of Mathematics and Statistics, 46(6), 1035-1042.
  • Çağman, N., Çıtak, F., Enginoğlu, S. (2010). Fuzzy parameterized fuzzy soft set theory and its applications. Turkish Journal of Fuzzy Systems, 1(1), 21-35.
  • Çağman, N., Çıtak, F., Enginoğlu, S. (2011a). FP-soft set theory and its applications. Annals of Fuzzy Mathematics and Informatics, 2(2), 219-226.
  • Çaǧman, N., Deli, İ. (2012). Means of FP-soft sets and their applications. Hacettepe Journal of Mathematics and Statistics, 41(5), 615-625.
  • Çağman, N., Enginoğlu, S. (2010). Soft set theory and uni-int decision making. European Journal of Operational Research, 207, 848-855.
  • Çağman, N., Enginoğlu, S. (2012). Fuzzy soft matrix theory and its application in decision making. Iranian Journal of Fuzzy Systems, 9(1), 109-119.
  • Çağman, N., Enginoğlu, S., Çıtak, F. (2011b). Fuzzy soft set theory and its applications. Iranian Journal of Fuzzy Systems, 8(3), 137-147.
  • Çıtak, F. (2018). Soft k-uni ideals of semirings and its algebraic applications. Journal of the Institute of Science and Technology, 8(4), 281-294.
  • Çıtak, F., Çaǧman, N. (2017). Soft k-int-ideals of semirings and its algebraic structures. Annals of Fuzzy Mathematics and Informatics, 13(4), 531-538.
  • De Vecchi, G., Lazzarini, L., Lünel, T., Mignucci, A., Visonà, D. (2000). The genesis and characterisation of marmor misium from Kozak (Turkey) a granit used antiquity. Journal of Cultural Heritage, 1, 145-153.
  • Deli, İ., Çağman, N. (2015). Relations on FP-soft sets applied to decision making problems. Journal of New Theory, (3), 98-107.
  • Enginoğlu, S. (2012). Soft matrices, PhD Dissertation, Gaziosmanpaşa University, Tokat, Turkey, (In Turkish).
  • Enginoǧlu, S., Çağman, N. Fuzzy parameterized fuzzy soft matrices and their application in decision-making. TWMS Journal of Applied and Engineering Mathematics, (In Press).
  • Enginoğlu, S., Çağman, N., Karataş, S., Aydın, T. (2015). On soft topology. El-Cezerî Journal of Science and Engineering, 2(3), 23-38.
  • Enginoğlu, S., Demiriz, S. (2015). A comparison with the convergent, Cesàro convergent and Riesz convergent sequences of fuzzy numbers. In: The 4th International
  • Fuzzy Systems Symposium, 5-6 November 2015 İstanbul, Turkey, pp. 413-416.
  • Enginoğlu, S., Dönmez, H. (2015). An application on decision making problem by using intuitionistic fuzzy parameterized intuitionistic fuzzy soft expert sets. In: The 4th International Fuzzy Systems Symposium, 5-6 November 2015 İstanbul, Turkey, pp. 413-415.
  • Enginoğlu, S., Memiş, S. (2018a). Comment on fuzzy soft sets [The Journal of Fuzzy Mathematics, 9(3), 2001, 589-602]. International Journal of Latest Engineering Research and Applications, 3(9), 1-9.
  • Enginoğlu, S., Memiş, S. (2018b). A review on an application of fuzzy soft set in multicriteria decision making problem. In: Proceedings of The International Conference on Mathematical Studies and Applications, pp. 173-178.
  • Enginoğlu, S., Memiş, S. (2018c). A configuration of some soft decision-making algorithms via fpfs-matrices. Cumhuriyet Science Journal, 39(4), 871-881.
  • Enginoǧlu, S., Memiş, S. (2018d). A review on some soft decision-making methods. In: Proceedings of The International Conference on Mathematical Studies and Applications, pp. 437-442.
  • Enginoğlu, S., Memiş, S., Arslan, B. (2018a). A fast and simple soft decision-making algorithm: EMA18an. In: Proceedings of The International Conference on Mathematical Studies and Applications, pp. 426-438.
