Operating system selection using fuzzy replacement analysis and analytic hierarchy process

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Int. J. Production Economics 97 (2005) 89–117 www.elsevier.com/locate/dsw

Operating system selection using fuzzy replacement analysis and analytic hierarchy process Ethem Tolgaa, Murat Levent Demircana,, Cengiz Kahramanb a Faculty of Engineering and Technology, Galatasaray University, 80840, I˙stanbul, Turkey Department of Industrial Engineering, Istanbul Technical University, Mac- ka 80680, I˙stanbul, Turkey

b

Received 29 July 2003; accepted 7 July 2004 Available online 2 October 2004

Abstract This study aims at creating an Operating System (OS) selection framework for decision makers (DMs). Since DMs have to consider both economic and non-economic aspects of technology selection, both factors have been considered in the developed framework. The economic part of the decision process has been developed by Fuzzy Replacement Analysis. Non-economic factors and financial figures have been combined using a fuzzy analytic hierarchy process (Fuzzy AHP) approach. Since there exists incomplete and vague information of future cash flows and the crisp AHP cannot reflect the human thinking style in capturing the expert’s knowledge, the fuzzy sets theory has been applied to both AHP and replacement analysis, which compares two OSs with and without license, respectively. A real numerical application has also been demonstrated. Both the theoretical and the practical background of this paper have shown that fuzzy AHP and fuzzy replacement analysis can cover the uncertainty of assigning crisp concepts in related investment decision-making topics. r 2004 Elsevier B.V. All rights reserved. Keywords: Fuzzy sets; Replacement analysis; AHP; Technology selection

1. Introduction The ultimate challenge of IT technologies pushes business professionals to a competitive environment. Enterprises, and even individuals, face technology replacement decisions more frequently as technology upgrades accelerate. Fleischer (1994) cites the reasons of replacement analysis in his milestone book as follows:




The existing asset can no longer satisfy current or anticipated needs. Corresponding author. Tel.:+90-212-227-4480X427; Fax: +90-212-259-5557.

E-mail address: [email protected] (M.L. Demircan). 0925-5273/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2004.07.001

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Technology upgrades are available. Improved assets are less expensive, can operate with less maintenance cost and are technologically more efficient. A major breakdown occurred. Existing asset can no longer operate.

Since the late 1950s there exist both theoretical and practical efforts in replacement analysis: Bellman (1955) based his replacement analysis study to conventional dynamic programming. Dreyfus (1960) built on the framework of Bellman’s seminal work (1955) and added a repair decision to the replacement analysis problem. Lake and Muhlemann (1979) developed a simulated replacement model for a particular wrapping machine in food industry in order to analyze the cost sensitivity according to changing resale figures. Their study argues that the weakness of the pure economic life models is that they ignore unpredicted situations before the end of economic life. Oakford et al. (1984) presented Dreyfus and Wagner’s (1972) dynamic replacement model on several numerical examples. They stated that computational advances permitted detailed sensitivity analysis on engineering economy issues, but they also expressed that the difficulty of forecasting functional relationships between cash flows of the defender and prospective challengers would well discourage the use of new economic decision approaches. Lohmann (1986) ameliorated the study of Oakford et al. (1984) with a stochastic approach. The study states the principal difference between deterministic and stochastic treatment of replacement problems. It argues that deterministic models can conclude the optimal sequence of future challengers to be installed after current optimal defender whereas stochastic models cannot. The study determines the probability that each prospective challenger is optimal for finite and infinite horizon and it determines the corresponding cumulative distributions of economic life, net present value and equivalent finite horizon time of each alternative, as well. Usher and Whitfield (1993) presented a model for estimating the total life cycle costs of each component in a used, multi-component system through the use of fuzzy set theory and linguistic variables. The economic and non-economic factors in a replacement analysis can be handled using AHP. AHP is a comprehensive approach to multi-criteria decision-making problems. Saaty and Vargas (2001) designed AHP to cope with both the rational and the intuitive to select the best from a number of alternatives evaluated with respect to several criteria. DMs carry out pairwise comparison judgments, which are used to develop overall priorities for ranking the alternatives. AHP involves the principles of decomposition, pairwise comparisons, and priority vector generation and synthesis. Fuzzy multiple attribute decision making (MADM) methods are proposed to solve problems which involve fuzzy data. Bellmann and Zadeh (1970) were the first to relate fuzzy set theory to decision-making problems. In 1977, Baas and Kwakernaak (1977) proposed a fuzzy MADM method that is widely regarded as the classic work of fuzzy MADM method. During the past 15 years, several fuzzy methods have been proposed. The only systematic reviews of fuzzy MADM methods have been conducted by Kickert (1978) and Zimmermann (1987a, b). Zimmermann (1987a), among others, treated the fuzzy MADM method as a two-phase process. The first phase requires finding the fuzzy utilities (fuzzy final ratings) of alternatives. The second phase requires applying fuzzy ranking methods to determine the ranking order of alternatives. There exist a total of 18 fuzzy MADM methods (e.g., ELECTRE, TOPSIS, outranking methods, data envelopment analysis). The classification is based on four categories: (1) their capability of solving largesize problems, (2) the type of data allowed, (3) the classical MADM method each fuzzy MADM method relates to, and (4) the technique each method uses. In this paper, we have chosen Saaty’s fuzzy AHP approach, which is one of the methods stated above. Saaty (1977, 1978) states that there are two types of fuzziness: fuzziness in perception and fuzziness in meaning. The first one is caused by complexity of objects or ideas which cannot be apprehended at once, and the second one is attributed to relativism of meaning, the meaning of objects is tied to what function those objects perform in the fulfillment of different purposes. When we decompose the objects, they appear fuzzy because they have different meanings according to the context of the decomposition. This method is proposed to give meaning to both kinds of fuzziness. It measures the relativity of fuzziness by structuring the functions of a system

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hierarchically in a multiple-attribute framework. Fuzzy AHP method does not directly use fuzzy numbers or membership functions to express fuzzy information. Rather, it uses the estimation of an underlying ratio scale, together with the measure of consistency to measure the fuzziness of a MADM problem. The algorithm provides a good way to represent fuzziness, which reveals the properties of consistency, stability and pareto optimality. There are many fuzzy AHP methods proposed by various authors. These methods are systematic approaches to the alternative selection and justification problem by using the concepts of fuzzy set theory and hierarchical structure analysis. The earliest work in fuzzy AHP appeared in van Laarhoven and Pedrycz (1983), which compared fuzzy ratios described by triangular membership functions. Buckley (1985) determined fuzzy priorities of comparison ratios whose membership functions are trapezoidal. Stam et al. (1996) explored how recently developed artificial intelligence techniques can be used to determine or approximate the preference ratings in AHP. They conclude that the feed-forward neural network formulation appears to be a powerful tool for analyzing discrete alternative multi-criteria decision problems with imprecise or fuzzy ratio-scale preference judgments. Chang (1996) introduced a new approach for handling fuzzy AHP, with the use of triangular fuzzy numbers for pairwise comparison scale of fuzzy AHP, and the use of the extent analysis method for the synthetic extent values of the pairwise comparisons. Ching-Hsue (1997) proposed a new algorithm for evaluating naval tactical missile systems by the fuzzy analytical hierarchy process based on grade value of membership function. Cheng et al. (1999) proposed a new method for evaluating weapon systems by analytical hierarchy process based on linguistic variable weight. Zhu et al. (1999) made a discussion on the extent analysis method and applications of fuzzy AHP. In this paper, the economic aspect of technology selection is analyzed using fuzzy replacement methodologies. Then both the financial and the non-economic aspect of technology selection are analyzed using a fuzzy AHP framework. This two-way analysis approach leads DMs to a selection environment where they can neither omit the importance of non-economic parameters nor underestimate the financial side of technologic alternatives. In the following section, a fuzzy replacement analysis is developed in order to prepare a framework. Section 3 develops the required equations for fuzzy equivalent uniform annual worth. Section 4 describes Chang’s (1992, 1996) fuzzy extent analysis. Section 5 is based on prior sections and demonstrates a numerical application.

