A FUZZY AHP AND ELECTRE METHOD FOR SELECTING STABILIZING DEVICE IN SHIP INDUSTRY UDC 629

Roll stabilizer systems are studied for different types of ships by many researchers. It is well known that roll motion is caused by external disturbances (wave,wind etc) and large roll motion can cause capsizing easily. In addition, undesirable roll motion effect badly crew performance and passenger comfort. So, roll reduction has an important role for all types of ships. In our study, we proposed a fuzzy AHP (Analytic Hierarchy Process) and ELECTRE (Elemination and Choice Translating Reality English) method for selecting the most effective roll stabilizing system for a trawler type fishing vessel. Alternatives and criteria in relation to the stabilizers are determined by experts’ experiences and literature review. This paper intends to give a comprehensive procedure for determining the most suitable roll motion stabilizing system of trawler for safety and efficiency fishing in the open literature.


Introduction
Although significant advances have been made in fishing vessel, fishing still remains a highly dangerous profession.One of the fundemental means by which the operation of fishing vessel can be improved is through reduction in the roll motion.Excessive roll not only increases fuel consumption but also makes working on deck hazardous, affecting the efficiency and safety of the crew.So, roll motion stabilizing devices are very crucial in severe sea states.Many types of roll stabilizers are suggested for different ships by researchers in literature.
Van Amerongen et al. [1] examined rudder roll stabilization system for ships.They revealed that the rudder shows an effective roll reduction in severe sea states.Fortuna and Muscato [2] proposed an automatic roll reduction system for a new monohull ship.They evaluated system performance with simulations and experimental tests.Gawad et al. [3] suggested anti-roll passive tanks for roll motion stabilization.Also, they emphasized both anti-roll tanks and fins can be used for more control in critical operations.Do et al. [4] examined the problem of universal control for underactuated surface ships.They used different method for stabilization.Jones et al. [5] developed a more generic anti-roll tanks for fishing vessels.They suggested two control strategies for stabilizing.Moaleji and Greig [6] A Fuzzy Ahp and Electre Method for Selecting Erkan Celik, Fuat Alarçin Stabilizing Device in Ship Industry 62 reviewed the development of ship anti-roll tanks.They discussed using of roll stabilization tanks on high speed multi-hull craft.Alarcin and Gulez [7] used a neural network (NN) controller for a fishing vessel rudder roll stabilizer system.Marzouk and Nayfeh [8] investigated the performance of passive and active anti-roll tank for a cargo ship in three different sea conditions.Su [9] reviewed the anti-rolling fin control system for ship stabilization.Alarcin et al. [10] suggested the fin roll stabilizer system for a fishing ship.Kula [11] evaluated operational efficiency of roll stabilizers and examined applicability of advanced control methods for stabilizers.Ayob and Yaakob [12] improved method for roll reduction and assessed performance of moving mass device in relation to stabilization.It is known that the purpose of roll stabilizer systems is to minimize the roll amplitudes of a ship.As can be understood from the above-mentioned studies, roll stabilizer systems for ships have been technically evaluated and the rate of reduction of the roll amplitudes has been the most important criterion.However, a technically successful roll stabilizer system may not always be feasible for a ship.Different criteria, such as the economic criterion, can create an obstacle to the selection of a stabilizer system for that ship.Therefore, in this study, considering the different criteria, the most suitable one among the four stabilizer systems for a trawler type fishing boat was determined by means of the fuzzy AHP and ELECTRE method considering the expert opinions on these criteria and alternatives.This paper aims to present and contribute a robust methodological approach utilising AHP and ELECTRE under fuzzy environment which is able to deal with uncertainty of experts' judgement and expression in decision-making.The proposed approach is capable of for selecting stabilizing device in ship industry.

Research methodology
This section initially describes theoretical background of methods used in proposed approach.Then, the section shows how proposed approach is constructed.

