ABSTRACT
This paper presents a study of the fuzzy analytical hierarchy process (FAHP) for the prioritization of factors having important effects on the surface roughness of wood and woodbased materials in the planing process. Firstly, a threelevel hierarchical model was devised. Secondly, the FAHP method was employed to determine the weights of the factors. Finally, the prioritization of the factors was carried out taking into account the weights. The results showed that the most significant factors are feed speed (0.300), tool geometry (0.222), and material defect (0.107). Consequently, this study provides a valuable guide to the wood industry to improve the surface quality of wood and woodbased products.
Keywords:
Fuzzy analytical hierarchy process; Multicriteria decisionmaking; Planing; Wood
INTRODUCTION
Surface roughness can be defined as fine irregularities on a machined surface (Magoss, 2008MAGOSS, E. General regularities of wood surface roughness. Acta Silvatica & Lignaria Hungarica, v. 4, p. 8193, 2008.). The surface roughness of wood influences further manufacturing processes such as joining application, bonding quality, and its strength characteristics, and the appearance of a final product (Kilic et al., 2006KILIC, M.; HIZIROGLU, S.; BURDURLU, E. Effect of machining on surface roughness of wood. Building and Environment, v. 41, n. 8, p. 10741078, 2006. ; Buyuksari et al., 2011BUYUKSARI, U.; AKBULUT, T.; GULER, C.; AS, N. Wettability and surface roughness of natural and plantationgrown narrowleaved ash (Fraxinus angustifolia Vahl.) wood. BioResources, v. 6, n. 4, p. 47214730, 2011. ; Li et al., 2017LI, W.; ZHANG, Z.; PENG, X.; LI, B. The influences of circular saws with sawteeth of miczerodegree radial clearance angles on surface roughness in wood rip sawing. Annals of Forest Science, v. 74, n. 2, p. 37, 2017.). However, the determination of surface roughness is a complex process owing to cutting processes, machining conditions, and the anatomical structure of wood (Malkoçoğlu, 2007MALKOÇOĞLU, A. Machining properties and surface roughness of various wood species planed in different conditions. Building and Environment , v. 42, n. 7, p. 25622567, 2007. ). Although many roughness measurement methods (laser, light sectioning, pneumatic, stylus, etc.) are available, there is no accepted standard method to determine the surface roughness of wood and wood products. The stylus method has been successfully used in many studies (Tan et al., 2012TAN, P.L.; SHARIF, S.; SUDIN I. Roughness models for sanded wood surfaces. Wood Science and Technology, v. 46, n. 13, p. 129142, 2012.; Hiziroglu et al., 2013HIZIROGLU, S.; ZHONG, Z.W.; TAN, H.L. Measurement of bonding strength of pine, kapur and meranti wood species as function of their surface quality. Measurement, v. 46, n. 9, p. 31983201, 2013.; Ulker, 2018ULKER, O. Surface roughness of composite panels as a quality control tool. Materials, v. 11, n. 3, p. 407, 2018.).
Wood materials are processed through various steps, including planing, sawing, and sanding. The surface quality of wood subjected to machining is influenced by many factors related to wood characteristics and machining conditions (Pinkowski et al., 2018PINKOWSKI, G.; SZYMAŃSKI, W.; KRAUSS, A.; STEFANOWSKI, S. Effect of sharpness angle and feeding speed on the surface roughness during milling of various wood species. BioResources , v. 13, n. 3, p. 69526962, 2018.). The most significant factors related to the wood characteristics are wood species, anatomical properties, density, and moisture content (Aguilera, 2011AGUILERA, A. Cutting energy and surface roughness in medium density fiberboard rip sawing. European Journal of Wood and Wood Products, v. 69, n. 1, p. 1118, 2011. ; Ugulino and Hernández, 2017UGULINO, B.; HERNÁNDEZ, R.E. Assessment of surface properties and solventborne coating performance of red oak wood produced by peripheral planing. European Journal of Wood and Wood Products , v. 75, n. 4, p. 581593, 2017.). In addition to these factors, process parameters such as cutting speed, cutting depth, feed speed, and tool geometry significantly affect the surface quality of wood (Lu, 2008LU, C. Study on prediction of surface quality in machining process. Journal of Materials Processing Technology, v. 205, n. 13, p. 439450, 2008.; İşleyen and Karamanoğlu, 2019). To improve the surface quality of the final product, it is essential to have a basic knowledge of the factors related to both wood characteristics and machining conditions (Gurleyen, 2010GURLEYEN, L. The study for the strain of hardwood materials against machines and cutters in planning process. Scientific Research and Essays, v. 5, n. 24, p. 39033913, 2010.).
