A fuzzy TOPSIS framework for selecting fragile states ...

A fuzzy TOPSIS framework for selecting fragile states for support facility

Eric Afful-Dadzie, Stephen Nabareseh, Anthony Afful-Dadzie & Zuzana Komínková Oplatková Quality & Quantity International Journal of Methodology ISSN 0033-5177 Qual Quant DOI 10.1007/s11135-014-0062-3

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Author's personal copy Qual Quant DOI 10.1007/s11135-014-0062-3

A fuzzy TOPSIS framework for selecting fragile states for support facility Eric Afful-Dadzie · Stephen Nabareseh · Anthony Afful-Dadzie · Zuzana Komínková Oplatková

© Springer Science+Business Media Dordrecht 2014

Abstract Aid recipient-countries especially those classified as ‘fragile states’ look to donor agencies and other financial organizations for various forms of support facilities to rebuild institutions and repair infrastructure. As countries within the fragile states bracket increase around the world, competition for such assistances has also become keen. To select countries for the fragile states support facility run by the African and Asian development banks, expert ratings over sets of unquantifiable performance based criteria are used to determine the ultimate deserving countries. In order to ensure transparency and fairness in the face of competition, such multi-criteria ratings demand techniques that do not only model human judgements but take into account the effect of variations in expert ratings as a result of possible influences. This paper proposes a fuzzy TOPSIS framework for selecting fragile states for support facility based on the African Development Bank selection criteria. Using pre-defined linguistic terms parameterized by triangular fuzzy numbers, a numerical example is provided on how the framework can be used by decision makers towards final selection of competing countries for the fragile states support facility. The paper anticipating possible influences of lobbyists, further performs a sensitivity analysis to examine the effect that bias in expert ratings could have on the final selection. The result shows a framework that can be applied in instances of selecting countries and organizations for aid purposes.

E. Afful-Dadzie (B) · Z. K. Oplatková Faculty of Applied Informatics, Tomas Bata University in Zlin, T.G Masaryka 5555, 760 01 Zlin, Czech Republic e-mail: [email protected] S. Nabareseh Faculty of Management and Economics, Tomas Bata University in Zlin, Mostní 5139, 760 01 Zlin, Czech Republic e-mail: [email protected] A. Afful-Dadzie University of Ghana Business School, Accra, Ghana e-mail: [email protected]

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Keywords Fragile states · Fuzzy TOPSIS · Traingular fuzzy number (TFN) · Support facility · Evaluation model · Development banks

1 Introduction The definition and scope of what constitutes a fragile state still remains contentious in the donor community and among policy makers in general. This is mainly because fragility of a state tends to manifest itself in diverse forms (Stewart and Brown 2009; Cammack et al. 2006). Furthermore, no consensus is reached on the definition also because of the different programs and agenda designed by different donor organizations for different sets of ‘fragile states’. For example, organizations such as the UK’s Department for International Development (DFID), Canada’s Country Indicators for foreign Policy (CIFP), the Organization for Economic Cooperation and Development (OECD), the United States Agency for International Development (USAID), the African Development Bank (AfDD), the World Bank among others all have their own scope and definitions regarding what constitutes fragile states (Stewart and Brown 2009; Torres and Anderson 2004). In spite of the definitional differences, fragile states are largely accepted to be low-income countries and regions characterized by weak state capacity and where governments cannot deliver core functions to its citizens. Generally, a broad definition of fragile or failed states automatically brings about 2 billion of the world’s population under this category (The World Bank 2012). Countries that fall under this classification tend to have undernourished, undereducated and failed institutions. As often the trend, majority of these fragile or failed states happen to be in Africa and Asia (OECD 2013; IDA 2014; The World Bank 2012). To help ameliorate this situation, the African and Asian Development Banks have taken a front role in terms of providing financial facilities for the restoration of economies in affected states. A state applying for the fragile state support facility of the AfDB, must first have a Country Policy and Institutional Assessment (CPIA) score below or equivalent to 3.2 (Moore 2014). In addition, countries emerging from crisis or conflict, or those that have seen the presence of regional or United Nations peacekeeping operations or mediating operations during the past three years are also automatically considered for selection for the AfDB fragile state facility if the bank’s criteria are met. A selected fragile state by the African Development Bank (AfDB) qualifies for supplemental grant resources to support post conflict rehabilitation and reconstruction efforts. Additionally, selected countries that meet the bank’s criteria for selection also qualify for debt clearance, provision of technical assistance and capacity building support to accelerate state building (AfDB group 2013a; Kanaan 2012). Over the years, several aid instruments such as budget support, social funds, humanitarian aid and pooled funding have been designed for selected fragile states. However, the African and Asian development banks’ criteria for selecting deserving countries remain mostly subjective due to the varied contexts yet specific opportunities available to these fragile states (OECD 2013). The subjective nature of the selection criteria and the human judgements used in selection increases the complexity of the evaluation methodology. This demands a robust and an efficient methodology for capturing subjective expert ratings such as fuzzy set theory. Furthermore, the AfDB concedes that there are a couple of challenges it faces in selecting deserving countries for its Fragile States Facility (FSF) especially debt clearance eligible states (AfDB group 2012). In view of this, the paper proposes a fuzzy TOPSIS framework to rank deserving countries qualified for the support facility to ensure fairness in the final selection. For instance, if out of ten countries who meet the initial requirements for support only four of them can be supported by the bank in a given year, the paper looks at which

