Classification of the Monolithic Columns Produced in Troad And

Home , Troad

Bilge International Journal of Science and Technology Research Web : http://dergipark.gov.tr/bilgesci - E-mail: [email protected]

Received: 12.11.2019 ISSN: 2651-401X Accepted: 25.12.2019 e-ISSN: 2651-4028 DOI: 10.30516/bilgesci.646126 3(Special Issue), 21-34, 2019 Classification of the Monolithic Columns Produced in Troad and Mysia Region Ancient Granite Quarries in Northwestern Anatolia via Soft Decision-Making Serdar Enginoğlu1*, Murat Ay2, Naim Çağman3, Veysel Tolun2

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, they 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. Keywords: Ancient Granite Quarries, Classification, fpfs-matrices, Monolithic Columns, Soft Decision- Making

1. Introduction

In the Roman Imperial Period, Troad Region and For this reason, to locate the source of a column Mysia Region are two essential regions contained considered in an ancient city, the method ancient granite quarries (Figure 1. a.) (Galetti et commonly used is to compare some al., 1992; Williams-Thorpe and Thorpe, 1993; archaeological samples taken from this city and Williams-Thorpe and Henty, 2000) such as Koçali some geological samples taken from the granite (Figure 1. b.), Akçakeçili (Figure 1. c.), and quarries by using mineralogical-petrographic and Kozak (Figure 1. d.) which known to be produced geochemical analyses (Williams-Thorpe and monolithic granite columns in Anatolia. While Thorpe, 1993; Williams-Thorpe and Henty, 2000; Koçali and Akçakeçili ancient granite quarries in Williams-Thorpe et al., 2000; Potts, 2002; Troad Region (Ponti, 1995; Ay, 2017; Ay and Williams-Thorpe, 2008; Ay, 2017; Ay and Tolun, Tolun, 2017a, b) are located in Ezine/Çanakkale, 2017b). Kozak ancient granite quarry in Mysia Region (Williams-Thorpe et al., 2000) is located in The mineralogical-petrographic analyses are an Bergama/Izmir. examination of the samples in a microscopic environment using their thin sections. These However, there are not exist a sufficient number analyses carry out to determine the types, of an archaeological document about some quantities, sizes, and shapes of the minerals subjects such as the exportation of the columns forming the rock types, main and secondary produced in these centres located in Troad and components of the samples (Galetti et al., 1992; Mysia Region. Williams-Thorpe, 2008; Ay, 2017; Ay and Tolun, 1 Department of Mathematics, Faculty of Arts and Sciences, Çanakkale Citation (Atıf): Enginoğlu, S., Ay, M., Çağman, N., Tolun, V. Onsekiz Mart University, Çanakkale, Turkey 2 (2019). Classification of the Monolithic Columns Produced in Troad Department of Archaeology, Faculty of Arts and Sciences, Çanakkale and Mysia Region Ancient Granite Quarries in Northwestern Onsekiz Mart University, Çanakkale, Turkey 3 Anatolia via Soft Decision-Making. Bilge International Journal of Department of Mathematics, Faculty of Arts and Sciences, Tokat Science and Technology Research, 3(Special Issue):21-34. Gaziosmanpaşa University, Tokat, Turkey *Corresponding author (İletişim yazarı): [email protected] Bilge International Journal of Science and Technology Research 2019, 3(Special Issue): 21-34

2017b). The geochemical analyses perform in determining the type and number of major elements contained in the samples (Galetti et al., 1992; Potts, 2002; Williams-Thorpe, 2008).

Recently, Ay and Tolun have examined the distribution in Northwestern Anatolia of the monolithic columns produced in the ancient granite quarries, located in Troad Region and Mysia Region, by using archaeometric methods (Ay, 2017; Ay and Tolun, 2017b). For this aim, by using the qualitative mineralogical- petrographic and geochemical analyses, they have b. compared the geological samples taken from Koçali-Akçakeçili ancient quarries in Troad Region and Kozak ancient quarry in Mysia Region with the archaeological samples taken from Smintheion (Smintheion 1, Smintheion 2), Pergamon Red Hall/Serapeion, Smyrna Agora (Smyrna Agora 1, Smyrna Agora 2), Tlos Stadium, Tlos Theatre, and Side Theatre.

Moreover, Ay and Tolun have divided the samples into two groups as ancient granite quarries and ancient city (Figure 2). They first c. have compared the results of each group in itself. Afterwards, they have compared separately the archaeological samples with the geological samples and have revealed which archaeological samples are more similar to which geological.