  • Enginoǧlu, S., Memiş, S., Arslan, B. (2018b). Comment (2) on soft set theory and uni-int decision making [European Journal of Operational Research, (2010) 207, 848-855]. Journal New Theory, (25), 84-102.
  • Enginoğlu, S., Memiş, S., Öngel, T. (2018c). A fast and simple soft decision-making algorithm: EMO18o. In: Proceedings of The International Conference on Mathematical Studies and Applications, pp. 179-187.
  • Enginoğlu, S., Memiş, S., Öngel, T. (2018d). Comment on soft set theory and uni-int decision-making [European Journal of Operational Research, (2010) 207, 848-855]. Journal of New Results in Science, 7(3), 28-43.
  • Galetti, G., Lazzarini, L., Maggetti, M. (1992). A first characterization of the most important granites used in antiquity. In Ancient Stones: Quarrying, Trade and Provenance. Acta Archaeologica Lovaniensia Monographia, pp. 167-178.
  • Gulistan, M., Feng, F., Khan, M., Sezgin, A. (2018). Characterizations of right weakly regular semigroups in terms of generalized cubic soft sets. Mathematics, 6(293), 20 pages.
  • Karaaslan, F. (2016). Soft classes and soft rough classes with applications in decision making. Mathematical Problems in Engineering, Article ID 1584528, 11 pages.
  • Mahmood, T., Rehman, Z. U., Sezgi̇n, A. (2018). Lattice ordered soft near rings. Korean Journal of Mathematics, 26(3), 503-517.
  • Maji, P. K., Biswas, R., Roy, A. R. (2001). Fuzzy soft sets. The Journal of Fuzzy Mathematics, 9(3), 589-602.
  • Molodtsov, D. (1999). Soft set theory-first results. Computers and Mathematics with Applications, 37(4-5), 19-31.
  • Ponti, G. (1995). Granite quarries in the troad. a preliminary survey. In Studia Troica, pp. 291-320.
  • Potts, P. J. (2002). Geochemical and magnetic provenancing of Roman granite columns from Andalucia. Oxford Journal of Archaeology, 21(2), 167-194.
  • Riaz, M., Hashmi, M. R. (2018). Fuzzy parameterized fuzzy soft topology with applications. Annals of Fuzzy Mathematics and Informatics, 13(5), 593-613.
  • Riaz, M., Hashmi, M. R., Farooq, A. (2018). Fuzzy parameterized fuzzy soft metric spaces. Journal of Mathematical Analysis, 9(2), 25-36.
  • Şenel, G. (2016). A new approach to Hausdorff space theory via the soft sets. Mathematical Problems in Engineering, Article ID 2196743, 6 pages.
  • Şenel, G. (2018a). Analyzing the locus of soft spheres: Illustrative cases and drawings. European Journal of Pure and Applied Mathematics, 11(4), 946-957.
  • Şenel, G. (2018b). The relation between soft topological space and soft ditopological space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 67(2), 209-219.
  • Ullah, A., Karaaslan, F., Ahmad, I. (2018). Soft uni-Abel-Grassmann’s groups. European Journal of Pure and Applied Mathematics, 11(2), 517-536.
  • Williams-Thorpe, O. (2008). A thousand and one columns: Observations on the roman granite trade in the Mediterranean area. Oxford Journal of Archaeology, 27(1), 73-89.
  • Williams-Thorpe, O., Henty, M. M. (2000). The sources of Roman granite columns in Israel. Levant, 32, 155-170.
  • Williams-Thorpe, O., Thorpe, R. S. (1993). Magnetic susceptibility used in non-destructive provenancing of Roman granite columns. Archaeometry, 35(2), 185-195.
  • Williams-Thorpe, O., Webb, P. C., Thorpe, R. S. (2000). Non-destructive portable gamma ray spectrometry used in provenancing Roman granitoid columns from Leptis Magna, North Africa. Archaeometry, 42(1), 77-99.
  • Zorlutuna, İ., Atmaca, S. (2016). Fuzzy parametrized fuzzy soft topology. New Trends in Mathematical Sciences, 4(1), 142-152
Year 2019, Volume: 3 , 21 - 34, 31.12.2019
https://doi.org/10.30516/bilgesci.646126