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Author's personal copy A fuzzy TOPSIS framework for selecting fragile states for support facility

ones would deserve final selection. Some studies have been carried out to measure aid effectiveness of fragile states (Foster 2007; Corpin et al. 2009); however none of such studies has looked at comprehensively ranking these countries for final selection. The strength of the proposed method is its ability to compare the performance of competing countries against the evaluation criteria based on a single crisp score. The rest of the paper is organized in the following sections. Brief introduction of fuzzy set theory, the TOPSIS technique along with definitions and formulas of the method are presented. Then relevant literature on various fuzzy TOPSIS applications is also presented. A systematic outline of the steps involved in the fuzzy TOPSIS method is also presented. Finally, a numerical example of how fuzzy TOPSIS could be used to rank and select fragile states for support facility is introduced.

2 Modelling subjectivity with fuzzy set 2.1 Fuzzy set theory Zadeh (1965) introduced the concept of fuzzy logic as a mathematical tool based on the concept of relative graded membership. It is fundamentally used to deal with issues of uncertainty which often is as a result of subjectivities, vagueness and imprecision in our natural language used to communicate information (Sivanandam et al. 2007). In Multi-criteria decision making (MCDM), setting precise criteria weights and measuring alternative ratings in varied situations tends to be difficult. Fuzzy logic which is efficient at modeling human decisions and judgments becomes useful and has been widely applied. In the following, basic operations of the fuzzy set theory are briefly introduced. Definition 1 Fuzzy Set Let X be a nonempty set, the universe of discourse X = {x 1 , x2 , ..., xn }. A fuzzy set A of X is a set of ordered pairs {(x1 , f A (x1 )) , (x2 , f A (x2 )) , . . . , (xn , f A (xn ))}, characterized by a membership function f A (x) that maps each element x in X to a real number in the interval [0, 1]. The function value f A (x) stands for the membership degree x in A. A fuzzy number, which is a special case of a fuzzy set, is used to capture the vagueness and variation in the subjective ratings of an expert. Fuzzy numbers rate a set of possible values between a [0, 1] interval to capture the subjectivity, vagueness and imprecision of a subjective rating. The notable types of fuzzy numbers are the trapezoidal and triangular fuzzy numbers. This paper uses the Triangular Fuzzy Number (TFN) as defined by Kaufmann and Gupta (1991) below. Definition 2 Triangular fuzzy number A Triangular fuzzy number (TFN) is a fuzzy set with membership function y = f (x) expressed as a triplet (a, b, c) having the form presented in Fig. 1. The equation of the straight line defined by the points (a, 0) and A(b, 1) is given by y 1 x−a b−a = x−a or y = b−a . Similarly, the straight line defined by the points A(b, 1) and y 1 (c, 0) is given by c−b = c−x or y = c−x c−b . Therefore the membership function f A (x) of the triangular fuzzy number is defined as:

f A (x) =

⎧ ⎨0 ⎩

x−a b−a , c−x c−b ,

x < a, x > b a≤x ≤b b≤x ≤c

(1)

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Author's personal copy E. Afful-Dadzie et al. Fig. 1 Membership function of a TFN

A

1

fA (x)

0

a

A

B

b

b1

b

c

X

1

fA (x)

0

a

a1

c

c1

Fig. 2 Two triangular fuzzy numbers

In Fig. 1, the value of x at b gives the maximal value of f A (x), that is f A (x) = 1. The value x at a represents the minimal grade of f A (x), i.e f A (x) = 0. The constants a and c represents the lower and upper bounds of the available area data respectively and reflect the fuzziness of the data under evaluation. In Fig. 2, two triangular fuzzy numbers are presented to demonstrate the arithmetic operations underlying TFNs as seen in Eqs 2 to 6 below. Definition 3 Basic Triangular Fuzzy Number Operations Assuming A = (a, b, c) and B = (a1 , b1 , c1 )are two triangular fuzzy numbers, then the basic operations on these two fuzzy triangular numbers are as follows: A ⊕ B = (a, b, c) + (a1 , b1 , c1 ) = (a + a1 , b + b1 , c + c1 )

(2)

A − B = (a, b, c) − (a1 , b1 , c1 ) = (a − c1 , b − b1 , c − a1 )

(3)

A × B = (a, b, c) × (a1 , b1 , c1 ) = (aa1 , bb1 , cc1 )   a b c A ÷ B = (a, b, c) ÷ (a1 , b1 , c1 ) = , , c1 b 1 a 1

(4) (5)