2. Fuzzy set theory in replacement analysis Zadeh (1965) introduced the fuzzy set theory to deal with the uncertainty due to imprecision and vagueness. A major contribution of fuzzy set theory was its capability of representing vague data. The theory also allowed mathematical operators and programming to apply to the fuzzy domain. A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership function, which assigns to each object a grade of membership ranging between zero and one. Fig. 1 ~ Fuzzy set theory has also been applied to many demonstrates a triangular fuzzy number (TFN) P: engineering economic areas: Buckley (1987) developed fuzzy mathematics for compound interest problems. He determined the fuzzy present value and fuzzy future value of fuzzy cash amounts, using fuzzy interest rates. Chiu and Park (1994) developed comprehensive left and right side representation of fuzzy finance. Esogbue and Hearnes (1998) used triangular fuzzy numbers to model uncertainty in replacement decisions and compared the approach to Monte-Carlo simulation methods. Kahraman et al. (2002, 2003b) developed the fuzzy formulations of present value, equivalent uniform annual value, fuzzy future value, fuzzy benefit cost ratio, and fuzzy payback period techniques. Kahraman et al. (2000) and Kahraman (2001a, b) applied fuzzy present worth and fuzzy benefit/cost ratio analyses for the justification of manufacturing technologies and for public work projects. Karsak (1998) developed some measures of liquidity risk supplementing fuzzy discounted cash flow analysis. Boussabaine and Elhag (1999) examined the possible application of the fuzzy

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µ P~ (x ) µ P~ (x ) = 1, x = b 1

x−a µ P~ ( x ) = ,a < x < b b−a

µ P~ ( x ) =

c−x ,b < x < c c−b

α

µ P~ (x ) = 0, x ≥ c

µ P~ (x ) = 0, x ≤ a

x

0 a

b

c

P l(α) = (b + a )α + a P r(α) = (b − c ) α + c

~ Fig. 1. Left and right representation of a TFN, P:

set theory to the cash flow analysis in construction projects. Dimitrovski and Matos (2000) presented an approach to including non-statistical uncertainties in utility economic analysis by modeling uncertain variables with fuzzy numbers. Kuchta (2000) proposed fuzzy equivalents of all the classical capital budgeting methods. Recently, Chang (2004) has worked on replacement analysis with fuzzy approach for strategic purpose.

3. Fuzzy equivalent uniform annual worth The equivalent uniform annual worth (EUAW) means that all incomes and disbursements (irregular and uniform) must be converted into an equivalent uniform annual amount, which is the same each period. The major advantage of the method over all other methods is that it does not require making the comparison over the least common multiple of years when the alternatives have different lives (Blank and Tarquin, 1987). Kahraman et al. (2002), demonstrates the fuzzy EUAW as follows, where R is discount rate and T stands for period: EUAW ¼ A ¼ NPVg1 ðT; RÞ ¼ NPV 

ð1 þ RÞT R ; ð1 þ RÞT  1

ð1Þ

~ will be calculated and then the fuzzy where NPV is the net present value. In the case of fuzziness, NPV
~ A~ T Þ will be found. The membership function mðx
A~ T Þ for A~ T is determined by EUAWð


~ Þg1 ðT; f i ða
R~ ÞÞ; ð2Þ f T i ða
A~ T Þ ¼ f i ða
NPV where R~ represents fuzzy discount rate. TFN(a) for fuzzy EUAW is   NPVlðaÞ NPVrðaÞ ~ ; : AT ðaÞ ¼ gðT; RlðaÞ Þ gðT; RrðaÞ Þ

ð3Þ

Not slightly different from Kahraman et al. (2002), we have developed fuzzy replacement framework with another EUAW computation using TFNs. First, replacement analysis parameters have been defined: Let R~ be a fuzzy discount rate and T represents period. The fuzzy capital recovery factor is developed as follows; ~  ~ T RlðaÞ  ð1 þ RlðaÞ ÞT RrðaÞ  ð1 þ RrðaÞ ÞT  R~  ð1 RÞ A ~ ¼ ; : ð4Þ ; R; T ¼ ~ T 1 ð1 þ RrðaÞ ÞT  1 ð1 þ RlðaÞ ÞT  1 ð1 RÞ P~

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Let I~ be fuzzy initial investment, S~ T be fuzzy salvage value at period T. C~ T represents fuzzy capital recovery. Please note that, I~ will be considered as crisp in the numerical application, it is the initial investment and does not include fuzziness. Besides, S~ T will be considered as none for each period since there exists no Operating System (OS) salvage value. ~       A ~ rðaÞ ~ ~ ~ C T ¼ I ST  ; ð5Þ ; R; T R~  S~ T ¼ C lðaÞ T ; CT ~ P  lðaÞ lðaÞ ðI  SlðaÞ  ð1 þ RlðaÞ ÞT T ÞR ~ þ ðRlðaÞ  S lðaÞ CT ¼ T Þ; rðaÞ T ð1 þ R Þ  1  rðaÞ ðI rðaÞ  S rðaÞ  ð1 þ RrðaÞ ÞT rðaÞ rðaÞ T ÞR þ ðR  ST Þ : ð1 þ RlðaÞ ÞT  1

ð6Þ

P Let F~ T be the fuzzy operating and maintenance cost for period T. Whilst P~ T represents cumulative fuzzy present value of F~ T ’s, from t=1 to t=T: " # T T T lðaÞ rðaÞ X X X ~t  lðaÞ rðaÞ X F F F t t P~ T ¼ PT ; PT ¼ ¼ ; ð7Þ  t : rðaÞ t ~ t Þ t¼1 1 þ RlðaÞ t¼1 ð1 RÞ t¼1 ð1 þ R P  Let A~ P~ T be the EUAW of cumulative fuzzy present value of F~ T ’s over T period(s).  X  X  A~ ~ ~ ~ ~ A PT ¼ PT  ; R; T P~ " # lðaÞ rðaÞ rðaÞ T PlðaÞ  ð1 þ RlðaÞ ÞT PrðaÞ  R  ð1 þ R Þ T R ¼ ; T  : T ð1 þ RrðaÞ ÞT  1 1 þ RlðaÞ  1 ~ T be the total EAUW. Fig. 2 illustrates Eq. (9). Let W X   ~ T ¼ C~ T A~ W P~ T ¼ W lðaÞ ; W rðaÞ ¼ ððW T Þ1 ; ðW T Þ2 ; ðW T Þ3 Þ: T