Fuzzy sets
Fuzzy logic, introduced in 1965 by Lotfi A. Zadeh [13], is robust tool to deal with the vagueness, ambiguity and uncertainty of human judgments and assessment in making decisions process.In real world decision making problems, many decisions involve imprecision since goals, constraints, and possible actions are not known precisely [13].Instead of combining various experiences, opinions, ideas, and motivations of an individual or group decision maker, it is better to convert the linguistic terms into fuzzy numbers.Therefore, the problems of group decision-making have necessary produced fuzzy numbers in practice.A triangular fuzzy number can be defined as a triplet  ̃= (, , )where l, m and u denotes lower, medium and upper numbers of the fuzzy which is crisp and real numbers ( ≤  ≤ ).In this context, Figure 1 shows a triangular fuzzy number.The membership function of a triangular fuzzy number can be defined as follows.
A For any two triangular fuzzy numbers ̃1 = ( 1 ,  1 ,  1 ) and  ̃2 = ( 2 ,  2 ,  2 ), the mathematical calculation of the two triangular fuzzy numbers can be defined as follows: The addition operation between the triangular fuzzy numbers; The subtraction operation between the triangular fuzzy numbers; The multiplication operation between the triangular fuzzy numbers; The arithmetic operation for the triangular fuzzy numbers; 2.2 Fuzzy AHP AHP is a general tool for comparing a number of criteria or alternatives according to the an complete goal in a consistent manner [14,15,16].Decision-makers generally reveal that it is more suitable to answer interval judgments than fixed-value judgements regarding to the vagueness and uncertainty from the subjective perception in the decision-making process [17,18].This is mostly because usually he/she is unable to specific about his/her perception because of the fuzzy nature of the comparison process [19].The assessment rate of linguistic data are measured with Triangular Fuzzy Numbers (TFNs) [20].A TFN can be shown as (l|m, A Fuzzy Ahp and Electre Method for Selecting Erkan Celik, Fuat Alarçin Stabilizing Device in Ship Industry 64 m|u) or (l, m, u).The parameters l, m and u, denote the smallest possible, the most promising, and the largest possible value that describes a fuzzy case, respectively.The membership function of the TFN can be specified as.
( ) Several methods have been proposed to address fuzzy comparison matrices.For example, Logarithmic Least Squares Method (LLSM) is proposed by Van Laarhoven and Pedrycz [21] to get triangular fuzzy weights from a triangular fuzzy comparison matrix.a modified fuzzy LLSM is presented by Wang et al. [22].Buckley [23] employs the geometric mean method to compute fuzzy weights.Chang [24] proposes an extent analysis method, which derives crisp weights for fuzzy comparison matrices.Xu [25] brings forward a fuzzy Least Squares priority Method (LSM).A fuzzy Preference Programming Method (PPM) is also proposed by Mikhailov [26].Lambda-Max method is proposed by Csutora and Buckley [27] which is the fuzzification of the kmax method.
We use Buckley's Fuzzy-AHP to find importance weights since it is simple to cover to the fuzzy case and assurances a sole solution to the reciprocal comparison matrix [28].It is rather easier than the other Fuzzy-AHP approaches.The steps of the applied Buckley's Fuzzy-AHP algorithm can be presented as follows [23,29]:

Linguistic variables Fuzzy numbers
Absolutely Strong (AS) (7,9,9) Very Strong (VS) (5,7,9) Fairly Strong (FS) (3,5,7) Slightly Strong (SS) (1,3,5) Equally (E) ( Step 1. Build pairwise comparison matrices among all the criteria.The linguistic variable is assigned according to the Equation (9).It is questioned which is the more important of each two criteria, such as: where, Step 2. Apply geometric mean to explain the fuzzy geometric mean as follows: ( ) where in a is fuzzy comparison value of criterion i to criterion n , thus, is geometric mean of fuzzy comparison value of criterion i to each criterion.Step 3. Compute the fuzzy weights of each criterion ( ) where i w is the fuzzy weight of the ith criterion, can be indicated by ( , , ) Here Step 4. Apply Center of Area (COA) method to learn the Best Nonfuzzy Performance (BNP) value of each criterion by the Equation (12).
According to the BNP value for each of the alternatives, the ranking of each alternative can then continue.