Definition 4 Distance Measure for Fuzzy Numbers. Let A = (a, b, c) and B = (a1 , b1 , c1 ) be two TFNs as shown in Fig. 2. The distance between them is computed using the vertex method in Eq. (6):   d(A, B) = 1/3 (a − a1 )2 + (b − b1 )2 + (c − c1 )2 (6) 2.2 Fuzzy TOPSIS The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is one of the widely used techniques in Multiple Criteria Decision Making (MCDM). Proposed by Hwang and Yoon (1981), TOPSIS introduces simultaneously both the shortest distance

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from the Fuzzy Positive Ideal Solution (FPIS) and the farthest distance from the Fuzzy Negative Ideal Solution (FNIS), to determine the best alternative. The FNIS maximizes cost criteria and minimizes benefit criteria, whiles FPIS maximizes benefit criteria and minimizes cost criteria. The alternatives are ranked and selected according to their relative closeness combining two distance measures. The strength of the TOPSIS method as a multiple criteria decision technique is seen in its theoretical robustness (Deng et al. 2000), a sound logic that embodies the human rationale in selection, a scalar value that accounts for both the best and worst alternative at the same time (Shih et al. 2007) and its application in a variety of areas (Zanakis et al. 1998) where multi criteria decision making with alternatives selection is required. TOPSIS technique is frequently applied in research of evaluation, selection and ranking problems such as Kannan et al. (2014) where fuzzy TOPSIS was applied in selecting Green suppliers based on GSCM practices to rank suppliers, Sun and Lin (2009) applies fuzzy TOPSIS to evaluate the competitive advantages of shopping websites, Amiri (2010) uses the technique in project selection of oil-fields development whiles Awasthi et al. (2011) used fuzzy TOPSIS to evaluate sustainable transportation systems under partial or incomplete information circumstances. Further use of TOPSIS in evaluation and selection is used by other researchers such as (Chamodrakas and Martakos 2012; Yu et al. 2011; Lo et al. 2010; Wang and Chang 2007). There have been extensions of the fuzzy TOPSIS method by various researchers beyond the proposition by Deng et al. (2000). Chen and Tsao (2008) designed an extension of the TOPSIS method based on interval-valued fuzzy sets in decision analysis, Chu and Lin (2009) designed a fuzzy TOPSIS model based on interval arithmetic of fuzzy numbers, Abo-Sinna et al. (2008) proposed an extension of the TOPSIS approach in multiobjective large-scale nonlinear programming problems with block angular structure, Tian et al. (2013) used a fuzzy TOPSIS model via chi-square test for information source selection, Marbini et al. (2013) extended the compromise Ratio methodology for fuzzy group decision making with SWOT analysis and Li (2007) proposed a Compromise Ratio (CR) methodology for fuzzy multi-attribute group decision making (FMAGDM). Based on mathematical foundations of the fuzzy TOPSIS methodology from Kannan et al. (2014); Awasthi et al. (2011), Lo et al. (2010), and Wang and Chang (2007), a systematic fuzzy TOPSIS approach is proposed for the ranking and selection of fragile states for support facility with recognizance to the African Development bank criteria. The below procedure featured in literature would guide the study. Step 1: Determining linguistic variables In this step, determining the linguistic variables that represent the criteria for measuring performance or selection is carried out. The linguistic variables (criteria) are then expressed in linguistic terms and used to rate each linguistic variable. The linguistic terms are further transformed into fuzzy numbers. Linguistic terms are qualitative words that reflect the subjective view of an expert or decision maker about the criteria per each alternative under consideration (George and Bo 1995). This study uses TFNs and linguistic terms as shown in Tables 1 and 2 respectively to capture the ratings of the linguistic variables (criteria) and alternatives on a scale of 0–1. Step 2a: Determining importance weight of criteria To determine the importance or the weight of each criterion, the decision makers rate each criterion using the linguistic terms in Table 1. This is expressed in equation 7 as vector W˜ :  W˜ = w˜ 1 , w˜ 2 , . . . , w˜ n , j = 1, 2, . . . , n (7) where w j represents the weight of the jth criterion C j based on the linguistic preference assigned by a decision maker. Each weight w˜ kj = w kj1 w kj2 w kj3 is expressed as a triangular

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Author's personal copy E. Afful-Dadzie et al. Table 1 Linguistic scale for the importance of each criterion

Table 2 Linguistic scales representation for the ratings

Linguistic terms

Triangular fuzzy number

Very low (VL)

(0.0, 0.1, 0.3)

Low (L)

(0.1, 0.3, 0.5)

Medium(M)

(0.3, 0.5,0.7)

High (H)

(0.5, 0.7, 0.9)

Very high (VH)

(0.7, 0.9, 1.0)

Linguistic terms

Triangular fuzzy number

Off-track (OFT)

(0.0,0.1,0.3)

Possible to be achieved with(PA)

(0.1,0.3,0.5)

Very likely to be achieved (LA)

(0.3,0.5,0.7)

On track (OT)