ð9Þ

T

µW~T(α) 1

α

x

0

(W T)1

(W T)2

~ T: Fig. 2. Total fuzzy EUAW, W

(W T)3

ð8Þ

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4. Fuzzy analytic hierarchy process Though the purpose of AHP is to capture the expert’s knowledge, the conventional AHP cannot reflect the human thinking style. Therefore, fuzzy AHP and fuzzy extensions of AHP are developed to solve hierarchical fuzzy problems. Saaty (1978) proposed a method to give meaning to both fuzziness in perception and fuzziness in meaning. This method measures the relativity of fuzziness by structuring the functions of a system hierarchically in a multiple attribute framework. Buckley (1985) extended Saaty’s AHP method in which DMs can express their preference in fuzzy ratios instead of crisp values. The van Laarhoven and Pedrycz (1983)’s study used fuzzy scores for alternatives as well as sensitivities. Chang (1992) developed a fuzzy extent analysis for AHP which was relatively easier in computation than the other fuzzy AHP approaches and had similar steps of Saaty’s crisp AHP. Kahraman et al. (2003a, c) and Bozdag˘ et al. (2003) used Chan’s (1992) extent analysis for the selection of the best catering firm, the best facility location, and the best computer-integrated manufacturing system,   respectively. Let X ¼ fx1 ; x2 ; :::; xn g be an object set, and G ¼ g1 ; g2 ; :::; gm be a goal set. According to the method of Chang’s extent analysis, each object is taken and extent analysis for each goal performed respectively. Therefore, m extent analysis values for each object can be obtained, with the following signs: M 1gi ; M 2gi ; . . . ; M mgi ; i ¼ 1; 2; . . . ; n; where M jgi ðj ¼ 1; 2; . . . ; mÞ all are TFNs. The steps of Chang’s extent analysis can be given as in the following: Step 1: The value of fuzzy synthetic extent with respect to the ith object is defined as " #1 m n X m X X j j Si ¼ M gi  M gi : j¼1

i¼1

ð10Þ

j¼1

As it is known, the multiplication of two TFNs does not result in a TFN. In this step of the extent analysis, two TFNs are multiplied as in Eq. (10). The result will not be a TFN. However, in this paper, it will be assumed that Pmthe non-linear combination of TFNs approximates to a TFN as it is in Fig. 3 (Chang, 1996). To obtain j¼1 M jgi ; perform the fuzzy addition operation of m extent analysis values for a particular matrix such that ! m m m m X X X X j M gi ¼ lj ; mj ; uj ð11Þ j¼i

j¼1

j¼1

j¼1

µ M~

~ M2

~ M1

1

D

V (M 2 ≥ M 1 )

M

0 l2

m2 l1

d

u2 m1

~ 1 and M ~ 2: Fig. 3. The intersection between M

u1

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and to obtain such that n X m X i¼1

j¼i

hP P n n i1

j gi

M ¼

i¼1

n X

M jgi

li ;

i1

n X

i¼1

; perform the fuzzy addition operation of M jgi ðj ¼ 1; 2; :::; mÞ values

mi ;

n X

i¼1

! ui

ð12Þ

i¼1

and then compute the inverse of the vector above, such that 0 1 " #1 n X m X B 1 1 1 C C; where 8ui ; mi ; l i 40: M jgi ¼B ;P ;P n n n @P A i¼1 j¼1 ui mi li i¼1

95

i¼1

ð13Þ

i¼1

Step 2: The degree of possibility of M 2 ¼ ðl 2 ; m2 ; u2 Þ  M 1 ¼ ðl 1 ; m1 ; u1 Þ is defined as j k V ðM 2 XM 1 Þ ¼ sup minðmM 1 ðxÞ; mM 2 ðyÞÞ

ð14Þ

yXx

and can be equivalently expressed as follows: V ðM 2 XM 1 Þ ¼ hgtðM 1 \ M 2 Þ 8 1 > > < ¼ mM 2 ðdÞ ¼ 0 > > :

l 1 u2 ðm2 u2 Þðm1 l 1 Þ

if m2 Xm1 ; if l 1 Xu2 ;

ð15Þ

otherwise:

Fig. 3 illustrates Eq. (15) where d is the ordinate of the highest intersection point D between mM 1 and mM 2 : To compare M1 and M2, we need both the values of V ðM 1 XM 2 Þ and V ðM 2 XM 1 Þ: Step 3: The degree possibility for a convex fuzzy number to be greater than k convex fuzzy numbers M i ði ¼ 1; 2; . . . ; kÞ can be defined by V ðMXM 1 ; M 2 ; . . . ; M k Þ ¼ V ½ðMXM 1 Þ\ðM  M 2 Þ \ ::: \ ðM  M k Þ ¼ min V ðMXM i Þ;

i ¼ 1; 2; :::; k:

ð16Þ

Assume that dðAi Þ ¼ min V ðS i XS k Þ

ð17Þ

for k ¼ 1; 2; :::; n; kai: Then the weight vector is given by W 0 ¼ ðd 0 ðA1 Þ; d 0 ðA2 Þ; :::; d 0 ðAn ÞÞT

ð18Þ

where Ai ði ¼ 1; 2; :::; nÞ are n elements. Step 4: Via normalization, the normalized weight vectors are W ¼ ðdðA1 Þ; dðA2 Þ; :::; dðAn ÞÞT where W is a non-fuzzy number.

ð19Þ

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5. A numerical application of OS selection with fuzzy replacement analysis and fuzzy AHP 5.1. Application of fuzzy EUAW analysis In IT-related replacement decisions, technological and financial reasons become the leading factors. In most technology selection studies, the cost comparison parameter has been cited as one of other parameters without regarding its crucial role in DMs’ choice. In this application of fuzzy replacement analysis, two OSs, AX and BS will be evaluated by using fuzzy AHP and fuzzy EUAW analysis. In the following, first OS features and then the financial assessment of OS will be given. Migration issues in enterprise computing are becoming more compelling for companies. Firms want to experience benefits from server consolidation as well as IT staff reduction. In order to assess the financial aspect of enterprise computing migration, total cost of ownership (TCO) of both defender and challenger(s) should be determined. TCO is the cost figure over time taking into account the costs of acquiring and supporting the hardware and software required for each system workloads. System workloads are the group of related tasks and services of an OS. These workloads are Networking, File Server, Print Server, Web Server and Security Applications. Network workload provides the mere infrastructure services. It includes Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), Windows Internet Naming Service, Internet Connection Sharing, Remote Access Connection Manager (RACM), directory and caching services, and traditional services such as routers, hubs or switches. File Server workload includes File Transfer Protocol (FTP), Network File System (NFS), and Common Internet File System (CIFS). Print Server workload covers all print stream protocols as well as Internet Printing Protocol and Line Printer Daemon services. Web Server workload includes all internet, intranet and extranet services which deliver both static and dynamic Web pages. Security workload covers Virtual Private Networking (VPN), intrusion detection services, antivirus management services, authentication, access, and authorization services. Each workload has hardware- and software- related costs, which comprise the TCO. Costs include Hardware, Storage, Networking, Facilities, Software (OS), Software (Applications), Downtime, IT Staffing, IT Staff Training, and Outsourcing costs. Hardware, Storage and Facility costs include the purchase of specified physical equipment. Software costs covers acquisition and deployment of specified software. Since challenger(s) may benefit major CPUbased savings by server consolidation, Software costs need to be subcategorized as CPU Licensed and User Licensed. Downtime costs are the costs needed to repair, fix, or reconfigure the malfunctioning computing services. Platform selected and the knowledge and experience level of IT Staff Play an important role over downtime costs. IT Staff Training costs are both training expenditures and productivity loss for time spent in training. Support and maintenance are outsourced services, which generate a considerable cost. For ease of following and understanding the relation between the elements of TCO, Cost Breakdown Structure is given in Table 1. For ease of computation each workload and its software- and hardware- based costs are combined in periodic disbursements (operating costs). We defined OS alternative AX as open source and license free. Table 1 Cost Breakdown Structure (representing the elements of TCO) Total system cost Hardware