Fuzzy ELECTRE
ELECTRE method is first proposed by Benayoun et al. [30].A detailed comprehensive review of ELECTRE method is presented [31].They presented for four classification as applied papers; survey, review and overview papers; papers on MCDA method and model selection; preference disaggregation and theoretical and non-application papers application.Fuzzy sets might provide more flexibility to show the vague/imprecise information stemmin from the lack of information [32,33,34].Assume that there is a set X of alternatives, where Step 1.In a group decision environment, assume that a decision group has k decision makers, and the rating of alternatives according to each criterion can be calculated as: where the number of decision-makers.In this step, average operator is applied as aggregation operation.It is calculated the weight of each criterion by summing the assigned fuzzy sets by experts and then dividing the sum by the number of experts [35,36].Step 2. Construct the weighting matrix k W of the criteria of the kth decision-maker and build the average weighting matrix W, respectively, shown as follows: ( ) ( ) where   and k denotes the number of decision-makers.
Step 3. Given ( ) ,, ; the normalized performance rating for beneficial criterion can be calculated as: Where ,1 ,and 1 .
Vice versa the complementary subset named discordance set is a set of indicators that for each of them: , , , , Step 6. Compute the concordance fuzzy matrix.
Concordance fuzzy index is equal to the sum of fuzzy weights ( ) 1,2 Discordance fuzzy matrix for all pair wise comparisons of alternatives converts into a matrix with exact numbers which is: An effective and dominant alternative against the other alternatives is obtained with respect to the each element I in matrix F (effective concordance fuzzy matrix).
Step 9. Specify the effective discordance fuzzy matrix.

Elements
A Boolean matrix G (effective discordance matrix) is then built as: Dominance relations among alternatives is obtained to unit elements in matrix.

Common elements (
, kl h ) is obtained outranking matrix (H) for making decision from matrices F and G. , , , Step 11.Eliminate the less attractive alternatives.

The order of relative superiority of alternatives is presented by Outranking matrix (H). If
, x is superior to l x in terms of both concordance and discordance indices.
However, k x might be still dominated by other alternatives.Therefore, the condition which makes k x an effective alternative is as follows: In the cases where these two conditions are not simultaneously fulfilled, the effective alternatives from matrix (H) can be simply recognized.Then, we can exclude those columns of (H) which at least have a unit element (1) from matrix (H) because those columns are dominated by other row or rows.It is the threshold values of I and NI which are showed in steps 8 and 9 are approximate and used to enable generating a criterion to select the best alternative between all alternatives.As long as Eq. ( 30) is not true for any of the alternatives, we can increase I and reduce NI until the above condition is satisfied to come up with the best alternative.