(0.5,0.7,0.9)

Achieved (A)

(0.7,0.9,1.0)

fuzzy number. These preferences signify the importance attributed to a criterion by a decision maker. Step 2b: Constructing the fuzzy decision matrix Presented with m alternatives, n criteria and k decision-makers, (D1 , D2 , . . . , Dk ), a fuzzy multi-criteria group decision-making problem can be expressed in a matrix format as: A1 D˜ = A2 .. . Am

C1 x˜11 ⎢ x˜21 ⎢ ⎢ .. ⎣. x˜m1 ⎡

C2 x˜12 x˜22 .. . x˜m2

··· ··· .. . ···

Cn ⎤ x˜1n x˜2n ⎥ ⎥ , i = 1, 2, . . . , m; j = 1, 2, . . . , n .. ⎥ . ⎦ x˜mn

(8)

where xi j , i = 1, 2, . . ., m; j = 1, 2, . . ., n are linguistic triangular fuzzy numbers and x˜mn is the rating of alternative Am with respect to criterion C j . Note that for decision maker k,   x˜ikj = aikj , bikj , cikj is a triangular fuzzy number.

Step 3a: Aggregating criteria importance weights of decision makers The aggregation of the importance ascribed to each criterion by the decision makers is performed next. The graded mean integration technique (Chou 2003) is used to aggregate the fuzzy weights (w˜ i j ) for each criterion as in Eq. (9).   w˜ kj = w j1 , w j2 , w j3 where, ‘      w j1 = mink w jk1 , w j2 = k1 kk=1 w jk2 , w j3 = maxk w jk3 i = 1, 2, . . . , m; (9) j = 1, 2, . . . , n. Step 3b: Aggregating the alternative ratings of decision makers The aggregation is done in a similar method as in 3a to aggregate the preferences of decision makers for each alternative under each criterion. From step 2b, the aggregated fuzzy ratings, xi j of alternatives (i) withrespect to each  criterion ( j) can be expressed as using graded mean integration as: x˜ikj = aikj , bikj , cikj where,

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Author's personal copy A fuzzy TOPSIS framework for selecting fragile states for support facility k      ai j = min aikj bi j = 1/k bikj , ci j = max cikj i = 1, 2, . . . , m; j = 1, 2, . . . , n., k

k

k=1

(10) Step 4a: Normalizing the fuzzy decision matrix The next step in the modeling process is the normalization of the decision matrix obtained from step 3b. The normalized fuzzy decision matrix denoted by R˜ is defined as in Eq. (11):  R˜ = r˜i j m×n , i = 1, 2, . . . , m; j = 1, 2, . . . , n (11) The normalization of the fuzzy decision matrix is performed using Eq. (12) below   a˜ i j b˜i j c˜i j where r˜i j = , , c+j = max ci j i c+j c+j c+j

(12)

where the normalized is also a triangular fuzzy number. Step 4b: Weighting the Normalized fuzzy decision matrix The normalized decision matrix is the product of results from step 3a and 3b. The weighted fuzzy normalized decision matrix is as shown in V˜ below in Eqs. (13) and (14).  V˜ = v˜i j m×n , i = 1, 2, . . . , m; j = 1, 2, . . . , n (13) v˜i j = r˜i j ⊗ w j

(14)

Step 5: Determining FPIS and FNIS and distance of each alternative from FPIS and FNIS In the weighted normalized fuzzy decision matrix, the elements v˜i j are normalized positive triangular fuzzy numbers whose ranges belong to the closed interval [0, 1]. FPIS A+ and FNIS A− are expressed as in the following:   A+ = v˜1+ , v˜2+ , · · · , v˜n+ (15)   − − − − (16) A = v˜1 , v˜2 , · · · , v˜n − where v + j = (1, 1, 1) and v j = (0, 0, 0) , j = 1, 2, . . . , n + − The distances di and di the distances of each alternative A+ from A− are calculated as shown in Eq. (17) and (18) respectively

di+ =

n    v˜i j , v˜ + j , i = 1, 2, . . . , m; j = 1, 2, . . . , n

(17)

j=1

di− =

n    v˜i j , v˜ − j , i = 1, 2, . . . , m; j = 1, 2, . . . , n

(18)

j=1

Step 6: Closeness coefficient and ranking order of alternatives The relative closeness coefficient also known as relative gaps degree CCi , used to determine the ranking of the ith alternative, is computed by: CCi =

di+

di−

+ di−

, i = 1, 2, . . . , m

(19)

with CCi, the ranking of all the alternatives is determined which subsequently aid in selection.