Storage

Networking

Facilities

Software (OS)

Software (application)

Downtime

IT Staffing

IT Staff Training

Outsourcing

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Table 2 Initial investment and fuzzy operating and maintenance costs of alternatives AX and BS Period

Fuzzy CFs of AX

0 1 2 3 4 5 6

($10,000; ($24,000; ($24,500; ($25,500; ($27,500; ($30,500; ($34,500;

$10,000; $26,000; $26,500; $27,500; $29,500; $32,500; $36,500;

1

2

0

Fuzzy CFs of BS $10,000) $28,000) $28,500) $29,500) $31,500) $34,500) $38,500)

3

($30,000; $30,000; $30,000) ($8,000; $10,000; $12,000) ($7,000; $9,000; $11,000) ($6,000; $8,000; $10,000) ($5,000; $7,000; $9,000) ($4,000; $6,000; $8,000) ($3,000; $5,000; $7,000)

4

5

6

Fig. 4. Descending fuzzy cash flows of BS.

0

1

2

3

4

5

6

Fig. 5. Ascending fuzzy cash flows of AX.

In addition, BS is a licensed OS platform, which requires higher initial investment than AX. Table 2 shows the fuzzy initial investment and operating costs. BS’s operating costs will decrease over time since staff knowledge threshold will increase due to BS’s GUI capabilities and Support Availability (Fig. 4). While AX represents lower initial investment, we assume that it requires higher expertise to operate. Therefore, IT Staffing, IT Staff Training and Outsourcing costs will increase over time (Fig. 5). To apply a fuzzy replacement analysis to financial figures above, fuzzy discount rate R~ is set as R~ ¼ ð3%; 4%; and 5%Þ: Figs. 6–9 illustrate the fuzzy EUAW of capital recovery and operating and maintenance costs. Figs. 10 and 11 illustrate the total fuzzy EUAWs. For Figs. 7–11, please refer to Appendix B. When comparing the fuzzy EUAWs of AX’s and BS’s total costs, a DM may give moderate importance in favor of BS.

ARTICLE IN PRESS E. Tolga et al. / Int. J. Production Economics 97 (2005) 89–117 Fuzzy EUA Costs over Periods

Period

$5’000

$10’000

$15’000

$20’000

98

1

2

3

4

5

6

Fig. 6. Fuzzy EUAW of AX’s capital recovery costs.

5.2. Operating system features In order to meet enterprise computing needs, an OS should ensure tasks and service management features. Tanenbaum (1987) and Galvin (1994) categorized these features as follows: Process Management, Storage Management, Protection and Security, Distributed Structure and Software Features. Fig. 12 shows the hierarchy of OS selection problem. Sub-categories can be developed for each feature in order to analyze them in detail: (1) Storage Management (C1): (a) Memory Management (C11): Every memory address generated by the CPU must be checked for legality and possibly mapped to a physical address. (b) Virtual Memory (C12): Virtual memory is a technique that allows the execution of processes that may not be completely in memory. Virtual memory is not easy to implement, however, and may substantially decrease performance if it is used carelessly. (c) File System Interface (C13): File System provides the mechanism for online storage of and access to both data and programs belonging to the OS and all the users of the computer system. (d) File System Implementation (C14): The file system resides permanently on secondary storage, which has the main requirement that it must be able to hold a large amount of data, permanently. (e) Secondary Storage Structure (C15): Disk systems are the major secondary storage I/O device on most computers. Requests for disk I/O are generated both by the file system and by virtual memory systems. (2) Process Management (C2): A process can be thought of as a program in execution. A process will need certain resources, such as CPU time, memory, files and I/O devices, to accomplish its task. (a) Process Handling (C21): OS allow multiple programs to be loaded into memory and to be executed concurrently. This requires firmer control and more compartmentalization of the various programs. (b) CPU Scheduling (C22): CPU scheduling is the basis of multi-programmed OSs. By switching the CPU among processes, the OS can make the computer more productive.

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Fig. 12. The hierarchy of OS selection.

(3)

(4)

(5)

(6)

(c) Process Synchronization (C23): Given a collection of cooperating sequential processes that share data, mutual exclusion must be provided. (d) Deadlocks (C24): In a multi-programming environment, several processes may compete for a finite number of resources. A process requests resources, if the resources are not available at that time, the process enters a wait state. It may happen that waiting processes will never again change state, because the resources they have requested are held by other waiting processes. This situation is called deadlock. Protection and Security (C3): Protection mechanisms provide controlled access by limiting the types of file access that can be made by the various users. (a) Protection (C31). (b) Security (C32). Distributed Structure (C4): A distributed system is a collection of processors that do not share memory or a clock. (a) Network Structures (C41). (b) Distributed System Structures (C42). (c) Distributed File Systems (C43). (d) Distributed Coordination (C44). Software Features (C5). (a) Applications and Tools (C51). (b) Bugs and Coding (C52). (c) Graphical User Interface (C53). (d) Availability and Support (C54). Financial Figures (C6). (a) Fuzzy EUAW (C61).