The results show that the granite columns in Smintheion 1, Smintheion 2, Smyrna Agora 2, Tlos Stadium, and Side Theatre may originate from the Koçali-Akçakeçili granite quarries located in Troad Region while the others may originate from Kozak quarry located in Mysia Region. d. Figure 1. a. Troad and Kozak ancient quarries in the Roman period (Williams-Thorpe, 2008) b. Akçakeçili quarry c. Koçali quarry d. Kozak quarry (De Vecchi et al., 2000)

The concept of soft sets was introduced by Molodtsov (1999) to cope with uncertainty and have been applied to many areas from analysis to decision-making problems (Maji et al., 2001; Çağman and Enginoğlu, 2010; Çağman et al., 2010; Çağman et al., 2011a; Çağman and Deli, 2012; Deli and Çağman, 2015; Enginoğlu and Demiriz, 2015; Enginoğlu and Dönmez, 2015; Enginoğlu et al., 2015; Karaaslan, 2016; Şenel, a. 2016; Zorlutuna and Atmaca, 2016; Atmaca, 2017; Bera et al., 2017; Çıtak and Çağman, 2017; Şenel, 2017; Çıtak, 2018; Enginoğlu and Memiş,

22 Bilge International Journal of Science and Technology Research 2019, 3(Special Issue): 21-34

2018a, b, c, d; Enginoğlu et al., 2018a, b, c, d; 2017b). In Section 4, we propose a new method, Gulistan et al., 2018; Mahmood et al., 2018; Riaz i.e. MCCM. In section 5, we apply MCCM to the and Hashmi, 2018; Riaz et al., 2018; Şenel, 2018; MCC problem. Finally, we discuss the need for Ullah et al., 2018). Recently, some soft decision- further research. making methods constructed by fuzzy parameterized fuzzy soft matrices (fpfs-matrices) 2. Preliminaries have enabled data processing in many problems containing uncertainty. Being one of these In this section, we first present the concept of methods, Prevalence Effect Method (PEM) fuzzy soft matrices (fs-matrices) (Çağman and (Enginoğlu and Çağman, In Press) has been Enginoğlu, 2012). Throughout this paper, let 푈 be applied to a performance-based value assignment universal set, 퐸 be a parameter set, 퐹(퐸) be the to some methods used in noise removal so that the set of all fuzzy sets over 퐸, and 휇 ∈ 퐹(퐸). Here, a methods can be ordered in terms of performance. fuzzy set is denoted by {휇(푥)푥 ∶ 푥 ∈ 퐸}. We use this method for classification the monolithic columns mentioned in (Ay, 2017; Ay and Tolun, 2017b). The results show that Definition 2.1. (Çağman et al., 2011b) Let 푈 be a Monolithic Columns Classification Method universal set, 퐸 be a parameter set, and 훼 be a (MCCM) is successfully model the monolithic function from 퐸 to 퐹(푈). Then, the set columns classification (MCC) problem. Here, {(푥, 훼(푥)): 푥 ∈ 퐸} being the graphic of 훼 is called fpfs-matrices have a row consisting of the a fuzzy soft set (fs-set) parameterized via 퐸 over significance degrees (membership degrees) of the 푈 (or briefly over 푈). parameters. These values are usually determined by consulting an expert. In the present paper, the set of all fs-sets over 푈 is denoted by 퐹푆퐸(푈). In 퐹푆퐸(푈), since the graphic of 훼 (푔푟푎푝ℎ(훼)) and 훼 generate each other uniquely, the notations are interchangeable. Therefore, as long as it does not cause any confusion, we denote an fs-set 푔푟푎푝ℎ(훼) by 훼.

Example 2.1. Let 퐸 = {푥1, 푥2, 푥3, 푥4} and 푈 = {푢1, 푢2, 푢3, 푢4, 푢5}. Then, 0.9 0.5 0.3 0.5 훼 = {(푥1, { 푢1, 푢4}), (푥2, { 푢2, 푢3}), 0.7 0.8 0.6 0.9 (푥3, { 푢1, 푢3, 푢4}), (푥4, {푢3, 푢5})} is an fs-set over 푈. Here, for brevity, the notation 1 푢3 is used instead of 푢3 and also the elements Figure 2. The estimated-distribution of Troad 0 which have zero membership value such as 푢3 granite columns in Western Anatolia (Ay and does not show in the sets containing them. Tolun, 2017b) Definition 2.2. (Çağman and Enginoğlu, 2012) In this study, we have identified the values, that Let 훼 ∈ 퐹푆퐸(푈). Then, [푎푖푗] is called the matrix is, the weights of archaeometric and geochemical representation of 훼 (or briefly fs-matrix of 훼) and parameters, concerning the opinions mentioned in is defined by (Ay, 2017; Ay and Tolun, 2017b). Moreover, Ay 푎11 푎12 푎13 … 푎1푛 … and Tolun have considered of more effective the geochemical data than the archaeometric data. 푎21 푎22 푎23 ⋯ 푎2푛 ⋯ Therefore, we set a higher value to geochemical [푎푖푗] ≔ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ data than archaeometric data in the final decision 푎 푎 푎 … 푎 … step. 푚1 푚2 푚3 푚푛 [⋮ ⋮ ⋮ ⋱ ⋮ ⋱ ] In Section 2 of the present study, we present the such that for 푖 ∈ {1,2, ⋯ } and 푗 ∈ {1,2, ⋯ }, 푎푖푗 ≔ concept of fpfs-matrices and PEM. In Section 3, 훼(푥 )(푢 ), where 훼(푥 )(푢 ) refers to the we give all the results of the qualitative 푗 푖 푗 푖 membership degree of 푢 in the fuzzy set mineralogical-petrographic and geochemical 푖 훼(푥 ).Here, if |푈| = 푚 and |퐸| = 푛, then [푎 ] analyses provided in (Ay, 2017; Ay and Tolun, 푗 푖푗 has order 푚 × 푛.