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Ranking Fragile States for Support Facility

1st level criteria: Consolidation of Peace & Security

Signing global peace Agreement (C1)

Angola (A1)

Existence of a functional or transition government (C2)

Burundi (A2)

Unfulfilled Social & Economic needs (C3) Adverse economic effects of conflict (C4)

Central African Republic (C.A.R) (A3)

Very low level of human development (C5)

Côte d’Ivoire (A4)

Country’s growth prospects and debt management (C6)

2nd level criteria: Macroeconomic & Structural reforms

Implementation of public finance management practices (C7) Restoring an environment conducive to entrepreneurship and private sector development. (C8)

D.R Congo (A5) Guinea (A6) Liberia (A7) Sierra Leone (A8)

Increasing transparency and empowerment of institutions (C9)

Fig. 3 Conceptual framework of the research

3 Illustrative example of fragile states ranking This section illustrates the use of fuzzy TOPSIS method to rank and select fragile states for support facility from the AfDB. The new 21 member team, made of the experience and competence of the eminent members and the operations evaluation team, is used to select a deserved country (AfDB 2013b). This framework would help the bank to know which of their selection criteria are most important and which countries based on the evaluation deserve support. This paper demonstrates with the bank’s 9 evaluation criteria and eight arbitrary chosen countries that fall in the bank’s category of core fragile states i.e. Angola, Burundi, DR. Central African Republic (CAR), Côte d’Ivoire, D.R Congo, Guinea, Liberia and Sierra Leone to be ranked and selected as indicated in Fig. 3. The weights of each of the criterion is calculated using the fuzzy TOPSIS approach. The comparison and determination of the importance of one criterion or alternative over another would be done by the 8 eminent panel empowered for the evaluation. Calculation of the priority weights of the different decision alternatives is broken down into the following phases: Step 1: Determining the linguistic Variables Each of the nine criteria of the AfDB are evaluated using linguistic terms (Very Low, Low, Medium, High or Very high) to determine the Best Non-Fuzzy Performance value (BNP) for their weights. The demonstration uses a rating scale in triangular fuzzy number format as shown in Tables 1 and 2. This research demonstrates how the linguistic ratings can be used

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Author's personal copy A fuzzy TOPSIS framework for selecting fragile states for support facility Table 3 Importance weights of criteria from decision makers

D1

D2

D3

C1

L

L

VL

C2

M

L

M

C3

H

L

M

C4

VH

H

H

C5

L

H

M

C6

H

M

H

C7

VH

VH

VH

C8

VH

M

L

C9

VL

VL

VL

Table 4 Alternative ratings by decision maker 1 A1

A2

A3

A4

A5

A6

A7

A8

C1

PA

LA

LA

OFT

OT

A

PA

OT

C2

PA

OFT

OT

PA

LA

A

OT

A

C3

OFT

LA

OT

PA

LA

LA

OT

OFT

C4

LA

LA

A

OT

PA

OFT

OFT

OT

C5

OT

PA

LA

LA

PA

OT

PA

A

C6

A

PA

OT

PA

LA

OFT

OT

LA

C7

OFT

OFT

LA

PA

LA

LA

PA

OFT

C8

LA

OT

OFT

OT

PA

A

LA

A

C9

OT

OFT

OT

OT

LA

PA

PA

A

for a final decision making on which countries are selected for support. Furthermore, we consider the importance weights of the various criteria shown in Fig. 3 and the ratings of its qualitative criteria as linguistic. Step 2a: Determining importance weight of criteria The decision makers make their linguistic judgements about the importance weights of each criterion as shown in Table 3 using the linguistic terms in Table 1. Step 2b: Constructing the fuzzy decision matrix In ranking the fragile states to enable the bank support a deserved country or countries, the evaluation from the 21 member team is deemed important. The paper employs the use of the average value to aggregate the fuzzy/subjective judgments values from different evaluators regarding the same criterion on the assumption that each evaluator has the same importance. The evaluators would judge the alternatives (fragile countries) with the linguistic terms “oftrack”, “possible to be achieved”, “very likely to be achieved”, “on-track”, and “achieved”. These linguistic judgments would represent the opinions of the evaluators regarding the performance of each fragile state (alternative) in relation to the set criteria. In Tables 4, 5 and 6, we demonstrate with assumed results of the evaluator’s judgments and their aggregation on the five linguistic terms. Step 3a: Aggregating the importance weights criteria of decision makers We assume that after the construction of the fuzzy TOPSIS model and the subsequent judgment matrix from the 21-member panel, we arrive at the weights of each criterion as

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Author's personal copy E. Afful-Dadzie et al. Table 5 Alternative ratings by decision maker 2 A1