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5.3. Application of fuzzy AHP for OS selection To make a pairwise comparison among the parameters to create a priority matrix a relative importance scale has been developed. Fig. 13 and Table 3 shows this scale graphically and with explanations respectively. To create the Pairwise Comparison Matrix of the first level, 35 software developers and 18 Information Technology department managers have been interviewed. For interview questions please refer to Appendix A. By computing the average of test subjects’ responses, the Pairwise Comparison Matrix has been obtained (Table 4). From Table 4, SC1=(2.87, SC2=(3.50, SC3=(5.00, SC4=(4.50, SC5=(3.67, SC6=(5.00,

3.67, 5.00, 6.50, 6.00, 5.17, 7.00,

5.33) 6.50) 8.00) 9.50) 8.00) 9.00)

(0.02, (0.02, (0.02, (0.02, (0.02, (0.02,

0.03, 0.03, 0.03, 0.03, 0.03, 0.03,

0.04)=(0.06, 0.04)=(0.08, 0.04)=(0.11, 0.04)=(0.10, 0.04)=(0.08, 0.04)=(0.11,

0.11, 0.15, 0.20, 0.18, 0.16, 0.21,

0.22) 0.26) 0.33) 0.39) 0.33) 0.37)

are obtained. Using these vectors, V ðS C1 XSC2 Þ ¼ 1:00;

V ðS C1 XS C3 Þ ¼ 1:00;

V ðS C1 XS C4 Þ ¼ 1:00;

V ðS C1 XS C5 Þ ¼ 1:00;

V ðS C1 XSC6 Þ ¼ 1:00; V ðS C2 XSC5 Þ ¼ 1:00;

V ðS C2 XS C1 Þ ¼ 0:78; V ðS C2 XS C6 Þ ¼ 1:00;

V ðS C2 XS C3 Þ ¼ 1:00; V ðS C3 XS C1 Þ ¼ 0:56;

V ðS C2 XS C4 Þ ¼ 1:00; V ðS C3 XS C2 Þ ¼ 0:78;

V ðS C3 XSC4 Þ ¼ 0:95; V ðS C4 XSC2 Þ ¼ 0:85;

V ðS C3 XS C5 Þ ¼ 0:85; V ðS C4 XS C3 Þ ¼ 1:00;

V ðS C3 XS C6 Þ ¼ 1:00; V ðS C4 XS C5 Þ ¼ 0:90;

V ðS C4 XS C1 Þ ¼ 0:63; V ðS C4 XS C6 Þ ¼ 1:00;

V ðS C5 XSC1 Þ ¼ 0:75;

V ðS C5 XS C2 Þ ¼ 0:97;

V ðS C5 XS C3 Þ ¼ 1:00;

V ðS C5 XS C4 Þ ¼ 1:00;

V ðS C5 XSC6 Þ ¼ 1:0; V ðS C6 XSC4 Þ ¼ 0:90;

V ðS C6 XS C1 Þ ¼ 0:52; V ðS C6 XS C5 Þ ¼ 0:80;

V ðS C6 XS C2 Þ ¼ 0:72;

V ðS C6 XS C3 Þ ¼ 0:94;

are obtained. Thus, the weight vector from Table 4 is calculated as WG=(0.24, 0.18, 0.13, 0.15, 0.18, 0.12)T. The decision-making group now compares the sub-attributes with respect to main attributes. First, they compare the sub attributes of Storage Management. Table 5 gives the fuzzy comparison data of the sub attributes of Storage Management.

µ(x) MI

SI

VSI

DI

1

α

x

0 ½

1

3/2

2

5/2

Fig. 13. Triangular fuzzy importance scale.

3

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Table 3 Triangular fuzzy importance scale Linguistic scale

Explanation

Triangular fuzzy scale

Triangular fuzzy reciprocal scale

Equal importance (EI)

Two activities contribute equally to the objective Experience and judgment slightly favor one activity over another Experience and judgment strongly favor one activity over another An activity is favored very strongly over another; its dominance demonstrated in practice The evidence favoring one activity over another is the highest possible order of affirmation

(1, 1, 1)

(1, 1, 1)

(1/2, 1, 3/2)

(2/3, 1, 2)

(1, 3/2, 2)

(1/2, 2/3, 1)

(3/2, 2, 5/2)

(2/5, 1/2, 2/3)

(2, 5/2, 3)

(1/3, 2/5, 1/2)

Moderate importance (MI) Strong importance (SI) Very strong importance (VSI)

Demonstrated importance (DI)

Table 4 The fuzzy evaluation matrix with respect to the goal

C1 C2 C3 C4 C5 C6

C1

C2

C3

C4

C5

C6

(1,1,1) (1/2,1,3/2) (3/2,2,5/2) (3/2,2,5/2) (1,3/2,5/2) (3/2,2,5/2)

(2/3,1,2) (1,1,1) (1,1,1) (2/3,1,2) (2/3,1,2) (1,1,1)

(2/5,1/2,2/3) (1,1,1) (1,1,1) (2/3,1,2) (1/2,2/3,1) (1,3/2,2)

(2/5,1/2,2/3) (1/2,1,3/2) (1/2,1,3/2) (1,1,1) (1/2,1,3/2) (1,3/2,2)

(1/2,2/3,1) (1/2,1,3/2) (1,3/2,2) (2/3,1,2) (1,1,1) (1/2,1,3/2)

(2/5,1/2,2/3) (1,1,1) (1/2,2/3,1) (1/2,2/3,1) (2/3,1,2) (1,1,1)

Table 5 Evaluation of the sub-attributes with respect to Storage Management

C11 C12 C13 C14 C15

C11

C12

C13

C14

C15

(1,1,1) (1/2,1,3/2) (2/3,1,2) (2/3,1,2) (2/3,1,2)

(2/3,1,2) (1,1,1) (1/2,2/3,1) (1/2,2/3,1) (2/3,1,2)

(1/2,1,3/2) (1,3/2,2) (1,1,1) (1,1,1) (1/2,1,3/2)

(1/2,1,3/2) (1,3/2,2) (1,1,1) (1,1,1) (1,3/2,2)

(1/2,1,3/2) (1/2,1,3/2) (2/3,1,2) (1/2,2/3,1) (1,1,1)

From Table 5, S C11 ¼ ð0:09; 0:20; 0:41Þ;

SC12 ¼ ð0:11; 0:24; 0:43Þ;

SC13 ¼ ð0:10; 0:18; 0:38Þ;

SC14 ¼ ð0:10; 0:17; 0:32Þ;

S C15 ¼ ð0:10; 0:22; 0:46Þ; V ðS C11 XSC15 Þ ¼ 1:00;

V ðSC11 XS C12 Þ ¼ 1:00; V ðSC12 XS C11 Þ ¼ 0:88;

V ðSC11 XS C13 Þ ¼ 0:96; V ðSC12 XS C13 Þ ¼ 0:84;

V ðSC11 XS C14 Þ ¼ 0:90; V ðSC12 XS C14 Þ ¼ 0:77;

V ðS C12 XSC15 Þ ¼ 0:95;

V ðSC13 XS C11 Þ ¼ 1:00;

V ðSC13 XS C12 Þ ¼ 1:00;

V ðSC13 XS C14 Þ ¼ 0:94;

V ðS C13 XSC15 Þ ¼ 1:00; V ðS C14 XSC15 Þ ¼ 1:00;

V ðSC14 XS C11 Þ ¼ 1:00; V ðSC15 XS C11 Þ ¼ 0:94;

V ðSC14 XS C12 Þ ¼ 1:00; V ðSC15 XS C12 Þ ¼ 1:00;

V ðSC14 XS C13 Þ ¼ 1:00; V ðSC15 XS C13 Þ ¼ 0:89;