23 Bilge International Journal of Science and Technology Research 2019, 3(Special Issue): 21-34

From now on, the set of all fs-matrices Example 2.4. The fpfs-matrix of 훼 provided in parameterized via 퐸 over 푈 is denoted by 퐹푆퐸[푈]. Example 2.3 is as follows: Example 2.2. The fs-matrix of 훼 provided in 0.8 0 0.1 1

Example 2.1 is as follows: 0.9 0 0.7 0

0.9 0 0.7 0 0 0.3 0 0 [푎 ] = 푖푗 0 0.5 0.8 1 0 0.3 0 0 0.5 0 0.6 0 [푎푖푗] = 0 0.5 0.8 1 [0 0 0 0.9] 0.5 0 0.6 0 Definition 2.5. (Enginoğlu, 2012; Enginoğlu and [0 0 0 0.9] Çağman, In Press) Let [푎푖푗] ∈ 퐹푃퐹푆퐸[푈]. For all 푖 and 푗, if 푎푖푗 = 휆, then [푎푖푗] is called 휆-fpfs- Secondly, we present the concept of fpfs-matrices. matrix and is denoted by [휆]. Here, [0] is called empty fpfs-matrix and [1] is called universal fpfs- Definition 2.3. (Çağman et al., 2010; Enginoğlu, matrix. 2012) Let 푈 be a universal set, 휇 ∈ 퐹(퐸), and 훼 be a function from 휇 to 퐹(푈). Then, the set Definition 2.6. (Enginoğlu, 2012; Enginoğlu and {(휇(푥)푥, 훼(휇(푥)푥)): 푥 ∈ 퐸} being the graphic of 훼 Çağman, In Press) Let [푎푖푗], [푏푖푗], [푐푖푗] ∈ is called a fuzzy parameterized fuzzy soft set 퐹푃퐹푆퐸[푈]. For all 푖 and 푗, if 푐푖푗 ≔ |푎푖푗 − 푏푖푗|, (fpfs-set) parameterized via 퐸 over 푈 (or briefly then [푐 ] is called symmetric difference between over 푈). 푖푗 [푎 ] and [푏 ] and is denoted by [푎 ]∆̃[푏 ]. 푖푗 푖푗 푖푗 푖푗 In the present paper, the set of all fpfs-sets over 푈 Finally, we present the soft decision-making is denoted by 퐹푃퐹푆퐸(푈). In 퐹푃퐹푆퐸(푈), since the 푔푟푎푝ℎ(훼) and 훼 generate each other uniquely, method PEM provided in (Enginoğlu and Çağman, In Press). Throughout this paper, 퐼푛 ≔ the notations are interchangeable. Therefore, as ∗ long as it does not cause any confusion, we {1,2, … , 푛} and 퐼푛 ≔ {0,1,2, … , 푛}. denote an fpfs-set 푔푟푎푝ℎ(훼) by 훼. PEM Algorithm Steps Step 1. Construct an fpfs-matrix [푎 ] Example 2.3. Let 퐸 = {푥1, 푥2, 푥3, 푥4} and 푖푗 (푚+1)×푛 ∗ 푈 = {푢1, 푢2, 푢3, 푢4, 푢5}. Then, such that 푖 ∈ 퐼푚 and 푗 ∈ 퐼푛 0.8 0.9 0.5 0 0.3 0.5 훼 = {( 푥1, { 푢1, 푢4}), ( 푥2, { 푢2, 푢3}), Step 2. Obtain a matrix [푠 ] defined by 푖1 0.1 0.7 0.8 0.6 1 1 0.9 푛 1 푚 1 푛 ( 푥3, { 푢1, 푢3, 푢4}), ( 푥4, { 푢3, 푢5})} 푠푖1 ≔ ∑ [( ∑ 푎푘푗) ( ∑ 푎푖푡) 푎0푗푎푖푗] , 푖 ∈ 퐼푚 is an fpfs-set over 푈. 푗=1 푚 푘=1 푛 푡=1 푠푖1 max 푠 { k 푘1 } Definition 2.4. (Enginoğlu, 2012; Enginoğlu and Step 3. Obtain a decision set 푢푖 | 푢푖 ∈ 푈 Çağman, In Press) Let 훼 ∈ 퐹푃퐹푆퐸(푈). Then, [푎푖푗] is called the matrix representation of 훼 (or 3. The Qualitative Mineralogical-Petrographic briefly fpfs-matrix of 훼) and is defined by and Geochemical Analyses Results 푎01 푎02 푎03 … 푎0푛 …