A2

A3

A4

A5

A6

A7

A8

C1

LA

LA

OT

PA

OFT

PA

OT

A

C2

OFT

OT

A

PA

LA

OT

PA

PA

C3

OT

OFT

OFT

OFT

OT

PA

LA

A

C4

PA

PA

OT

PA

LA

OFT

LA

OT OT

C5

A

PA

OFT

LA

OT

PA

PA

C6

OT

PA

OT

OFT

OFT

OT

OFT

LA

C7

OFT

LA

PA

LA

OFT

LA

LA

OT

C8

PA

PA

LA

OT

LA

A

OFT

OFT

C9

OT

OFT

A

PA

PA

LA

OT

PA

A4

A5

A6

A7

A8

Table 6 Alternative ratings by decision maker 3 A1

A2

A3

C1

OT

LA

OT

PA

PA

OFT

PA

OT

C2

PA

OT

LA

OFT

LA

A

OFT

LA

C3

A

OT

OFT

LA

OT

OFT

LA

OFT

C4

LA

OFT

A

LA

OFT

PA

LA

PA

C5

OFT

PA

PA

OT

PA

LA

OT

A

C6

OFT

LA

A

OT

LA

OFT

OT

A

C7

LA

LA

PA

LA

OFT

OFT

OFT

LA

C8

A

OT

LA

PA

OFT

PA

OT

LA

C9

OFT

LA

OT

OFT

LA

A

PA

OT

shown in Table 7. The paper applies the center of area (COA) method in computing the Best Non-Fuzzy Performance value (BNP) for the weights of each criterion. The BNP value of the fuzzy number Wk = (L wk , Mwk , Uwk .) is calculated using the expression in Eq. (20). BNPwk =

L wk + [(Uwk − L wk ) + (Mwk − L wk )]/3

(20)

Using eqn. 20, the BNP value weight of C5, for example is computed as follows: = 0.1 + [(0.9 − 0.1) + (0.50 − 0.1)]/3 = 0.500

(21)

The remaining weights for the remaining criteria are also calculated as shown in Table 7. The fuzzy TOPSIS method shows that the first 3 important criteria for ranking fragile states are C7, C4 and C6. The less important criterion is C9 with a BNP of 0.133. Step 3b: Aggregating the alternative ratings of decision makers The fuzzy decisions of the criteria and the ratings assigned to the alternatives are aggregated using Eq. (10). The study uses the graded mean integration method to aggregate the weights of the criteria and the results are shown in Table 8 below. Step 4a: Normalizing the fuzzy matrix The fuzzy decision matrix is then normalized by using Eq. (12) as shown in Table 9.

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Author's personal copy A fuzzy TOPSIS framework for selecting fragile states for support facility Table 7 Weights of each criteria

Criteria

TFN

BNP

Rank

C1

(0.0, 0.233, 0.5)

0.244

8

C2

(0.1, 0.433, 0.7)

0.411

7

C3

(0.1, 0.500, 0.9)

0.500

5

C4

(0.5, 0.767, 1.0)

0.756

2

C5

(0.1, 0.500, 0.9)

0.500

5

C6

(0.3, 0.633, 0.9)

0.611

3

C7

(0.7, 0.900, 1.0)

0.867

1

C8

(0.1, 0.567, 1.0)

0.556

4

C9

(0.0, 0.100, 0.3)

0.133

9

Step 4b: Weighted normalized fuzzy decision matrix The weighted fuzzy normalized matrix v˜ for the criteria is computed using Eq. (14). The results are as shown in Table 10. Step 5 : Determining FPIS and FNIS and distance of each alternative from FPIS and FNIS The fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS), defined respectively as A+ and A− , are presented in eqns. 22 and 23 respectively. A+ = [(1, 1, 1), (1, 1, 1), (1, 1, 1), (1, 1, 1), (1, 1, 1), (1, 1, 1)] −

A = [(0, 0, 0), (0, 0, 0), (0, 0, 0), (0, 0, 0), (0, 0, 0), (0, 0, 0)]

(22) (23)

If the distance between two triangular fuzzy numbers is represented as A1 = (a1 , b1 , c1 ) and A2 = (a2 , b2 , c2 ), then the distance between the two fuzzy numbers is calculated using the vertex method as shown in Eq. (6) and Table 11. Step 6: Closeness coefficient and ranking order of alternatives In Table 11, the distances of d + and d − are shown together with their relative closeness 3.75 coefficient, CCi . The CCi for A1 is calculated using Eq. (19) as CCi = 6.88+3.75 = 0.3529 The final ranking by our demonstration would place Sierra Leone as the most deserving of the AfDB support facility followed by Liberia, Côte d’Ivoire, C.A.R, Angola, D.R Congo, Guinea and Burundi as shown in Fig. 4.

4 Remark set and evaluation criteria The African Development Bank has two sets of criteria for selecting countries for financial support facility aimed at fragile states. The first-level criteria assess a fragile state’s commitment to peace and security whiles the second-level concentrates on macroeconomic and structural reforms. As shown in Fig. 1 above, some of the main considerations in the first level criteria (Consolidation of peace and security) are C1 and C4. C1 looks for evidence of a country’s signature to a global peace agreement, emergence from crisis or reconciliation recognized by the international community. C2 considers the existence of low level of human development in the state. In the second level criteria (Macroeconomic and structural reforms), some of the features in the set criteria are C7 and C9. C7 assesses the level of implementation of public finance practices by a country whiles C9 considers whether a country has

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(0.0 0.57 1.0)

(0.1 0.43 0.7)

(0.0 0.57 1.0)

(0.0 0.57 1.0)

(0.0 0.23 0.7)

(0.1 0.57 1.0)