Application
Roll stabilization systems have been the subject of scientific investigation for many years.It is well known that the rolling motion of a ship is an undesirable feature of its behaviour.The variety of stabilizers have been proposed and installed successfully for the elimination or moderation of ship roll.Recently, interest has centered on the stabilizer types, which is better suited to which type of ship.This paper undertakes a review of the whole field of stabilization devices and proposes selection procedure of the most suitable roll motion stabilization system for a trawler type fishing vessel.Looked at in this way, the four major stabilizers: activated fins, anti-rolling tanks, bilge keel, rudder roll stabilization devices are The hierarchical structure adopted in this study to deal with the problems of selection of the roll motion stabilizing system for a trawler type fishing vessel is shown in Fig 2.
The key dimensions of the criteria for evaluation and selection of the roll motion stabilizing system for a trawler type fishing vessel were derived through comprehensive investigation and consultation with five experts, including two professor in the department of Naval Architecture and Marine Engineering.They were asked to rate the accuracy, adequacy and relevance of the criteria and dimensions and to verify their ''content validity'' in terms of the stabilizer assessment.Twelve types of criteria of high priority come forth when these criteria are examined.Criteria are coded as i C where i is the number of relevant criteria as below in Table 3.When aforementioned criteria which differ from one another on the basis of basic characteristics are examined with the intention of categorizing, it appears that each has a relationship with different stabilizer systems.It is also known that critera in certain experts develop a relationship along with the ones in other experts.As far as factors for criteria are concerned, stabilizer systems in connection with the criteria can be grouped in Table 4 According to Table 5 the fuzzy linguistic variables of criteria are shown.In this step, the fuzzy importance weights of criteria are determined using fuzzy AHP.The importance of each criterion is evaluated by experts.The linguistic variables are convert to the fuzzy sets using Table 1 and the aggregated fuzzy pairwise comparison is presented in Table 6.Finally, the fuzzy weights of the each criterion are calculated and it is presented in Table 7.The concordance and discordance fuzzy sets are specified.The fuzzy concordance matrix is calculated and it is presented in Table 11.The fuzzy discordance matrix is calculated.Then, the fuzzy discordance matrix is defuzzified using center of area defuzzification method and the results are presented in Table 12.The effective concordance matrix is specified (Table 13).The effective discordance matrix is obtained (Table 14).Next, we construct the effective and outranking matrix presented in Table 15 by multiplying the effective concordance and discordance level matrices to disregard the effects of the Boolean matrices, separately.The less attractive alternatives are eliminated.
Table 14 The effective discordance level Table 15 The global matrix The decision graph for stabilizer system Finally, we construct the decision graph that is presented in Fig. 3.This decision graph which is derived from a great deal of imprecise data shows the preferable, incomparable or indifferent action.We obtain the priority sequence of stabilizer systems are as A3>A1 and A4.A1>A2 and there is no compare between A2 and A4 also A1 and A4 according to matrix H. Thus, it is clear that the most suitable stabilizer system A3 (Activated Fins).In this study, the most suitable stabilizer system is determined by considering twelve different criteria.Stabilizer systems are used in a wide variety of applications for many years.Recently, the field of stabilizing systems in shipping industry has received the attention of many researchers.It is essentially important the determining of effective stabilizer for ships that serving a specific area.As mentioned above, each area has its own specific requirements.This paper presents the selection procedures of the most effective roll stabilization system for trawler type fishing vessel.Tanks, bilge keels, activated fins and rudder roll stabilization system are examined taking into account their advantages and disadvantages for trawler.
In this study, all criteria determined for roll motion stabilizing systems of trawler are evaluated by experts' and literature review.
The fuzzy AHP and ELECTRE method is proposed to select the better effective roll motion stabilizing system for trawler ship industry.Since the proposed methodology has the ability of taking care of all kinds of evaluations from experts, it has been successfully applied to a stabilizer selection for trawler ship industry.In application case, four stabilizer system alternatives are compared for determining the most effective roll motion system of trawler ship industry.The ranking of these alternatives has been obtained as A3>A1 and A4.A1>A2 and there is no compare between A2 and A4 also A1 and A4.

FuzzyFig. 1
Fig. 1 Triangular fuzzy number i uw represent the lower, middle and upper values of the fuzzy weight of the ith criterion.

=
and assume that there are k decision-makers 12 , ,..., k D D D .Then, the steps of the proposed method are as given below.

Step 7 .
Calculate the discordance fuzzy matrix.Hakan Demirel, Abit Balin, A Fuzzy Ahp and Electre Method for Selecting Erkan Celik

Step 8 .A
have subsidiary relationship such that fuzzy matrix I is descriptive of the weights resulted from concordance indices, and asymmetrical matrix NI reflects the high relative difference of for each discordance indices.Specify the effective concordance fuzzy matrix.The values of indices , kl I of concordance fuzzy matrix should be compared against a threshold value so that the superiority chance of k x according to l x is better judged.In the case when , kl I exceeds from a minimum threshold I this chance increases.Also, we can compute the average of each arbitrary fuzzy index I from concordance fuzzy indices in the following manner: Boolean matrix F is constructed based upon minimum threshold I which has elements 0

Table 2
Linguistic variables for alternative ratings

,
kl NI from discordance matrix that is provided in Step 6 is assessed according to a threshold value.This threshold value ( NI ) is calculated with the following formula.

A
Fuzzy Ahp and Electre Method for Selecting Erkan Celik, Fuat Alarçin Stabilizing Device in Ship Industry 70 taken up one by one, evaluated and discussed in detail.Various criteria for determining the most suitable roll motion stabilizer for a trawler type of fishing vessel are compared.Stabilizers are classified and their relative merits discussed.The general approach developed in this paper is applied for a trawler type fishing vessel as an example.

Table 5
The pairwise comparisons of criteria

Table 6
The fuzzy weights of each criterion

Table 13
The effective concordance level