Abstract

Project Number

SYL-2015-521 & 2009-72 and 2010/89

References

  • Atmaca, S. (2017). Relationship between fuzzy soft topological spaces and (X,τ_e ) parameter spaces. Cumhuriyet Science Journal, 38(4), 77-85.
  • Ay, M. (2017). Distribution of the granite columns from the Troadic quarries in Western Anatolia an archaeometric approach, Master's Thesis, Çanakkale Onsekiz Mart University, Çanakkale, Turkey (In Turkish).
  • Ay, M., Tolun, V. (2017a). Ancient granite quarries in Troad: New findings. The Turkish Yearbook of Çanakkale Studies, 15(23), 265-295 (In Turkish).
  • Ay, M., Tolun, V. (2017b). An archaeometric approach on the distribution of Troadic granite columns in the Western Anatolian coasts. Journal of Archaeology & Art, 156, 119-130 (In Turkish).
  • Bera, S., Roy, S. K., Karaaslan, F., Çağman, N. (2017). Soft congruence relation over lattice. Hacettepe Journal of Mathematics and Statistics, 46(6), 1035-1042.
  • Çağman, N., Çıtak, F., Enginoğlu, S. (2010). Fuzzy parameterized fuzzy soft set theory and its applications. Turkish Journal of Fuzzy Systems, 1(1), 21-35.
  • Çağman, N., Çıtak, F., Enginoğlu, S. (2011a). FP-soft set theory and its applications. Annals of Fuzzy Mathematics and Informatics, 2(2), 219-226.
  • Çaǧman, N., Deli, İ. (2012). Means of FP-soft sets and their applications. Hacettepe Journal of Mathematics and Statistics, 41(5), 615-625.
  • Çağman, N., Enginoğlu, S. (2010). Soft set theory and uni-int decision making. European Journal of Operational Research, 207, 848-855.
  • Çağman, N., Enginoğlu, S. (2012). Fuzzy soft matrix theory and its application in decision making. Iranian Journal of Fuzzy Systems, 9(1), 109-119.
  • Çağman, N., Enginoğlu, S., Çıtak, F. (2011b). Fuzzy soft set theory and its applications. Iranian Journal of Fuzzy Systems, 8(3), 137-147.
  • Çıtak, F. (2018). Soft k-uni ideals of semirings and its algebraic applications. Journal of the Institute of Science and Technology, 8(4), 281-294.
  • Çıtak, F., Çaǧman, N. (2017). Soft k-int-ideals of semirings and its algebraic structures. Annals of Fuzzy Mathematics and Informatics, 13(4), 531-538.
  • De Vecchi, G., Lazzarini, L., Lünel, T., Mignucci, A., Visonà, D. (2000). The genesis and characterisation of marmor misium from Kozak (Turkey) a granit used antiquity. Journal of Cultural Heritage, 1, 145-153.
  • Deli, İ., Çağman, N. (2015). Relations on FP-soft sets applied to decision making problems. Journal of New Theory, (3), 98-107.
  • Enginoğlu, S. (2012). Soft matrices, PhD Dissertation, Gaziosmanpaşa University, Tokat, Turkey, (In Turkish).
  • Enginoǧlu, S., Çağman, N. Fuzzy parameterized fuzzy soft matrices and their application in decision-making. TWMS Journal of Applied and Engineering Mathematics, (In Press).
  • Enginoğlu, S., Çağman, N., Karataş, S., Aydın, T. (2015). On soft topology. El-Cezerî Journal of Science and Engineering, 2(3), 23-38.
  • Enginoğlu, S., Demiriz, S. (2015). A comparison with the convergent, Cesàro convergent and Riesz convergent sequences of fuzzy numbers. In: The 4th International
  • Fuzzy Systems Symposium, 5-6 November 2015 İstanbul, Turkey, pp. 413-416.
  • Enginoğlu, S., Dönmez, H. (2015). An application on decision making problem by using intuitionistic fuzzy parameterized intuitionistic fuzzy soft expert sets. In: The 4th International Fuzzy Systems Symposium, 5-6 November 2015 İstanbul, Turkey, pp. 413-415.
  • Enginoğlu, S., Memiş, S. (2018a). Comment on fuzzy soft sets [The Journal of Fuzzy Mathematics, 9(3), 2001, 589-602]. International Journal of Latest Engineering Research and Applications, 3(9), 1-9.
  • Enginoğlu, S., Memiş, S. (2018b). A review on an application of fuzzy soft set in multicriteria decision making problem. In: Proceedings of The International Conference on Mathematical Studies and Applications, pp. 173-178.
  • Enginoğlu, S., Memiş, S. (2018c). A configuration of some soft decision-making algorithms via fpfs-matrices. Cumhuriyet Science Journal, 39(4), 871-881.
  • Enginoǧlu, S., Memiş, S. (2018d). A review on some soft decision-making methods. In: Proceedings of The International Conference on Mathematical Studies and Applications, pp. 437-442.
  • Enginoğlu, S., Memiş, S., Arslan, B. (2018a). A fast and simple soft decision-making algorithm: EMA18an. In: Proceedings of The International Conference on Mathematical Studies and Applications, pp. 426-438.