(0.0 0.5 0.9)

C4

C5

C6

C7

C8

C9

C2

C3

(0.1 0.5 0.9)

(0.0 0.23 0.5)

C1

A1

(0.0 0.23 0.7)

(0.1 0.57 0.9)

(0.0 0.37 0.7)

(0.1 0.04 0.7)

(0.1 0.3 0.5)

(0.0 0.3 0.7)

(0.0 0.43 0.9)

(0.0 0.5 0.9)

(0.3 0.5 0.7)

A2

Table 8 Fuzzy aggregated decision matrix

(0.5 0.77 1.0)

(0.0 0.37 0.7)

(0.1 0.37 0.7)

(0.5 0.77 1.0)

(0.0 0.3 0.7)

(0.5 0.83 1.0)

(0.0 0.3 0.9)

(0.3 0.7 1.0)

(0.3 0.63 0.9)

A3

(0.0 0.37 0.9)

(0.1 0.57 0.9)

(0.1 0.43 0.7)

(0.0 0.37 0.9)

(0.3 0.57 0.9)

(0.5 0.5 0.9)

(0.0 0.3 0.7)

(0.0 0.23 0.5)

(0.0 0.23 0.5)

A4

(0.1 0.43 0.7)

(0.0 0.3 0.7)

(0.00.23 0.7)

(0.0 0.37 0.7)

(0.1 0.43 0.9)

(0.0 0.3 0.7)

(0.3 0.63 0.9)

(0.3 0.5 0.7)

(0.0 0.43 0.9)

A5

(0.1 0.57 1.0)

(0.1 0.7 1.0)

(0.0 0.37 0.7)

(0.0 0.3 0.9)

(0.1 0.5 0.9)

(0.0 0.17 0.5)

(0.0 0.3 0.7)

(0.5 0.83 1.0)

(0.0 0.43 1.0)

A6

(0.1 0.43 0.9)

(0.0 0.43 0.9)

(0.0 0.3 0.7)

(0.0 0.5 0.9)

(0.1 0.43 0.9)

(0.0 0.37 0.7)

(0.5 0.57 0.9)

(0.0 0.37 0.9)

(0.1 0.43 0.9)

A7

(0.1 0.63 1.0)

(0.0 0.5 1.0)

(0.0 0.43 0.9)

(0.3 0.63 1.0)

(0.5 0.83 1.0)

(0.1 0.57 0.9)

(0.0 0.37 1.0)

(0.1 0.57 1.0)

(0.5 0.77 1.0)

A8

Author's personal copy E. Afful-Dadzie et al.

(0.1 0.5 0.9)

(0.0 0.23 0.5)

(0.0 0.57 1.0)

(0.1 0.43 0.7)

(0.0 0.57 1.0)

(0.0 0.57 1.0)

(0.0 0.23 0.7)

(0.1 0.57 1.0)

(0.0 0.5 0.9)

C1

C2

C3

C4

C5

C6

C7

C8

C9

A1

(0.0 0.26 0.78)

(0.1 0.63 1.0)

(0.0 0.4 0.78)

(0.1 0.04 0.78)

(0.1 0.3 0.56)

(0.0 0.3 0.78)

(0.0 0.48 1.0)

(0.0 0.56 1.0)

(0.3 0.56 0.78)

A2

Table 9 Normalization of fuzzy decision matrix

(0.5 0.77 1.0)

(0.0 0.37 0.7)

(0.1 0.37 0.7)

(0.5 0.77 1.0)

(0.0 0.3 0.7)

(0.5 0.83 1.0)

(0.0 0.3 0.9)

(0.3 0.7 1.0)

(0.3 0.63 0.9)

A3

(0.0 0.41 1.0)

(0.1 0.63 1.0)

(0.1 0.48 0.78)

(0.0 0.41 1.0)

(0.3 0.63 1.0)

(0.1 0.56 1.0)

(0.0 0.3 0.78)

(0.0 0.26 0.56)

(0.0 0.26 0.56)

A4

(0.1 0.48 0.78)

(0.0 0.3 0.78)

(0.0 0.26 0.78)

(0.0 0.41 0.78)

(0.1 0.48 1.0)

(0.0 0. 3 0.78)

(0.3 0.7 1.0)

(0.3 0.56 0.78)

(0.0 0.48 1.0)

A5

(0.1 0.57 1.0)

(0.1 0.7 1.0)

(0.0 0.37 0.7)

(0.0 0.3 0.9)

(0.1 0.5 0.9)

(0.0 0.17 0.5)

(0.0 0.3 0.7)

(0.5 0.83 1.0)

(0.0 0.43 1.0)

A6

(0.0 0.48 1.0)

(0.0 0.48 1.0)

(0.0 0.3 0.78)

(0.0 0.56 1.0)

(0.1 0.48 1.0)

(0.0 0.41 0.78)

(0.56 0.63 1.0)

(0.0 0.41 0.9)

(0.1 0.48 1.0)