In this section, we give tables of the results of the 푎11 푎12 푎13 … 푎1푛 … qualitative mineralogical-petrographic and [푎푖푗] ≔ ⋮ ⋮ ⋮ ⋱ ⋮ ⋮ geochemical analyses provided in (Ay, 2017; Ay 푎 푎 푎 … 푎 … and Tolun, 2017b). The qualitative mineralogical- 푚1 푚2 푚3 푚푛 petrographic analyses result from Koçali and [⋮ ⋮ ⋮ ⋱ ⋮ ⋱ ] Akçakeçili are the same, and the geochemical such that for 푖 ∈ {0,1,2, ⋯ } and 푗 ∈ {1,2, ⋯ }, analyses results are close to each other. Since 휇(푥푗), 푖 = 0 Koçali and Akçakeçili ancient quarries are the 푎 ≔ { 푖푗 휇(푥푗) same structure, Ay and Tolun have compared 훼( 푥푗)(푢푖), 푖 ≠ 0 Here, if |푈| = 푚 − 1 and |퐸| = 푛, then [푎 ] has eight samples with two sources: Bergama Kozak 푖푗 and Koçali-Akçakeçili in (Ay, 2017; Ay and order 푚 × 푛. Tolun, 2017b). Therefore, in the next section, we

use the mean results from Koçali and Akçakeçili. Herein, the set of all fpfs-matrices parameterized via 퐸 over 푈 is denoted by 퐹푃퐹푆퐸[푈].

24 Bilge International Journal of Science and Technology Research 2019, 3(Special Issue): 21-34

Table 1. Results of the mineralogical-petrographic analyses of alkali feldspars in thin sections

Alkali Feldspars

Surfaced

Coarse−Medium−Fine

Side Theatre 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 Tlos Theatre 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 Tlos Stadium 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 Smyrna Agora 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 Smyrna Agora 2 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 Pergamon Red Hall 1 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 Smintheion 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 Smintheion 2 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 Bergama Kozak 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 0 Koçali 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1 Akçakeçili 1 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 0 1

Table 2. Results of the mineralogical-petrographic analyses of amphiboles in thin-sections

Amphiboles

Surfaced

Coarse−Medium−Fine

Side Theatre 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 Tlos Theatre 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 Tlos Stadium 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 Smyrna Agora 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Smyrna Agora 2 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 Pergamon Red Hall 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 Smintheion 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Smintheion 2 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Bergama Kozak 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 Koçali 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 Akçakeçili 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0

Table 3. Results of the mineralogical-petrographic analyses of biotite in thin-sections

Biotite

Surfaced

Coarse −Medium Coarse Medium−Fine Fine Chloritised Sericitised Pertitic Mirmekitic Carbonated Clayed Idiomorphic Hypidiomorphic Xenomorphic Homogeneous Recrystallised Prismatic Flat Prismatic Clean Twinning Coarse−Medium−Fine Side Theatre 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 Tlos Theatre 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 Tlos Stadium 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 Smyrna Agora 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 Smyrna Agora 2 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 Pergamon Red Hall 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 Smintheion 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Smintheion 2 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 Bergama Kozak 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 Koçali 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 Akçakeçili 0 0 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0

25 Bilge International Journal of Science and Technology Research 2019, 3(Special Issue): 21-34

Table 4. Results of the mineralogical-petrographic analyses of plagioclase in thin-sections

Plagioclase

Surfaced

Coarse−Medium−Fine

Side Theatre 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 Tlos Theatre 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 Tlos Stadium 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 Smyrna Agora 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 Smyrna Agora 2 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0 1 0 0 Pergamon Red Hall 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 Smintheion 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 Smintheion 2 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 Bergama Kozak 0 0 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 Koçali 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1 Akçakeçili 1 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 1

Table 5. Results of the mineralogical-petrographic analyses of quartz in thin-sections

Quartz

Surfaced

Coarse−Medium−Fine

Side Theatre 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 Tlos Theatre 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 Tlos Stadium 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 Smyrna Agora 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Smyrna Agora 2 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 Pergamon Red Hall 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 Smintheion 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 Smintheion 2 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 Bergama Kozak 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 Koçali 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 Akçakeçili 0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0

Table 6. Results of the geochemical analyses of thin-sections

5 2

O 2

O O

2 a

Geochemical Analyses 2

CaO

MgO P Ti

MnO

Al Fe Side Theatre 5.9 5.0 2.0 0.7 59.5 16.3 5.1 0.2 3.4 0.8 Tlos Theatre 5.0 4.5 2.2 0.3 63.5 15.8 3.7 0.1 3.2 0.7 Tlos Stadium 5.3 4.9 1.9 0.6 60.5 16.6 5.1 0.1 3.5 0.7 Smyrna Agora 1 4.4 3.9 1.0 0.1 67.4 15.7 2.8 0.1 3.4 0.5 Smyrna Agora 2 5.7 5.2 2.3 0.5 59.6 16.8 4.1 0.1 3.6 0.9 Pergamon Red Hall 5.5 4.6 2.1 0.3 61.9 16.3 3.4 0.1 3.3 0.7 Smintheion 1 4.6 3.8 1.7 0.4 63.6 15.9 4.4 0.1 3.5 0.6 Smintheion 2 4.8 3.9 1.7 0.4 63.8 15.8 4.3 0.1 3.5 0.6 Bergama Kozak 4.7 4.2 2.0 0.3 64.2 15.9 3.7 0.1 3.4 0.7 Koçali 5.0 4.6 1.9 0.5 61.5 16.4 4.5 0.1 3.6 0.7 Akçakeçili 5.0 4.4 1.9 0.5 61.6 16.1 4.7 0.1 3.5 0.7 Koçali-Akçakeçili 5.0 4.5 1.9 0.5 61.55 16.25 4.6 0.1 3.55 0.7