V ðS C15 XSC14 Þ ¼ 0:83

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are obtained and the weight factor from Table 5 is calculated as WC1=(0.20, 0.17, 0.21, 0.23, 0.19)T. The other matrices of pairwise comparisons and the weight vector of each matrix (Tables 6–34) are given in Appendix C. Main attributes of the goal table is given in Table 35 (Appendix C). 6. Conclusion OSs are the core components of IT systems. Because traditional engineering economic models do not take care of the inherent strategic benefits of OSs, a multi-attribute decision-making method should be used to justify them. In order to achieve an optimum decision, business professionals should consider both the performance features and cost figures of each OS alternative. This study developed a fuzzy AHP framework to select the best OS alternative. While fuzzy AHP requires cumbersome computations, it is a more systematic method than the others, and it is more capable of capturing a human’s appraisal of ambiguity when complex multi-attribute decision-making problems are considered. This is true because pairwise comparisons provide a flexible and realistic way to accommodate real-life data. The financial side of the framework is based on fuzzy replacement analysis. The results of fuzzy replacement analysis are included into fuzzy AHP analysis. Using fuzzy AHP concept in replacement analysis investment decisions in fuzzy environment results a very effective way to evaluate alternatives. Using the very same developed framework, a subjective comparison, such as the comparison of diverse operating systems, has been conducted and demonstrated to readers. For further research, the authors suggest the other multi-attribute approaches such as fuzzy TOPSIS and fuzzy outranking methods to be used with fuzzy replacement analysis for OS selection. Appendix A Questionnaire Read the following questions and put check marks on the pairwise comparison matrices. If an attribute on the left is more important than the one matching on the right, put your check mark to the left of the importance ‘‘Equal’’ under the importance level you prefer. If an attribute on the left is less important than the one matching on the right, put your check mark to the right of the importance ‘‘Equal’’ under the importance level you prefer.

QUESTIONS With respect to the overall goal ‘‘selection of the best Operating System’’, Q1. How important is Storage Management (C1) when it is compared with Process Management (C2)? Q2. How important is Storage Management (C1) when it is compared with Protection and Security (C3)? Q3. How important is Storage Management (C1) when it is compared with Distributed Structure (C4)? Q4. How important is Storage Management (C1) when it is compared with Software Features (C5)? Q5. How important is Storage Management (C1) when it is compared with Financial Figures (C6)? Q6. How important is Process Management (C2) when it is compared with Protection and Security (C3)?

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Q7. How important is Process Management (C2) when it is compared with Distributed Structure (C4)? Q8. How important is Process Management (C2) when it is compared with Software Features (C5)? Q9. How important is Process Management (C2) when it is compared with Financial Figures (C6)? Q10. How important is Protection and Security (C3) when it is compared with Distributed Structure (C4)? Q11. How important is Protection and Security (C3) when it is compared with Software Features (C5)? Q12. How important is Protection and Security (C3) when it is compared with Financial Figures (C6)? Q13. How important is Distributed Structure (C4) when it is compared with Software Features (C5)? Q14. How important is Distributed Structure (C4) when it is compared with Financial Figures (C6)? Q15. How important is Software Features (C5) when it is compared with Financial Figures (C6)?

Q15

X X X X X X X X X X X X X X X

Attributes

Demonstrated (1/3, 2/5, 1/2)

Very Strong (2/5, 1/2, 2/3)

Strong (1/2, 2/3, 1)

Moderate (2/3, 1, 2)

Equal (1, 1, 1)

Moderate (1/2, 1, 3/2)

Strong (1, 3/2, 2)

C1 C1 C1 C1 C1 C2 C2 C2 C2 C3 C3 C3 C4 C4 C5

Very Strong (3/2, 2, 5/2)

Attributes

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14

Importance (or preference) of one main-attribute over another

Demonstrated (2, 5/2, 3)

Questions

With respect to the Best Operating System

C2 C3 C4 C5 C6 C3 C4 C5 C6 C4 C5 C6 C5 C6 C6

With respect to the main attribute ‘‘Storage Management (C1)’’, Q11. How important is Memory Management (C11) when it is compared with Virtual Memory (C12)? Q12. How important is Memory Management (C11) when it is compared with File System Interface (C13)?

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Q13. How important is Memory Management (C11) when it is compared with File System Implementation (C14)? Q14. How important is Memory Management (C11) when it is compared with Secondary Storage Structure (C15)? Q15. How important is Virtual Memory (C12) when it is compared with File System Interface (C13)? Q16. How important is Virtual Memory (C12) when it is compared with File System Implementation (C14)? Q17. How important is Virtual Memory (C12) when it is compared with Secondary Storage Structure (C15)? Q18. How important is File System Interface (C13) when it is compared with File System Implementation (C14)? Q19. How important is File System Interface (C13) when it is compared with Secondary Storage Structure (C15)? Q20. How important is File System Implementation (C14) when it is compared with Secondary Storage Structure (C15)?

X

Sub – attributes

Demonstrated (1/3, 2/5, 1/2)

Very Strong (2/5, 1/2, 2/3)

Strong (1/2, 2/3, 1)

Moderate (2/3, 1, 2)

Equal (1, 1, 1)

C14

Moderate (1/2, 1, 3/2)

Q20

Strong (1, 3/2, 2)

C11 C11 C11 C11 C12 C12 C12 C13 C13

Very Strong (3/2, 2, 5/2)

Sub - attributes

Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19

Importance (or preference) of one sub-attribute over another

Demonstrated (2, 5/2, 3)

Questions

With respect to Storage Management

C12 C13 C14 C15 C13 C14 C15 C14 C15

X X X X X X X X X

C15

With respect to the main attribute ‘‘Process Management (C2)’’, Q21. How important is Process Handling (C21) when it is compared with CPU Scheduling (C22)? Q22. How important is Process Handling (C21) when it is compared with Process Synchronization (C23)? Q23. How important is Process Handling (C21) when it is compared with Deadlocks (C24)? Q24. How important is CPU Scheduling (C22) when it is compared with Process Synchronization (C23)? Q25. How important is CPU Scheduling (C22) when it is compared with Deadlocks (C24)? Q26. How important is Process Synchronization (C23) when it is compared with Deadlocks (C24)?

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X

Sub - attributes

Demonstrated (1/3, 2/5, 1/2)

Very Strong (2/5, 1/2, 2/3)

Strong (1/2, 2/3, 1)

Moderate (2/3, 1, 2)

Equal (1, 1, 1)

C 23

Moderate (1/2, 1, 3/2)

Q26

Strong (1, 3/2, 2)

C21 C21 C21 C22 C22

Very Strong (3/2, 2, 5/2)

Sub - attributes

Q21 Q22 Q23 Q24 Q25

Importance (or preference) of one sub-attribute over another

Demonstrated (2, 5/2, 3)

Questions

With respect to Process Management

105

C 22 C23 C24 C23 C24

X X X X X

C24

With respect to the main attribute ‘‘Protection and Security (C3)’’, Q27. How important is Protection (C31) when it is compared with Security (C32)?

