Scholarly article on topic 'Decision Making on an Optimal Port Choice under Z-information'

Decision Making on an Optimal Port Choice under Z-information Academic research paper on "Economics and business"

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{"discrete Z-number" / "port choice" / "expert opinion" / "partial reliability"}

Abstract of research paper on Economics and business, author of scientific article — Pınar Sharghi, Konul Jabbarova, Kamala Aliyeva

Abstract The decision of shipping lines as to which port to use is a strategic one, and it is one of the most crucial factors to influence the operational and business performance of the organizations. The existing decision theories are not sufficiently adequate to account for imprecision and partial reliability of decision-relevant information in real-world problems. Prof. Zadeh suggested the concept of a Z-number which is able to formalize imprecision and partial reliability of information. In this article, we consider a hierarchical multiattribute decision problem of an optimal port choice under Z-number-based information. The solution of the problem is based on the use of Z-number-valued weighted average aggregation operator. The obtained results show validity of the suggested approach.

Academic research paper on topic "Decision Making on an Optimal Port Choice under Z-information"

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Procedia Computer Science 102 (2016) 378 - 384

12th International Conference on Application of Fuzzy Systems and Soft Computing, ICAFS 2016, 29-30 August

2016, Vienna, Austria

Decision making on an optimal port choice under z-information

Pinar Sharghia, Konul Jabbarovab, Kamala Aliyevac*

aUniversity of Kyrenia, Department of Maritime Management, Kemal Pars Street no: 1, Kyrenia, North Cyprus

Abstract

Azerbaijan State University of Oil and Industry, Department of Computer-Engineering, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan Azerbaijan

c Azerbaijan State University of Oil and Industry, Department of Instrument-making Engineering, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan

The decision of shipping lines as to which port to use is a strategic one, and it is one of the most crucial factors to influence the operational and business performance of the organizations. The existing decision theories are not sufficiently adequate to account for imprecision and partial reliability of decision-relevant information in real-world problems. Prof. Zadeh suggested the concept of a Z-number which is able to formalize imprecision and partial reliability of information. In this article, we consider a hierarchical multiattribute decision problem of an optimal port choice under Z-number-based information. The solution of the problem is based on the use of Z-number-valued weighted average aggregation operator. The obtained results show validity of the suggested approach.

© 2016 The Authors. Published by ElsevierB.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the Organizing Committee of ICAFS 2016 Keywords: discrete Z-number, port choice, expert opinion, partial reliability

1. Introduction

Port selection decisions of shippers are crucial for policy formulation in ports and shipping lines1. Researches use a discrete choice model where each shipper faces a choice of 14 alternatives based on shipping line and port combinations, and makes his decision on the basis of various shipper and port characteristics. The results show that the distance of the shipper from port, distance to destination, port congestion and shipping line's the play an important role.

* Pinar Sharghi. Tel:00903926802028; E-mail address: pinar.sharghi@kyrenia.edu.tr

1877-0509 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the Organizing Committee of ICAFS 2016 doi:10.1016/j.procs.2016.09.415

Providers of port infrastructure and services are interested in finding out critical port choice factors as rational basis for formulating sustainable port reform policy. In Ref.2, questionnaires were distributed to collect data on observed port choice made by shippers under study. A discrete choice model was applied to estimate the shipper's port utility function. Policy implications of the estimated utility function are discussed.

In Ref. 3 fuzzy analytic network process and extended fuzzy VIKOR methodologies are used for solving the problem of cruise port place selection in Istanbul. Comparison of the obtained results is provided.

Analysis proposed in Ref. 4 is based on a survey conducted among major shipping lines operating in Singapore and Malaysia. The results show that port charges and wide range of port services are the only significant factors in port choice. However, the results show no consistency between the stated and revealed preferences of shipping lines.

In Ref. 5 appraisal of the container terminals or ports is implemented by using a fuzzy multicriteria decision making method. This model is illustrated with a numerical example.

In Ref. 6 five port intangible resources were identified. A survey questionnaire was sent to 21 experts. It was found that customer and relational resource contributes most to the delivery of port service quality. The port of Hong Kong appeared to be the port where intangible resources were most highly evaluated. This research helps to enrich the literature on port service quality and port choice evaluation.