26 Bilge International Journal of Science and Technology Research 2019, 3(Special Issue): 21-34

Table 7. Results of the geochemical analyses of thin-sections (normalised via maximum value in Table 6)

5 2

O 2

O O

Geochemical Analyses 2

O O

CaO

MgO P Ti MnO

(Normalised) N

Al Fe Side Theatre 0.0875 0.0742 0.0297 0.0104 0.8828 0.2418 0.0757 0.0030 0.0504 0.0119 Tlos Theatre 0.0742 0.0668 0.0326 0.0045 0.9421 0.2344 0.0549 0.0015 0.0475 0.0104 Tlos Stadium 0.0786 0.0727 0.0282 0.0089 0.8976 0.2463 0.0757 0.0015 0.0519 0.0104 Smyrna Agora 1 0.0653 0.0579 0.0148 0.0015 1.0000 0.2329 0.0415 0.0015 0.0504 0.0074 Smyrna Agora 2 0.0846 0.0772 0.0341 0.0074 0.8843 0.2493 0.0608 0.0015 0.0534 0.0134 Pergamon Red Hall 0.0816 0.0682 0.0312 0.0045 0.9184 0.2418 0.0504 0.0015 0.0490 0.0104 Smintheion 1 0.0682 0.0564 0.0252 0.0059 0.9436 0.2359 0.0653 0.0015 0.0519 0.0089 Smintheion 2 0.0712 0.0579 0.0252 0.0059 0.9466 0.2344 0.0638 0.0015 0.0519 0.0089 Bergama Kozak 0.0697 0.0623 0.0297 0.0045 0.9525 0.2359 0.0549 0.0015 0.0504 0.0104 Koçali-Akçakeçili 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104

4. Research Method Pre-processing Steps for Geochemical Data Step 1. Construct fs-matrices [푎 ] for In this section, we first present MCCM and which 푖푗 푚×푛 also uses the abilities of PEM (Enginoğlu and archaeological samples Step 2. Construct fs-matrices [푏 ] for Çağman, In Press). 푖푗 푚×푛 geological samples Algorithm Steps of MCCM Step 3. Obtain fs-matrices [푐푘 ] defined by 푖푗 푚×푛 Pre-processing Steps for Archaeometric 푘 푐푖푗 ≔ 푏푘푗 such that 푘 ∈ 퐼푟 Data 푘 푧 Step 4. Obtain fs-matrices [푑푖푗] defined by Step 1. Construct fs-matrices [푎푖푗] for 푚×푛 푚×푛 푘 푘 ̃ [푑푖푗] ≔ [1] − [푐푖푗]∆[푎푖푗] such that 푘 ∈ 퐼푟 archaeological samples, for all 푧 ∈ 퐼푤 Step 2. Construct fs-matrices [푏푧 ] for Main Steps for Geochemical Data 푘푗 푟×푛 Step 1. Construct fpfs-matrices [푒푘 ] geological samples, for all 푧 ∈ 퐼푤 푖푗 (푚+1)×푛 Step 3. Obtain [푐푧푘] defined by 푐푧푘 ≔ 푏푧 such that 푖 ∈ 퐼∗ , 푗 ∈ 퐼 , and 푖 ≠ 0 ⇒ 푒푘 ≔ 푑푘 푖푗 푚×푛 푖푗 푘푗 푚 푛 푖푗 푖푗 푘 such that 푧 ∈ 퐼푤 and 푘 ∈ 퐼푟 Step 2. Apply PEM to [푒푖푗] for all 푘 ∈ 퐼푟. That Step 4. Obtain [푑푧푘] defined by [푑푧푘] ≔ is, obtain [푓 ] defined by 푖푗 푚×푛 푖푗 푖푘 푚×푟 [1] − [푐푧푘]∆̃[푎푧 ] such that 푧 ∈ 퐼 and 푘 ∈ 퐼 푛 푛 푚 푖푗 푖푗 푤 푟 1 푘 1 푘 푘 푘 푓푖푘 ≔ ( ∑ 푒푖푙) ∑ [( ∑ 푒푝푗) 푒0푗푒푖푗] Main Steps for Archaeometric Data 푛 푙=1 푗=1 푚 푝=1 Step 1. Construct fpfs-matrices [푒푧푘] 푖푗 (푚+1)×푛 such that 푖 ∈ 퐼푚 and 푘 ∈ 퐼푟 ∗ 푧푘 푧푘 [ 2 ] such that 푖 ∈ 퐼푚, 푗 ∈ 퐼푛, and 푖 ≠ 0 ⇒ 푒푖푗 ≔ 푑푖푗 Step 3. Obtain 푠푖푘 푚×푟 defined by Step 2. Apply PEM to [푒푧푘] for all 푧 ∈ 퐼 and 푓푖푘 푖푗 푤 , max 푓푖푡 ≠ 0 푘 ∈ 퐼 . That is, obtain [푓 푧 ] defined by 2 max 푓푖푡 푡∈퐼푟 푟 푖푘 푚×푟 푠푖푘 ≔ { 푡∈퐼푟 1 푛 푛 1 푚 푓푖푘, max 푓푖푡 = 0 푧 푧푘 푧푘 푧푘 푧푘 푡∈퐼푟 푓푖푘 ≔ ( ∑ 푒푖푙 ) ∑ [( ∑ 푒푝푗 ) 푒0푗 푒푖푗 ] 푛 푙=1 푗=1 푚 푝=1 Output Steps such that 푧 ∈ 퐼푤 and 푘 ∈ 퐼푟 Step 1. Obtain the decision matrix [푠푖푘]푚×푟 1 2 Step 3. Obtain [푔푖푘]푚×푟 defined by 푔푖푘 ≔ such that 푠푖푘 = 0.25푠푖푘 + 0.75푠푖푘 1 ∑푤 푓푧 Step 2. Obtain the decision sets 퐷푘 ≔ 푤 푧=1 푖푘 1 {푢푖 |푠푖푘 = max 푠푖푝} such that 푘, 푝 ∈ 퐼푟 Step 4. Obtain [푠푖푘]푚×푟 defined by 푝