Many researchers have evaluated the effects of various factors on the surface roughness of wood (Sütçü, 2013SÜTÇÜ, A. Investigation of parameters affecting surface roughness in CNC routing operation on wooden EGP. BioResources , v. 8, n. 1, p. 795805, 2013. ; Lopes et al., 2014LOPES, C.S.D.; NOLASCO, A.M.; FILHO, M.T.; DIAS, C.T.D.S. Evaluation of wood surface roughness of eucalypt species submitted to cutterhead rotation. CERNE, v. 20, n. 3, p. 471476, 2014.; Tiryaki et al., 2015TIRYAKI, S.; HAMZAÇEBI, C.; MALKOÇOĞLU, A. Evaluation of process parameters for lower surface roughness in wood machining by using Taguchi design methodology. European Journal of Wood and Wood Products , v. 73, n. 4, p. 537545, 2015.; Tiryaki et al., 2017). The studies in the related literature have revealed that the importance of each factor is different. Therefore, the determination of the importance of factors influencing the surface roughness of wood is necessary. Multicriteria decisionmaking (MCDM) methods can be used to obtain the priority values of main factors and subfactors. However, tangible and intangible factors cause vagueness and ambiguity in the decisionmaking process. The fuzzy set theory can convert human judgments into meaningful results. Therefore, in this study, the use of the fuzzy MCDM is preferred. The fuzzy analytical hierarchy process (FAHP) is the most popular fuzzy MCDM method. Prioritizing the factors by utilizing FAHP yields supportive and logical results (Bozbura et al., 2007BOZBURA, F.T.; BESKESE, A.; KAHRAMAN, C. Prioritization of human capital measurement indicators using fuzzy AHP. Expert Systems with Applications, v. 32, n. 4, p. 11001112, 2007.; Heo et al., 2010HEO, E.; KIM, J.; BOO, K.J. Analysis of the assessment factors for renewable energy dissemination program evaluation using fuzzy AHP. Renewable and Sustainable Energy Reviews, v. 14, n. 8, p. 22142220, 2010.; Beşikçi et al., 2016BEŞIKÇI, E.B.; KECECI, T.; ARSLAN, O.; TURAN, O. An application of fuzzyAHP to ship operational energy efficiency measures. Ocean Engineering, v. 121, p. 392402, 2016.).
The MCDM methods have been successfully employed in the field of wood science. Smith et al. (1995SMITH, R.L.; BUSH, R.J.; SCHMOLDT, D.L. A hierarchical model and analysis of factors affecting the adoption of timber as a bridge material. Wood and Fiber Science, v. 27, n. 3, p. 225238, 1995.) employed the analytical hierarchy process (AHP) to analyze factors affecting the adoption of timber as a bridge material. Azizi (2008AZIZI, M. A model of supplying poplar wood for Iranian paper & wood factories. Journal of Forestry Research, v. 19, n. 4, p. 323328, 2008. ) selected the best wood supply alternative by employing the analytic network process (ANP) and the BOCR approach. Lipušček et al. (2010LIPUŠČEK, I.; BOHANEC, M.; OBLAK, L.; STIRN, L.Z. A multicriteria decisionmaking model for classifying wood products with respect to their impact on environment. International Journal of Life Cycle Assessment, v. 15, n. 4, p. 359367, 2010.) employed the AHP method to classify wood products in terms of their impact on the environment. Azizi and Modarres (2011) selected the best construction panel by using the AHP and ANP methods. Azizi et al. (2012) used the AHP method to select the best medium density fiberboard (MDF) product. Kuzman and Grošelj (2012KUZMAN, M.K.; GROŠELJ, P. Wood as a construction material: comparison of different construction types for residential building using the analytic hierarchy process. Wood Research, v. 57, n. 4, p. 591600, 2012. ) compared different construction types by utilizing the AHP method. Sarfi et al. (2013SARFI, F.; AZIZI, M.; ARIAN, A. A multiple criteria analysis of factors affecting markets of engineered wood products with respect to customer preferences: a case study of particleboard and MDF. Forest Science and Practice, v. 15, n. 1, p. 6169, 2013.) used the AHP method to analyze factors influencing the markets of particleboard and MDF. Karakuş et al. (2017KARAKUŞ, K.; AYDEMIR, D.; ÖZTEL, A.; GUNDUZ, G.; MENGELOGLU, F. Nanoboron nitridefilled heattreated wood polymer nanocomposites: comparison of different multicriteria decisionmaking models to predict optimum properties of the nanocomposites. Journal of Composite Materials, v. 51, n. 30, p. 42054218, 2017. ) employed the technique for order preference by similarity to ideal solutions (TOPSIS), the multiple attribute utility theory (MAUT), and the compromise programming (CP) to predict the optimum properties of some nanocomposites.