In Ref. 7 they identify the factors affecting shipping companies' port choice based on a survey to a sample of shipping companies. Six factors were considered: local cargo volume; terminal handling charge; berth availability; port location; transshipment volume and feeder network. Exploratory factor and confirmatory factor analyses identified five port choice categories, i.e. advancement/convenience of port; physical/operational ability of port; operational condition of shipping lines; marketability; and port charge. Moreover, the main haul shipping lines are more sensitive to port cost factors.

The studies investigating the port selection process had one thing in common: they analyze the declared preferences of the port agents. In Ref. 8 it is suggested to study the port choice through revealed port selection instead of asking port stakeholders about the main factors in port selection.

In Ref. 9 they identified factors that affect port selection. They consider three ports: Antwerp, Rotterdam and Hamburg and three types of decision makers: shippers, carriers and freight forwarders. Also, it is discussed how port policymakers must continuously make an effort to understand what factors influence port users' port choice. The Analytical Hierarchy Process method was applied. The results show the following ranking of port selection criteria in decreasing order of importance: port costs, geographical location, quality of hinterland connections, productivity and capacity. Of the three ports studied, Antwerp was found to be the most attractive, followed by Rotterdam and then Hamburg.

Several authors have been invested decision making by use of fuzzy approach10-15. However, it is needed to mention that a port selection problem, as a real-world problem, is characterized by imprecise and partially reliable information. Unfortunately, this is not taken into account in the existing studies. In order to deal with imprecise and partially reliable information, Prof. Zadeh suggested the concept of a Z-number. A Z-number, is a pair of fuzzy numbers Z=(A,B), where A is a soft constraint on a value of a variable of interest, and B is a soft constraint on a value of a probability measure of A, playing a role of reliability of A. In this paper we consider multiattribute decision making on port selection under Z-number-valued information. All the criteria evaluations and criteria importance weights are described by Z-numbers.

The remainder of this paper is organized as follows. Section 2 introduces preliminary information such as operations over Z-numbers which are used in the sequel. In Section 4, an application of decision making on port selection under imprecise and partially reliable information is considered. The problem is solved by using aggregation of Z-number valued information on the basis of operations over Z-numbers. Section 5 the concludes the paper.

2. Preliminaries

Definition. A discrete Z-number13'14'16. A discrete Z-number is an ordered pair Z=(A,B) where A is a discrete fuzzy number playing a role of a fuzzy constraint on values of a random variable X : X is A . is a discrete fuzzy number with a membership function nB :{b1,n..,bn} ^ [0,1], {b1,...,bn} c [0,1], playing a role of a fuzzy

constraint on the probability measure of A : P(A) = X MA (xi)P(xi) is B .

Operations over Discrete Z-numbers: Let X, and Z2 = (A2,B2) be discrete Z-numbers describing information about values of X, andX2 . Consider computation ofZ12 = Zj * Z2,* e {+, -, ■,/} . The first stage is computation of A12 = A1* A2 13.

The second stage involves construction of B12 We realize that in Z-numbers Z1 andZ2 , the 'true' probability distributions p1 and p2 are not exactly known. In contrast, fuzzy restrictions represented in terms of the membership functions are available

Mp, (A) = Mb, (x,k)P1(x1k)j , (P2) = MB2 ^Z¿"a (x2k)P2(x2k)j .

Probability distributions p^(xjk),k = 1,..,n induce probabilistic uncertainty over X12 = X1 + X2 . Given any possible pair p11, p2l, the convolution p12s = pu ° p2l is computed as

p12s (x) = Z pu (x1)P2I (x2)' Vx 6 X12; x1 6 XU X2 6 X2 .

Xi + x-2 = x

Given p,25, the value of probability measure of A,2 is computed: P(A^) = Z ^a12 (x,2k )p,2s (x,2k ) .

However, p, and p2i are described by fuzzy restrictions which induce fuzZyJset of convolutions:

Ap,2( p,2) = max{ pj,p2:pj2 = pjo p2} min{Ap,( p,), Up2( p2)} (1)

Fuzziness of information on pj2s induces fuzziness of P(A12) as a discrete fuzzy number Bj2. The membership function pB is defined as

Mb12 (b12s ) = sup(^pj2l (p,2s )) (2)

subject to

b12s = Z p,2s (xk )Ma2 (xk )

As a result, Z12 = Z, * Z2 is obtained as Zj2 = (A2,Bj2) . A scalar multiplication Z ^Zj, ^ e R is a determined as Z = (AA,,B,) 13.