푔푖푘 , max 푔푖푡 ≠ 0 Secondly, we illustrate MCCM for 푧 = 푘 = 2, 1 max 푔푖푡 푡∈퐼푟 푠푖푘 ≔ { 푡∈퐼푟 that is, for the Amphibols data given in the 푔푖푘, max 푔푖푡 = 0 previous. Faithfully to the Ay and Tolun's 푡∈퐼 푟 opinions, we set

27 Bilge International Journal of Science and Technology Research 2019, 3(Special Issue): 21-34

[0.01, 0.01, 0.01, 0.01, 1, 1, 1, 1, 1, 1, 0.01, 0.01, 푥11 =Idiomorphic (Self-Shaped), 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01] 푥12 =Hypidiomorphic (Semi-Self-Shaped), and 푥13 =Xenomorphic (Self-Shapeless), 푥14 = [0.6, 0.6, 0.01, 0.7, 1, 0.8, 1, 0.01, 0.7, 0.01] Homogeneous, 푥15 =Recrystallised (Wavy), to the weights of the archaeometric and 푥16 =Prismatic, 푥17 =Flat Prismatic, geochemical parameters, respectively. Moreover, 푥18 =Clean Surfaced, and 푥19 =Twinning. Ay and Tolun (2017b) consider more effective the geochemical data than archaeometric data. Therefore, the fs-sets of the Amphiboles data are Therefore, we set 0.25 and 0.75 values to these as follows: data as weights, respectively, in the final decision 훼 = { (푥 , {푢 , 푢 }), (푥 , {푢 , 푢 , 푢 , 푢 }), stage. 1 5 6 3 3 5 6 8 (푥4, {푢1, 푢2, 푢4, 푢7}), (푥5, {푢6}), (푥9, {푢6}), Pre-process Steps for Archaeometric Data (푥11, {푢1, 푢2, 푢3}), (푥12, 푈), (푥14, {푢5, 푢6}), Step 1. and Step 2. (푥16, {푢5, 푢6})} Let 푈 = {푢푖: 푖 ∈ 퐼8}, 푉 = {푣푘: 푘 ∈ 퐼2}, and 퐸1 = 훽 = {(푥 , 푉), (푥 , 푉),(푥 , {푣 }), (푥 , 푉), (푥 , 푉), {푥푗: 푗 ∈ 퐼19} such that 푢1 =Side Theatre, 3 9 11 1 12 14 푢 =Tlos Theatre, 푢 =Tlos Stadium, 2 3 (푥16, 푉)} 푢 =Smyrna Agora 1, 푢 =Smyrna Agora 2, 4 5 where ∅ denotes empty fuzzy set. Here, for 푢6 =Pergamon Red Hall / Serapeion, brevity, the notation 푢3 has been used instead of 푢7 =Smintheion 1, 푢8 =Smintheion 2, 1 0 푢3. Also, the elements such 푢3 and (푥4, ∅) 푣1 =Bergama Kozak, 푣2 =Koçali-Akçakeçili, 푥 = Coarse-Medium-Fine, 푥 = Coarse - have not been shown in the sets containing them. 1 2 Medium, 푥 = Medium-Fine, 푥 = Fine, 푥 = 3 4 5 The fs-matrices corresponded to the fs-sets 훼 and Chloritised, 푥 = Sericitised, 푥 = Pertitic, 푥 = 6 7 8 훽, respectively, are as follows: Mirmekitic, 푥 = Carbonated, 푥 = Clayed, 9 10

0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 [푎2 ] = 푖푗 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0

2 0 0 1 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 [푏푖푗] = 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0

Step 3.