There are many attempts on solving various decisionmaking problems in the field of wood science. However, a MCDM method has not yet been used to prioritize factors influencing the surface roughness of wood and woodbased materials in the planing process. Therefore, the objectives of this study are to determine the importance of each factor by employing the FAHP method and to provide a useful guide to the wood industry.
MATERIAL AND METHODS
Fuzzy Sets and Fuzzy Numbers
The fuzzy set theory was developed by Zadeh (1965ZADEH, L.A. Fuzzy sets. Information and Control, v. 8, n. 3, p. 338353, 1965.) in order to represent the uncertainty, vagueness, and ambiguity of judgments (Lee et al., 2011LEE, S.K.; MOGI, G.; LEE, S.K.; KIM, J.W. Prioritizing the weights of hydrogen energy technologies in the sector of the hydrogen economy by using a fuzzy AHP approach. International Journal of Hydrogen Energy, v. 36, n. 2, p. 18971902, 2011.). In a classical set, an element belongs to, or does not belong to, a set whereas an element of a fuzzy set naturally belongs to the set with a membership value from the interval [0,1] (Kahraman and Kaya, 2010KAHRAMAN, C.; KAYA, İ. A fuzzy multicriteria methodology for selection among energy alternatives. Expert Systems with Applications , v. 37, n. 9, p. 62706281, 2010. ).
The most commonly used fuzzy numbers are triangular and trapezoidal fuzzy numbers (Ebadi et al., 2013EBADI, M.J.; SULEIMAN, M.; ISMAIL, F.B.; AHMADIAN, A.; BALOOCH SHAHRYARI, M.R.; SALAHSHOUR, S. A new distance measure for trapezoidal fuzzy numbers. Mathematical Problems in Engineering, v. 2013, Article ID 424186, p. 14, 2013.). In this study, triangular fuzzy numbers will be used to represent the linguistic terms due to their ease of calculation (Tsai and Chou, 2011TSAI, K.M.; CHOU, F.C. Developing a fuzzy multiattribute matching and negotiation mechanism for sealedbid online reverse auctions. Journal of Theoretical and Applied Electronic Commerce Research, v. 6, n. 3, p. 8596, 2011.). A triangular fuzzy number can be represented as (l, m, u), and its membership function µM(x) can be given as follows (Büyüközkan and Çifçi, 2012BÜYÜKÖZKAN, G.; ÇIFÇI, G. A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic service quality in healthcare industry. Expert Systems with Applications , v. 39, n. 3, p. 23412354, 2012.):
Let and be M 2 = ( l 2 , m 2 , u 2 )triangular fuzzy numbers. The operations on these triangular fuzzy numbers are defined as follows (Lee et al., 2011LEE, S.K.; MOGI, G.; LEE, S.K.; KIM, J.W. Prioritizing the weights of hydrogen energy technologies in the sector of the hydrogen economy by using a fuzzy AHP approach. International Journal of Hydrogen Energy, v. 36, n. 2, p. 18971902, 2011.):
The triangular fuzzy conversion scale used in this study is given in Table 1.