Ranking of Discrete Z-numbers. According to R.Aliev's approach13, Z-numbers are ordered pairs, for ranking of which there can be no unique approach. For purpose of comparison, the author suggests to consider a Z-number as a pair of values of two attributes - "one attribute measures value of a variable, the other one measures the associated reliability13. Then it will be adequate to compare Z-numbers as multiattribute alternatives. Basic principle of comparison of multi-attribute multi-criteria alternatives in this case is the Fuzzy Pareto optimality principle.

3. Decision Making on Port Selection under Z-number-valued Information

The literature review reveals a considerable range of factors that have an influence on the decision of port choice studies. The key influencing factors for port selection are identified in Refs. 17-21. After carefully examining the relevant literature, selected experts have determined the all possible evaluation criteria prior to port choice selection (Tablel). Each criterion and sub-criterion also has its importance weight.

Table 1 : Evaluation criteria Criteria & Sub-criteria

C1: HINTERLAND CONDITION

C2: PORT SERVICES

C3:LOGISTICS COST

C4:CONNECTIVITY

1. Professionals and skilled labors in port 1. Prompt response

operation

2. Size and activity of FTZ in port hinterland

3. Volume of total container cargo

C5:CONVENIENCE

1.Wather depth in approach channel and at berth

2. Sophistication level of port information & its application scope

3. Stability of Port's labour

2. 24hours/7 a week service

3. Zero waiting time

C6: AVAILABILITY

1.Availability of vessel berth on arrival in port

2. Port Congestion

1. Inland transportation cost

2. Cost related vessel and cargo entering

3. Free dwell time on the terminal

C7:REGIONAL CENTER

1.Port Accessibility

2.Deviation from main trunk routes

1. Land distance and connectivity to major supplier

2.Efficient inland transport network

Thus, we have seven criteria Cj, j -1,...,7 : hinterland condition, Q , port services, C2, logistics cost, C3 , connectivity, C4, convenience, C5, availability, C6, regional center, C7. Suppose that a decision maker should choose the best port by using the criteria and sub-criteria given in Table 1. The considered alternatives are: port of Busan, port of Tokyo, port of Hong Kong, port of Qingdao, port of Shanghai, port of Kaohsiung, port of Shenzhen22. Decision relevant information in the considered problems is characterized by imprecision and partial reliability. In view of this, criteria evaluations and importance weights are expressed by Z-numbers.

Codebooks of fuzzy numbers as A and B components of Z-numbers are shown in Table 2 and Table 3.

Table 2.The encoded linguistic terms for A components of Z-numbers

Scale Level

1. Very Low

2. Low

3. Medium

4. High

5. Very High

Linguistic value

Table 3.The encoded linguistic terms for B components of Z-numbers

Scale Level Linguistic value

1. Unlikely {/ V } (./ 0.05 / 0.05 / 0.25 )

2. Not very likely {0/ y y\ W 0.05 / 0.25 / 0.5 )

3. Likely {/ I 0.25 0.5 0.75

4. Very likely y y >0/} 1/0.5/0.75/1 )

5. Extremely likely y y y} 1/0.75/1 /1 )

Let us solve the considered problem of choosing the best alternative. At first we should compute overall evaluation of each port. Below we provide computation for the port of Hong Kong, computation for the other ports is analogous.

Step 1. Compute the Z-valued criteria evaluations Z^ for i-th alternative, i = 1,...,7 , with respect to j-th criterion, j = 1,...,7, by using weighted average-based aggregation of the corresponding sub-criteria evaluations.

The weighted average is based on operations over Z-numbers which are given in Section 2 and is expressed as follows:

у z ■ z

xyk wß

Z =-k-

where Zx is a Z-number-valued evaluation of z'-th alternative with respect to k-th sub-criterion of j-th criterion,

Zw is a Z-number-valued importance weight of k-th sub-criterion ofj-th criterion. The obtained results for the port of Hong Kong are as follows.