0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 [푐22] = 푖푗 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0

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Step 4.

1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 [푑22] = 푖푗 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1

Main Steps for Archaeometric Data

Step 1. 0.01 0.01 0.01 0.01 1 1 1 1 1 1 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 0 1 1 1 22 [푒푖푗 ] = 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 1 Step 4. Step 2. 0.7933 0.7383 3.6520 3.3886 0.8177 0.7627 3.6520 3.3886 0.8021 0.7771 4.1821 3.9178 1 0.7935 0.7624 [푠푖푘] = 2 3.3886 3.6538 0.9519 0.9392 [푓푖푘] = 4.1768 4.4435 1.0000 0.9416 3.5453 3.7724 0.8127 0.8478 3.3886 3.6538 0.7932 0.8631 3.9178 4.1842 Pre-process Steps for Geochemical Data

Step 3. Step 1. and Step 2. 3.5157 3.2720 Let 푈 = {푢 : 푖 ∈ 퐼 }, 푉 = {푣 : 푘 ∈ 퐼 }, and 퐸 = 3.6240 3.3803 푖 8 푘 2 2 {푦 : 푙 ∈ 퐼 } such that 푢 =Side Theatre, 푢 =Tlos 3.5548 3.4438 푙 10 1 2 Theatre, 푢3 =Tlos Stadium, 푢4 =Smyrna Agora

3.5167 3.3788 1, 푢5 =Smyrna Agora 2, 푢6 =Pergamon Red Hall [푔푖푘] = 4.2189 4.1625 / Serapeion, 푢7 =Smintheion 1, 푢8 =Smintheion 4.4318 4.1732 2, 푣1 =Bergama Kozak, 푣2 =Koçali-Akçakeçili, 푦 = 퐶푎푂, 푦 = 퐹푒 푂 , 푦 = 푀푔푂, 푦 = 푃 푂 , 3.6016 3.7574 1 2 2 3 3 4 2 5 푦5 = 푆푖푂2, 푦6 = 퐴푙푂3, 푦7 = 퐾2푂, 푦8 = 푀푛푂, 3.5155 3.8252 푦9 = 푁푎2푂, and 푦10 = 푇푖푂2. Therefore, the fs- sets of the Amphiboles data are as follows:

29 Bilge International Journal of Science and Technology Research 2019, 3(Special Issue): 21-34

0.0875 0.0742 0.0786 0.0653 0.0846 0.0846 0.0682 0.0712 훾 = {(푦1, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.0742 0.0668 0.0727 0.0579 0.0772 0.0682 0.0564 0.0579 (푦2, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.0297 0.0326 0.0282 0.0148 0.0341 0.0312 0.0252 0.0252 (푦3, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.0104 0.0045 0.0089 0.0015 0.0074 0.0045 0.0059 0.0059 (푦4, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.8828 0.9421 0.8976 1,0000 0.8843 0.9184 0.9436 0.9466 (푦5, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.2418 0.2344 0.2463 0.2329 0.2493 0.2418 0.2359 0.2344 (푦6, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.0757 0.0549 0.0757 0.0415 0.0608 0.0504 0.0653 0.0638 (푦7, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.0030 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015 (푦8, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.0504 0.0475 0.0519 0.0504 0.0534 0.0490 0.0519 0.0519 (푦9, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8}), 0.0119 0.0104 0.0104 0.0074 0.0134 0.0104 0.0089 0.0089 (푦10, { 푢1, 푢2, 푢3, 푢4, 푢5, 푢6, 푢7, 푢8})}

0.0697 0.0742 0.0623 0.0668 0.0297 0.0282 훿 = {(푦1, { 푣1, 푣2}), (푦2, { 푣1, 푣2}), (푦3, { 푣1, 푣2}), 0.0045 0.0074 0.9525 0.9132 0.2359 0.2411 (푦4, { 푣1, 푣2}), (푦5, { 푣1, 푣2}) , (푦6, { 푣1, 푣2}), 0.0549 0.0682 0.0015 0.0015 0.0504 0.0527 (푦7, { 푣1, 푣2}), (푦8, { 푣1, 푣2}), (푦9, { 푣1, 푣2}), 0.0104 0.0104 (푦10, { 푣1, 푣2})}

The fs-matrices corresponded to the fs-sets 훾 and 훿, respectively, are as follows:

0.0875 0.0742 0.0297 0.0104 0.8828 0.2418 0.0757 0.0030 0.0504 0.0119 0.0742 0.0668 0.0326 0.0045 0.9421 0.2344 0.0549 0.0015 0.0475 0.0104 0.0786 0.0727 0.0282 0.0089 0.8976 0.2463 0.0757 0.0015 0.0519 0.0104 0.0653 0.0579 0.0148 0.0015 1.0000 0.2329 0.0415 0.0015 0.0504 0.0074 [푎푖푗] = 0.0846 0.0772 0.0341 0.0074 0.8843 0.2493 0.0608 0.0015 0.0534 0.0134 0.0816 0.0682 0.0312 0.0045 0.9184 0.2418 0.0504 0.0015 0.0490 0.0104 0.0682 0.0564 0.0252 0.0059 0.9436 0.2359 0.0653 0.0015 0.0519 0.0089 0.0712 0.0579 0.0252 0.0059 0.9466 0.2344 0.0638 0.0015 0.0519 0.0089

0.0697 0.0623 0.0297 0.0045 0.9525 0.2359 0.0549 0.0015 0.0504 0.0104 [푏 ] = 푖푗 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104

Step 3. 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104 [푐2 ] = 푖푗 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104 0.0742 0.0668 0.0282 0.0074 0.9132 0.2411 0.0682 0.0015 0.0527 0.0104

Step 4. 0.9867 0.9926 0.9985 0.9970 0.9696 0.9993 0.9925 0.9985 0.9977 0.9985 1 1 0.9956 0.9971 0.9711 0.9933 0.9867 1 0.9948 1 0.9956 0.9941 1 0.9985 0.9844 0.9948 0.9925 1 0.9992 1 0.9911 0.9911 0.9866 0.9941 0.9132 0.9918 0.9733 1 0.9977 0.9970 [푑2 ] = 푖푗 0.9896 0.9896 0.9941 1 0.9711 0.9918 0.9926 1 0.9993 0.9970 0.9926 0.9986 0.9970 0.9971 0.9948 0.9993 0.9822 1 0.9963 1 0.9940 0.9896 0.9970 0.9985 0.9696 0.9948 0.9971 1 0.9992 0.9985 0.9970 0.9911 0.9970 0.9985 0.9666 0.9933 0.9956 1 0.9992 0.9985

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Main Steps for Geochemical Data

Step 1. 0.6 0.6 0.01 0.7 1 0.8 1 0.01 0.7 0.01 0.9867 0.9926 0.9985 0.9970 0.9696 0.9993 0.9925 0.9985 0.9977 0.9985 1 1 0.9956 0.9971 0.9711 0.9933 0.9867 1 0.9948 1 0.9956 0.9941 1 0.9985 0.9844 0.9948 0.9925 1 0.9992 1 2 [푒푖푗] = 0.9911 0.9911 0.9866 0.9941 0.9132 0.9918 0.9733 1 0.9977 0.9970 0.9896 0.9896 0.9941 1 0.9711 0.9918 0.9926 1 0.9993 0.9970 0.9926 0.9986 0.9970 0.9971 0.9948 0.9993 0.9822 1 0.9963 1 0.9940 0.9896 0.9970 0.9985 0.9696 0.9948 0.9971 1 0.9992 0.9985 0.9970 0.9911 0.9970 0.9985 0.9666 0.9933 0.9956 1 0.9992 0.9985

Step 2. Step 2. 5.1804 5.2810 Side Theatre Koçali-Akçakeçili 5.3326 5.2865 Tlos Theatre Bergama Kozak 5.2087 5.3150 Tlos Stadium Koçali-Akçakeçili 5.2470 5.1519 [푓 ] = 푖푘 5.1927 5.2767 Smyrna Agora 1 Bergama Kozak 5.2773 5.3157 Smyrna Agora 2 Koçali-Akçakeçili 5.3211 5.2906 Pergamon Red Hall Bergama Kozak 5.3276 5.2869 Smintheion 1 Koçali-Akçakeçili

Step 3. Smintheion 2 Koçali-Akçakeçili 0.9715 0.9903 5. Conclusion 1.0000 0.9913

0.9768 0.9967 We, in this paper, proposed a novel method 0.9840 0.9661 MCCM to model an MCC problem. We then [푠2 ] = 푖푘 0.9738 0.9895 applied MCCM to the data provided in (Ay, 2017; 0.9896 0.9968 Ay and Tolun, 2017b). The results affirmed those obtained by archaeometric analyses. Since this

0.9978 0.9921 method is the first, it could not be compared with 0.9991 0.9914 other methods for now. Soon, however, if another soft decision-making method that differs from Output Steps PEM is applied to this problem, then a comparison of these methods can be given. Step 1. 0.9269 0.9273 Acknowledgements 0.9544 0.9342 We thank Ayten Çalık (PhD) and Ömer Can

0.9331 0.9418 Yıldırım (MA) for technical support. The 0.9363 0.9152 archaeological portion of this work was supported [푠푖푘] = 0.9683 0.9769 by the Office of Scientific Research Projects 0.9922 0.9830 Coordination at Çanakkale Onsekiz Mart University, Grant number: SYL-2015-521. The 0.9516 0.9560 mathematical portion of this work was supported 0.9476 0.9594 by the Office of Scientific Research Projects Coordination at Tokat Gaziosmanpaşa University, Grant numbers: 2009-72 and 2010/89.

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