Fuzzy Analytical Hierarchy Process Method
AHP is a useful method to solve complex MCDM problems involving multiple qualitative and quantitative criteria (Saaty, 1980SAATY, T.L. The analytic hierarchy process: planning, priority setting, resource allocation. McGrawHill International Book Company, 1980. ). The AHP method breaks down a complex MCDM problem into a hierarchy of decision elements (see Figure 1). To construct evaluation matrices, pairwise comparisons must be made by experts. Once pairwise comparison matrices are normalized, the rows of these matrices are averaged to determine the importance of each decision element. Moreover, the consistency ratio (CR) can be computed to check the consistency of judgments. If the CR value exceeds 0.10, the decisionmaker must revise comparisons (Saaty, 1980; Işıklar and Büyüközkan, 2007; Rajak et al., 2016RAJAK, A.K.; NIRAJ, M.; KUMAR, S. Designing of fuzzy expert heuristic models with cost management toward coordinating AHP, fuzzy TOPSIS and FIS approaches. Sadhana, v. 41, n. 10, p. 12091218, 2016.).
The traditional AHP method is based on crisp judgments. However, it is very difficult to acquire precise data owing to the uncertainty on the judgments of decisionmakers. Each decisionmaker prefers natural language expressions rather than crisp numbers. In order to capture uncertainties, the FAHP method has been employed by several researchers (Heo et al., 2010HEO, E.; KIM, J.; BOO, K.J. Analysis of the assessment factors for renewable energy dissemination program evaluation using fuzzy AHP. Renewable and Sustainable Energy Reviews, v. 14, n. 8, p. 22142220, 2010.). There are various FAHP methods. Brief information about some FAHP methods can be found in Bozbura et al. (2007BOZBURA, F.T.; BESKESE, A.; KAHRAMAN, C. Prioritization of human capital measurement indicators using fuzzy AHP. Expert Systems with Applications, v. 32, n. 4, p. 11001112, 2007.). In this study, Chang’s extent analysis method (Chang, 1996CHANG, D.Y. Applications of the extent analysis method on fuzzy AHP. European Journal of Operational Research, v. 95, n. 3, p. 649655, 1996.) is used owing to its computational simplicity and effectiveness. The procedure of the FAHP approach is as follows (Bozbura et al., 2007; Beşikçi et al., 2016BEŞIKÇI, E.B.; KECECI, T.; ARSLAN, O.; TURAN, O. An application of fuzzyAHP to ship operational energy efficiency measures. Ocean Engineering, v. 121, p. 392402, 2016.):
Step 1: The value of fuzzy synthetic extent with respect to the ith object is calculated using the following equation, where shows a triangular fuzzy number related to the jth target.
To obtain , the fuzzy addition operation of m extent analysis values is performed using Equation (6).
The fuzzy addition operation of (j = 1,2,...,m) values is performed to obtain .
The inverse of the vector in Equation (8) is calculated using the following equation:
Step 2: The degree of possibility of 10 is defined as follows, where d is the ordinate of the highest intersection point between and (see Figure 2).
In order to compare M1 and M2 the values of V(M1≥ M2) and V(M2≥ M1) are required.
Step 3: The degree of possibility for a convex fuzzy number to be greater than k convex fuzzy numbers Mi(i = 1,2,…,k) can be defined as follows:
Assume that 13 for 14 . Then the weight vector is given by 15 where Ai (i = 1,2,...,n) are n elements.
Step 4: The normalized weight vector is obtained as below, where W is a nonfuzzy number.
Fuzzy Analytical Hierarchy Process Analysis
In this study, the FAHP method is used to determine the importance of some factors affecting the surface roughness of wood and woodbased materials in the planing process. The solution methodology adopted for this study is given in Figure 3.
A threelevel hierarchical model is devised to prioritize the factors. The research model is presented in Figure 4. As seen in this figure, the goal of the decisionmaking problem is placed at the highest level of the hierarchy. Moreover, there are four main factors at the second level and eighteen subfactors at the third level.