Y z • z

Lu x'!k w

Z _ k=1 x''k w'k _ (M, EL) ■ (H, EL) + (H, L) • (H, VL) + (VH, EL) ■ (H, EL)

(H, EL) + (H, VL) + (H, EL)

Lu w'k k=1

= ((1.7 4 8 (0.52 0.57 0.93));

Y Z • Z

¿—i x'2k

{VH, VL) • (M, L) + {VH, EL) ■ {VH, L) + {VH, VL) ■ (H, VL)

У'2 3

(M, L) + (VH, L) + (H ,VL)

= ((^.2 5 8.5 (0.96 0.99 1)) Y Z • Z

Lu x'3k

У'3 3

(L, L) • (M, L) + (M, NVL) • (H, VL) + (L, L) • (H, L) (M, L) + ( H ,VL) + ( H, L)

Z Z, k=1

= ((0.7 2.4 6 (0.5 0.7 0.8));

Z ;4k 'Zw4k = (M,NVL) •(M,L) + ( L,L) •(M,L) =((0.5 2.5 7.6) (0.4 0.6 0.7));

y'4 Y (M, L) + (M, L) u "

У Z • Z

Z _ T^X x'5k "5k _ (VH, VL) ■ (H, EL) + (H, L) • (M, VL) + (M, VL) ■ (H, VL) _ У5 " ^^ Z (H, EL) + (M, VL) + (H, VL)

Lu w5k k=1

= ((1.44 4 8.48) (0.65 0.71 0.72));

Z =S ;6k 'Zw6k = (H,EL)•(VH,EL) + (VH,EL)•(VH,VL) =((^36 4.5 6.23)(0.94 0.98 0.99)); У6 ^ (VH, EL) + (VH ,VL) u A ''

Lu w6k k=1

Z, =S^x'7k 'Zw7k = (M,L)•(M,L) + (L,L)•(L,L) =((0.45 2.6 11.6(0.44 0.77 0.8)).

Z7 z (M, L) + ( L)

Step 2. Compute the overall port evaluation Zy as the weighted average-based aggregation of the criteria evaluations Z , j = 1,...,7 obtained at Step 1:

IZ,•Z,

Z = -= ((0.89 3.9 9.5) (0.85 0.98 0.99)).

' lZWj

Analogously we computed the overall port evaluations Z y for all the other ports: ZByUsa" =((0.8 3.5 10.7 )(0.5 0.7 0.8)) ; ZSyha"ghal =((0.5 3.32 12.9) (0.48 0.81 0.82)) ; ZKyaohslU"g =((0.62 2.98 10.3) (0.48 0.7 0.72)) ;

ZyQmgdao =((00.7 3.5 13.4) (0.66 0.96 0.97 ));

ZyShenzhen = ((0.71 3.54 13.6) (0.4 0.6 0.7));

ZTyokyo =((00.48,3,10) (00.48 0.7 0.8)).

Step 3. Rank the obtained overall evaluations of the all seven ports. For this purpose we use the approach proposed in Ref. 13 and is given in Section 2. The obtained results are given below: Port Hong-Kong vs. Port of Busan:

do (ZHK ) = 1, do (ZByusan)= 0.08;

Port Hong-Kong vs. Port of Qingdao:

do (ZyHK ) = 1, do (ZQingdao) = 0.91;

Port Hong-Kong vs. Port of Tokyo:

do (ZyHK ) = 1, do (z^ ) = 0;

Port Hong-Kong vs. Port of Shanghai:

do (ZHK ) = 1, do (Zyhanghai ) = 0.26;

Port Hong-Kong vs. Port of Kaohsiung: do (ZyHK ) = 1, do (ZyKaohsiung ) = 0;

Port Hong-Kong vs. Port of Shenzhen: do (ZyHK ) = 1, do (ZShenzhen) = 0.23.

Thus, the port of Hong-Kong is the best port.

4. Conclusion

In this study we consider application of Z-number valued information processing to hierarchical multiattribute decision making on port selection under imprecise and partially reliable information. As a decision rule, the Z-valued weighted arithmetic mean based on operations over Z-numbers is used. For determination of the best port, a

fuzzy Pareto optimality principle based procedure for ranking of Z-numbers is applied. The results show validity of the proposed study on an optimal port choice by using Z-number valued information processing.

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