  • Enginoǧlu, S., Memiş, S., Arslan, B. (2018b). Comment (2) on soft set theory and uni-int decision making [European Journal of Operational Research, (2010) 207, 848-855]. Journal New Theory, (25), 84-102.
  • Enginoğlu, S., Memiş, S., Öngel, T. (2018c). A fast and simple soft decision-making algorithm: EMO18o. In: Proceedings of The International Conference on Mathematical Studies and Applications, pp. 179-187.
  • Enginoğlu, S., Memiş, S., Öngel, T. (2018d). Comment on soft set theory and uni-int decision-making [European Journal of Operational Research, (2010) 207, 848-855]. Journal of New Results in Science, 7(3), 28-43.
  • Galetti, G., Lazzarini, L., Maggetti, M. (1992). A first characterization of the most important granites used in antiquity. In Ancient Stones: Quarrying, Trade and Provenance. Acta Archaeologica Lovaniensia Monographia, pp. 167-178.
  • Gulistan, M., Feng, F., Khan, M., Sezgin, A. (2018). Characterizations of right weakly regular semigroups in terms of generalized cubic soft sets. Mathematics, 6(293), 20 pages.
  • Karaaslan, F. (2016). Soft classes and soft rough classes with applications in decision making. Mathematical Problems in Engineering, Article ID 1584528, 11 pages.
  • Mahmood, T., Rehman, Z. U., Sezgi̇n, A. (2018). Lattice ordered soft near rings. Korean Journal of Mathematics, 26(3), 503-517.
  • Maji, P. K., Biswas, R., Roy, A. R. (2001). Fuzzy soft sets. The Journal of Fuzzy Mathematics, 9(3), 589-602.
  • Molodtsov, D. (1999). Soft set theory-first results. Computers and Mathematics with Applications, 37(4-5), 19-31.
  • Ponti, G. (1995). Granite quarries in the troad. a preliminary survey. In Studia Troica, pp. 291-320.
  • Potts, P. J. (2002). Geochemical and magnetic provenancing of Roman granite columns from Andalucia. Oxford Journal of Archaeology, 21(2), 167-194.
  • Riaz, M., Hashmi, M. R. (2018). Fuzzy parameterized fuzzy soft topology with applications. Annals of Fuzzy Mathematics and Informatics, 13(5), 593-613.
  • Riaz, M., Hashmi, M. R., Farooq, A. (2018). Fuzzy parameterized fuzzy soft metric spaces. Journal of Mathematical Analysis, 9(2), 25-36.
  • Şenel, G. (2016). A new approach to Hausdorff space theory via the soft sets. Mathematical Problems in Engineering, Article ID 2196743, 6 pages.
  • Şenel, G. (2018a). Analyzing the locus of soft spheres: Illustrative cases and drawings. European Journal of Pure and Applied Mathematics, 11(4), 946-957.
  • Şenel, G. (2018b). The relation between soft topological space and soft ditopological space. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 67(2), 209-219.
  • Ullah, A., Karaaslan, F., Ahmad, I. (2018). Soft uni-Abel-Grassmann’s groups. European Journal of Pure and Applied Mathematics, 11(2), 517-536.
  • Williams-Thorpe, O. (2008). A thousand and one columns: Observations on the roman granite trade in the Mediterranean area. Oxford Journal of Archaeology, 27(1), 73-89.
  • Williams-Thorpe, O., Henty, M. M. (2000). The sources of Roman granite columns in Israel. Levant, 32, 155-170.
  • Williams-Thorpe, O., Thorpe, R. S. (1993). Magnetic susceptibility used in non-destructive provenancing of Roman granite columns. Archaeometry, 35(2), 185-195.
  • Williams-Thorpe, O., Webb, P. C., Thorpe, R. S. (2000). Non-destructive portable gamma ray spectrometry used in provenancing Roman granitoid columns from Leptis Magna, North Africa. Archaeometry, 42(1), 77-99.
  • Zorlutuna, İ., Atmaca, S. (2016). Fuzzy parametrized fuzzy soft topology. New Trends in Mathematical Sciences, 4(1), 142-152
There are 48 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Serdar Enginoğlu 0000-0002-7188-9893

Murat Ay This is me

Naim Çağman 0000-0003-3037-1868

Veysel Tolun This is me

Project Number SYL-2015-521 & 2009-72 and 2010/89
Publication Date December 31, 2019
Acceptance Date December 25, 2019
Published in Issue Year 2019 Volume: 3

Cite

APA Enginoğlu, S., Ay, M., Çağman, N., Tolun, V. (2019). Classification of The Monolithic Columns Produced in Troad and Mysia Region Ancient Granite Quarries in Northwestern Anatolia via Soft Decision-Making. Bilge International Journal of Science and Technology Research, 3, 21-34. https://doi.org/10.30516/bilgesci.646126

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