The main factors of this study are cutting tool properties (F1), machining parameters (F2), wood structure and properties (F3), and cutting phenomena (F4). The cutting tool properties factor includes three subfactors: tool geometry (F11), type of cutting tool material (F12), and tool sharpness (F13). The machining parameters factor consists of six subfactors: number of cutter (F21), cutting angle (F22), cutting depth (F23), feed speed (F24), cutting direction (F25), and cutting speed (F26). The wood structure and properties factor is composed of six subfactors: moisture content (F31), density (F32), hardness (F33), sapwoodheartwood (F34), material defect (F35), and ring width (F36). Finally, the cutting phenomena factor includes three subfactors: cutting force variation (F41), vibrations (F42), and chip shape and thickness (F43).
After creating the hierarchical structure, the factors used in this study are assigned weights by using the FAHP method. This method employs pairwise comparisons to determine the importance of each decision element (Işıklar and Büyüközkan, 2007). Therefore, a decisionmaking team consisting of wood science experts is constructed. The experts of this study are academicians who have at least 10 years’ experience on surface roughness.
A questionnaire is used to collect the data. The experts use the linguistic terms to make the pairwise comparisons of the factors. It is not possible to carry out arithmetical operations with the linguistic terms. Therefore, each linguistic term is associated with a triangular fuzzy number. The overall results are computed by taking the geometric mean of the individual evaluations. The final evaluation matrix of the main factors is given in Table 2. The calculation of the weights of the main factors will be explained below.
The values of fuzzy synthetic extents are calculated using Equation (5).
The values of Si are compared, and the degrees of possibility are calculated using Equation (11). Table 3 shows the values of V(SiS j).
The minimum of the degrees of possibility are found as follows:
The weight vector is obtained as W=(0.526, 1.000, 0.512, 0.000). After the normalization process, the weights of the cutting tool properties, machining parameters, wood structure and properties, and cutting phenomena factors are obtained as 0.258, 0.491, 0.251, and 0.000, respectively. The results obtained for the main factors are compatible with the results of Laina et al. (2017LAINA, R.; SANZLOBERA, A.; VILLASANTE, A.; LÓPEZESPÍ, P.; MARTÍNEZROJAS, J.A.; ALPUENTE, J.; SÁNCHEZMONTERO, R.; VIGNOTE, S. Effect of the anatomical structure, wood properties and machining conditions on surface roughness of wood. Maderas. Ciencia y tecnología, v. 19, n. 2, p. 203212, 2017.).
The same calculations are applied to the other matrices. The pairwise comparison matrices of the subfactors can be seen from Tables 47.
The weights of the factors are summarized in Table 8. The global weight of the subfactor can be computed by multiplying its local weight with its corresponding weight. The global weights calculated for the subfactors are presented in the last column of Table 8.
RESULTS AND DISCUSSION
In this study, the importance of each factor is determined by employing the FAHP method. The pairwise comparison matrices are obtained through experts’ opinions. Then the weights of the factors are calculated. The weights calculated for each factor are summarized in Table 8.
When the weights given in Table 8 are analyzed, it is observed that the highest weighted main factor is machining parameters (0.491). Therefore, machining parameters should be considered as the most significant main factor. The subfactor with the highest weight of this main factor is tool geometry (0.860). It is followed by tool sharpness with the weight of 0.140.
The second highest weighted main factor is cutting tool properties (0.258), and the highest weighted subfactors of this main factor are feed speed (0.611) and cutting speed (0.149). From Table 8, it is clear that feed speed (0.300) is the main factor that significantly influences the surface roughness of wood and woodbased materials in the planing process.
The third highest weighted main factor is wood structure and properties (0.251), and the highest weighted subfactors of this main factor are material defect (0.425), density (0.267), and moisture content (0.246). The lowest important degree is allocated to sapwoodheartwood (weight is 0.000).
The results presented in Table 8 show that the lowest weighted main factor is cutting phenomena (0.000). The ranking of the subfactors of this main factor in descending order with respective weights is chip shape and thickness (1.000) > cutting force variation (0.000) = vibrations (0.000). This ranking result shows that chip shape and thickness is the most important subfactor.