X

Sub – attributes

Demonstrated (1/3, 2/5, 1/2)

Very Strong (2/5, 1/2, 2/3)

Strong (1/2, 2/3, 1)

Moderate (2/3, 1, 2)

Equal (1, 1, 1)

Moderate (1/2, 1, 3/2)

Strong (1, 3/2, 2)

C31

Very Strong (3/2, 2, 5/2)

Sub - attributes

Q27

Importance (or preference) of one sub-attribute over another

Demonstrated (2, 5/2, 3)

Questions

With respect to Protection and Security

C32

With respect to the main attribute ‘‘Distributed Structure (C4)’’, Q28. How important is Network Structures (C41) when it is compared with Distributed System Structures (C42)? Q29. How important is Network Structures (C41) when it is compared with Distributed File Systems (C43)? Q30. How important is Network Structures (C41) when it is compared with Distributed Coordination (C44)? Q31. How important is Distributed System Structures (C42) when it is compared with Distributed File Systems (C43)? Q32. How important is Distributed System Structures (C42) when it is compared with Distributed Coordination (C44)? Q33. How important is Distributed File Systems (C43) when it is compared with Distributed Coordination (C44)?

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106 With respect to Distributed Structure

Sub - attributes

Demonstrated (1/3, 2/5, 1/2)

Very Strong (2/5, 1/2, 2/3)

Strong (1/2, 2/3, 1)

X

Moderate (2/3, 1, 2)

C43

Equal (1, 1, 1)

Q33

Moderate (1/2, 1, 3/2)

X

Strong (1, 3/2, 2)

C41 C41 C41 C42 C42

Very Strong (3/2, 2, 5/2)

Sub - attributes

Q28 Q29 Q30 Q31 Q32

Demonstrated (2, 5/2, 3)

Questions

Importance (or preference) of one sub-attribute over another

C42 C43 C44 C43 C44

X X X X

C44

With respect to the main attribute ‘‘Software Features (C5)’’, Q34. How important is Applications and Tools (C51) when it is compared with Bugs and Coding (C52)? Q35. How important is Applications and Tools (C51) when it is compared with Graphical User Interface (C53)? Q36. How important is Applications and Tools (C51) when it is compared with Availability and Support (C54)? Q37. How important is Bugs and Coding (C52) when it is compared with Graphical User Interface (C53)? Q38. How important is Bugs and Coding (C52) when it is compared with Availability and Support (C54)? Q39. How important is Graphical User Interface (C53) when it is compared with Availability and Support (C54)?

X X X X X X

Sub – attributes

Demonstrated (1/3, 2/5, 1/2)

Very Strong (2/5, 1/2, 2/3)

Strong (1/2, 2/3, 1)

Moderate (2/3, 1, 2)

Equal (1, 1, 1)

C 53

Moderate (1/2, 1, 3/2)

Q39

Strong (1, 3/2, 2)

C51 C51 C51 C52 C52

Very Strong (3/2, 2, 5/2)

Sub - attributes

Q34 Q35 Q36 Q37 Q38

Importance (or preference) of one sub-attribute over another

Demonstrated (2, 5/2, 3)

Questions

With respect to Software Features

C52 C53 C54 C 53 C54 C54

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With respect to the sub-attribute ‘‘(Cxy)’’, respectively, Q40 Cxy. How important is AX when it is compared with BS? With respect to Sub Attribute

Alternative

Demonstrated (1/3, 2/5, 1/2)

Very Strong (2/5, 1/2, 2/3)

Strong (1/2, 2/3, 1)

Moderate (1/2, 1, 3/2)

Q40 C12

AX

Q40 C13

AX

X

BS

Q40 C14

AX

X

BS

Q40 C15

AX

Q40 C21

AX

Q40 C22

AX

Q40 C23

AX

Q40 C24

AX

Q40 C31

AX

X

BS

Q40 C32

AX

X

BS

Q40 C41

AX

X

BS

Q40 C42

AX

X

BS

Q40 C43

AX

X

BS

Q40 C44

AX

X

BS

Q40 C51

AX

Q40 C52

AX

Q40 C53

AX

Q40 C54

AX

Q40 C61

AX

Moderate (2/3, 1, 2)

AX

Equal (1, 1, 1)

Q40 C11

Strong (1, 3/2, 2)

Alternative

Very Strong (3/2, 2, 5/2)

Questions

Demonstrated (2, 5/2, 3)

Importance (or preference) of one sub-attribute over another

X

BS X

BS

X

BS

X

BS X

BS

X

BS X

BS

X X

BS BS

X

BS X

X

BS BS

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Appendix B

Fuzzy EUA Costs over Periods

Period

$15’000

$30’000

$45’000

$60’000

Figs. 6–9 illustrate the fuzzy EUAW of capital recovery and operating and maintenance costs. Figs. 10 and 11 illustrate the total fuzzy EUAWs.

1

2

3

4

5

6

Fuzzy EUA Costs over Periods

Period

$15’000

$30’000

$45’000

$60’000

Fig. 7. Fuzzy EUAW of BS’s capital recovery costs.

1

2

3

4

5

6

Fig. 8. Fuzzy EUAW of AX’s operating costs.

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Fuzzy EUA Costs over Periods

Period

$10’000

$15’000

$20’000

$25’000

E. Tolga et al. / Int. J. Production Economics 97 (2005) 89–117

1

2

3

4

5

6

Fuzzy EUA Costs over Periods

Period

$20’000

$40’000

$60’000

$80’000

Fig. 9. Fuzzy EUAW of BS’s operating costs.

1

2

3

4

5

6

Fig. 10. Fuzzy EUAW of AX’s total costs.

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Period

$25’000

$45000

$65’000

$75’000

110

1

2

3

4

5

6

Fig. 11. Fuzzy EUAW of BS’s total costs.

Appendix C. Tables 6–34 Table 6 Evaluation of the sub-attributes with respect to Process Management

C21 C22 C23 C24

C21

C22

C23

C24

(1,1,1) (1,1,1) (2,1,3/2) (3/2,2,5/2)

(1,1,1) (1,1,1) (2/3,1,2) (1,1,1)

(2/3,1,1/2) (1/2,1,3/2) (1,1,1) (1/2,1,3/2)

(2/5,1/2,2/3) (1,1,1) (2/3,1,2) (1,1,1)

The weight vector from Table 6 is calculated as WC2=(0.59, 0.33, 0.00, 0.08)T.

Table 7 Evaluation of the sub-attributes with respect to Protection and Security

C31 C32

C31

C32

(1,1,1) (1,3/2,2)

(1/2,2/3,1) (1,1,1)

The weight vector from Table 7 is calculated as WC3=(0.68, 0.32)T.

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Table 8 Evaluation of the sub-attributes with respect to Distributed Structure

C41 C42 C43 C44

C41

C42

C43

C44

(1,1,1) (1,1,1) (1/2, 1,3/2) (1/2,1,3/2)

(1,1,1) (1,1,1) (1/2,1,3/2) (1/2,1,3/2)

(2/3,1,2) (1,1,1) (1,1,1) (1,1,1)

(2/3,1,2) (2/3,1,2) (1,1,1) (1,1,1)

The weight vector from Table 8 is calculated as WC4=(0.25, 0.25, 0.25, 0.25)T. Table 9 Evaluation of the sub-attributes with respect to Software Features

C51 C52 C53 C54

C51

C52

C53

C54

(1,1,1) (1,3/2,2) (1,1,1) (1,1,1)

(1/2,2/3,1) (1,1,1) (1,3/2,2) (3/2,2,5/2)

(1,1,1) (1/2,2/3,1) (1,1,1) (1,3/2,2)

(1,1,1) (2/5,1/2,2/3) (1/2,2/3,1) (1,1,1)

The weight vector from Table 9 is calculated as WC5=(0.32, 0.32, 0.25, 0.11)T. Table 10 Evaluation of the OSs with respect to Memory Management

AX BS

AX

BS

(1,1,1) (1/2,2/3,1)

(1,3/2,2) (1,1,1)

Table 11 Evaluation of the OSs with respect to Virtual Memory

AX BS

AX

BS

(1,1,1) (1,1,1)

(1,1,1) (1,1,1)

The weight vectors from Tables 10 and 11 are calculated as WC11=(0.32, 0.68)T and WC12=(0.50, 0.50)T, respectively. Table 12 Evaluation of the OSs with respect to File System Interface

AX BS

AX

BS

(1,1,1) (2/3,1,2)

(1/2,1,3/2) (1,1,1)

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Table 13 Evaluation of the OSs with respect to File System Implementation

AX BS

AX

BS

(1,1,1) (2/3,1,2)

(1/2,1,3/2) (1,1,1)

The weight vectors from Tables 12 and 13 are calculated as WC13=(0.50, 0.50)T and WC14=(0.50, 0.50)T, respectively. Table 14 Evaluation of the OSs with respect to Secondary Storage Structure

AX BS

AX

BS

(1,1,1) (1,1,1)

(1,1,1) (1,1,1)

Table 15 Evaluation of the OSs with respect to Process Handling

AX BS

AX

BS

(1,1,1) (1/2,2/3,1)

(1,3/2,2) (1,1,1)

The weight vectors from Tables 14 and 15 are calculated as WC15=(0.50, 0.50)T and WC21=(0.32, 0.68)T respectively. Table 16 Evaluation of the OSs with respect to CPU Scheduling

AX BS

AX

BS

(1,1,1) (2/3,1,2)

(1/2,1,3/2) (1,1,1)

Table 17 Evaluation of the OSs with respect to Process Synchronization

AX BS

AX

BS

(1,1,1) (1/2,2/3,1)

(1,3/2,2) (1,1,1)

The weight vectors from Tables 16 and 17 are calculated as WC22=(0.50, 0.50)T and WC23=(0.32, 0.68)T, respectively.

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Table 18 Evaluation of the OSs with respect to Deadlocks

AX BS

AX

BS

(1,1,1) (2/3,1,2)

(1/2,1,3/2) (1,1,1)

AX

BS

(1,1,1) (1,3/2,2)

(1/2,2/3,1) (1,1,1)

Table 19 Evaluation of the OSs with respect to Protection

AX BS

The weight vectors from Tables 18 and 19 are calculated as WC24=(0.50, 0.50)T and WC31=(0.68, 0.32)T, respectively.

Table 20 Evaluation of the OSs with respect to Security

AX BS

AX

BS

(1,1,1) (1,3/2,2)

(1/2,2/3,1) (1,1,1)

Table 21 Evaluation of the OSs with respect to Network Structures

AX BS

AX

BS

(1,1,1) (1/2,1,3/2)

(2/3,1,2) (1,1,1)

The weight vectors from Tables 20 and 21 are calculated as WC32=(0.68, 0.32)T and WC41=(0.50, 0.50)T, respectively.

Table 22 Evaluation of the OSs with respect to Distributed System Structures

AX BS

AX

BS

(1,1,1) (1/2,1,3/2)

(2/3,1,2) (1,1,1)

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Table 23 Evaluation of the OSs with respect to Distributed File Systems

AX BS

AX

BS

(1,1,1) (1/2,1,3/2)

(2/3,1,2) (1,1,1)

The weight vectors from Tables 22 and 23 are calculated as WC42=(0.50, 0.50)T and WC43=(0.50, 0.50)T, respectively. Table 24 Evaluation of the OSs with respect to Distributed Coordination

AX BS

AX

BS

(1,1,1) (1/2,1,3/2)

(2/3,1,2) (1,1,1)

Table 25 Evaluation of the OSs with respect to Applications and Tools

AX BS

AX

BS

(1,1,1) (2,5/2,3)

(1/3,2/5,1/2) (1,1,1)

The weight vectors from Tables 24 and 25 are calculated as WC44=(0.50, 0.50)T and WC51=(1.00, 0.00)T, respectively.

Table 26 Evaluation of the OSs with respect to Bugs and Coding

AX BS

AX

BS

(1,1,1) (1,1,1)

(1,1,1) (1,1,1)

Table 27 Evaluation of the OSs with respect to Graphical User Interface

AX BS

AX

BS

(1,1,1) (1,3/2,2)

(1/2,2/3,1) (1,1,1)

The weight vectors from Tables 26 and 27 are calculated as WC52=(0.50, 0.50)T and WC53=(0.68, 0.32)T, respectively.

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Table 28 Evaluation of theOSs with respect to Availability and Support

AX BS

AX

BS

(1,1,1) (3/2,2,5/2)

(2/5,1/2,2/3) (1,1,1)

Table 29 Evaluation of the OSs with respect to EUAW

AX BS

AX

BS

(1,1,1) (1/2,1,3/2)

(2/3,1,2) (1,1,1)

The weight vectors from Tables 28 and 29 are calculated as WC54=(1.00, 0.00)T and WC61=(0.50, 0.50)T respectively. The combination of priority weights for sub-attributes, attributes, and alternatives to determine priority weights for the best OS are given in Tables 30–35.

Table 30 Sub-attributes of Storage Management

Weight AX BS

C11

C12

C13

C14

C15

Alternative priority vector

0.20 0.32 0.68

0.17 0.50 0.50

0.21 0.50 0.50

0.23 0.50 0.50

0.19 0.50 0.50

0.46 0.54

Table 31 Sub-attributes of Process Management

Weight AX BS

C21

C22

C23

C24

Alternative priority vector

0.59 0.32 0.68

0.33 0.50 0.50

0.00 0.32 0.68

0.08 0.50 0.50

0.39 0.61

Table 32 Sub-attributes of Protection and Security

Weight AX BS

C31

C32

Alternative priority vector

0.68 0.68 0.32

0.32 0.68 0.32

0.68 0.32

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Table 33 Sub-attributes of Distributed Structure

Weight AX BS

C41

C42

C43

C44

Alternative priority vector

0.25 0.50 0.50

0.25 0.50 0.50

0.25 0.50 0.50

0.25 0.50 0.50

0.50 0.50

C51

C52

C53

C54

Alternative priority vector

0.32 1.00 0.00

0.32 0.50 0.50

0.25 0.68 0.32

0.11 1.00 0.00

0.76 0.24

Table 34 Sub-attributes of Software Features

Weight AX BS

Table 35 Main attributes of the goal

Weight AX BS

C1

C2

C3

C4

C5

C6

Alternative priority vector

0.24 0.46 0.54

0.18 0.39 0.61

0.13 0.68 0.32

0.15 0.50 0.50

0.18 0.76 0.24

0.12 0.50 0.50

0.54 0.40

AX is the preferred OS.

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