From the last column of Table 8, it can be concluded that feed speed, tool geometry, and material defect play an important role in enhancing the product quality. The wood industry should focus on the abovementioned factors to improve surface quality. Many researchers have investigated the influence of feed speed on surface roughness. The experimental results have showed that feed speed is the most dominating factor for surface roughness (De Deus et al., 2015; Stanojevic et al., 2017STANOJEVIC, D.; MANDIC, M.; DANON, G.; SVRZIC, S. Prediction of the surface roughness of wood for machining. Journal of Forestry Research , v. 28, n. 6, p. 12811283, 2017.; Hazir et al., 2018HAZIR, E.; ERDINLER, E.S.; KOC, K.H. Optimization of CNC cutting parameters using design of experiment (DOE) and desirability function. Journal of Forestry Research , v. 29, n. 5, p. 14231434, 2018.). Several researchers have stated that tool geometry has a large impact on the quality of the machined surface (Sinn et al., 2009SINN, G.; SANDAK, J.; RAMANANANTOANDRO, T. Properties of wood surfaces  characterization and measurement. A review. Holzforschung, v. 63, n. 2, p. 196203, 2009.; Öhman et al., 2016ÖHMAN, M.; GRUBÎI, V.; SANDBERG, D.; EKEVAD, M. Moistening of the wood surface before planing for improved surface quality. Wood Material Science & Engineering, v. 11, n. 3, p. 156163, 2016.). On the other hand, previous studies have noted that material defect is the subfactor that significantly influences surface roughness (Sütçü, 2013SÜTÇÜ, A. Investigation of parameters affecting surface roughness in CNC routing operation on wooden EGP. BioResources , v. 8, n. 1, p. 795805, 2013. ; Cetiner et al., 2016CETINER, I.; VAR, A.A.; CETINER, H. Classification of knot defect types using wavelets and KNN. Elektronika ir Elektrotechnika, v. 22, n. 6, p. 6772, 2016.). Consequently, it can be said that the results of this study are compatible with the literature.
The type of cutting tool material, cutting angle, cutting direction, sapwoodheartwood, cutting force variation, and vibrations are undoubtedly important factors. However, the obtained results indicate that the contribution of these subfactors to surface roughness is less than the other subfactors.
Wood is the basic raw material for the furniture industry. Machining is applied to wood materials to create different geometries and shapes. Surface defects due to a machining process reduce the quality of wood and woodbased products. Therefore, the analysis of factors affecting the surface roughness of wood and woodbased materials is very important. There are many studies about surface roughness. However, the use of the FAHP method to prioritize factors affecting the surface roughness of wood and woodbased materials in planing is a new concept.
The main contributions of the current study are twofold. First, the evaluation of factors influencing the surface roughness of wood and woodbased materials in planing is considered as a complex MCDM problem. Second, this study prioritizes the weights of these factors. The findings of this study are highly important from an industrial viewpoint. Consequently, it can be said that this study presents a route map for further studies on surface roughness.
CONCLUSION
The objective of this study is to prioritize some factors affecting the surface roughness of wood and woodbased materials in the planing process. Four main factors and eighteen subfactors are analyzed using the FAHP method. The data obtained from the experts are used in the prioritization model to determine the importance of the factors.
According to the prioritization model, the most significant subfactors are feed speed, tool geometry, and material defect. The wood industry should focus on these subfactors to achieve a high quality surface. Consequently, the results obtained in this study can provide a useful guide to the wood industry to improve the surface quality of wood and woodbased products. In further research, the findings of this study can be compared with the results of experimental studies.
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HIGHLIGHTS

Some factors influencing the surface roughness of wood and woodbased materials in the planing process are analyzed.

The FAHP method is proposed to determine the weights of the factors.

The most significant factors are feed speed, tool geometry, and material defect.

The findings of this study can be used in the wood industry to enhance product quality.
Publication Dates

Publication in this collection
17 June 2020 
Date of issue
JanMar 2020
History

Received
17 Aug 2019 
Accepted
11 Feb 2020