A7

(0.1 0.63 1.0)

(0.0 0.5 1.0)

(0.0 0.43 0.9)

(0.3 0.63 1.0)

(0.5 0.83 1.0)

(0.1 0.57 0.9)

(0.0 0.37 1.0)

(0.1 0.57 1.0)

(0.5 0.77 1.0)

A8

Author's personal copy

A fuzzy TOPSIS framework for selecting fragile states for support facility

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(0.0 0.12 0.45)

(0.0 0.10 0.35)

(0.0 0.25 0.9)

(0.05 0.33 0.7)

(0.0 0.29 0.9)

(0.0 0.36 0.9)

(0.0 0.21 0.7)

(0.01 0.29 1.0)

(0.0 0.05 0.27)

C1

C2

C3

C4

C5

C6

C7

C8

C9

A1

(0.0 0.03 0.23)

(0.01 0.32 1.0)

(0.0 0.37 0.78)

(0.03 0.03 0.7)

(0.01 0.17 0.5)

(0.0 0.26 0.78)

(0.0 0.21 0.9)

(0.0 0.24 0.7)

(0.0 0.13 0.39)

A2

(0.0 0.08 0.3)

(0.0 0.19 0.7)

(0.07 0.33 0.7)

(0.15 0.49 0.9)

(0.0 0.15 0.63)

(0.25 0.64 1.0)

(0.0 0.13 0.81)

(0.03 0.3 0.7)

(0.0 0.15 0.45)

A3

Table 10 Weighted normalized fuzzy decision matrix

(0.0 0.04 0.3)

(0.01 0.32 1.0)

(0.08 0.43 0.78)

(0.0 0.26 0.9)

(0.03 0.32 0.9)

(0.06 0.43 1.0)

(0.0 0.14 0.7)

(0.0 0.11 0.39)

(0.0 0.06 0.28)

A4

(0.0 0.05 0.23)

(0.0 0.17 0.78)

(0.0 0.23 0.78)

(0.0 0.26 0.7)

(0.01 0.24 0.9)

(0.0 0.26 0.78)

(0.0 0.3 0.9)

(0.03 0.24 0.54)

(0.0 0.11 0.5)

A5

(0.0 0.06 0.3)

(0.01 0.35 1.0)

(0.0 0.33 0.7)

(0.0 0.19 0.81)

(0.01 0.25 0.81)

(0.0 0.13 0.5)

(0.0 0.3 0.63)

(0.05 0.36 0.7)

(0.0 0.1 0.5)

A6

(0.0 0.06 0.3)

(0.0 0.29 1.0)

(0.0 0.27 0.7)

(0.0 0.32 0.81)

(0.01 0.32 0.9)

(0.0 0.28 0.7)

(0.0 0.36 0.9)

(0.0 0.16 0.63)

(0.0 0.15 0.5)

A7

(0.0 0.06 0.3)

(0.0 0.25 1.0)

(0.0 0.39 0.9)

(0.09 0.4 0.9)

(0.05 0.42 0.9)

(0.05 0.44 0.9)

(0.0 0.16 0.9)

(0.01 0.25 0.7)

(0.0 0.18 0.5)

A8

Author's personal copy E. Afful-Dadzie et al.

Author's personal copy A fuzzy TOPSIS framework for selecting fragile states for support facility Table 11 The distance measurement

di+

di−

CCi

Rank

Angola (A1)

6.88

3.75

0.3529

5

Burundi (A2)

6.98

3.62

0.3415

8

Côte d’Ivoire (A3)

6.48

3.90

0.3759

3

C.A.R (A4)

6.80

3.83

0.3601

4

D.R Congo (A5)

6.89

3.69

0.3489

6

Guinea (A6)

6.83

3.66

0.3487

7

Liberia (A7)

6.77

40.9

0.3765

2

Sierra Leone (A8)

6.50

4.32

0.3992

1

Fig. 4 Final ranking of fragile states

put in measures to restore an environment conducive to entrepreneurship and private sector development. All the nine criteria used for this work were unquantifiable hence a tailor-made remark set was constructed to suit the evaluation of the criteria as shown in Table 2.

5 Sensitivity analysis This part of the paper uses sensitivity analysis to investigate the effect on the weights of the criteria and ranking of alternatives if a decision maker’s preference for a perceived major criterion is influenced. It analyses the congruent effect of influenced criteria on the preference rating of the selected best alternatives. Using the ranked criteria in Table 7, the first four most influential criteria C7, C4, C6 and C8 are used in the case study of the sensitivity analysis. The preference ratings of these criteria by the decision makers mostly range between ‘H’ and ‘VH’. The case study uses five different types of scenarios with 4 cases each. In scenario 1, i.e. cases 1 to 4, the linguistic preference rating of a decision maker for C7, C4 and C8 are set from ‘VH’ to ‘VL’ while that of C6 is set from ‘H’ to ‘VL’. All other original linguistic preference ratings for all other criteria are maintained. This therefore affects the respective TFN and BNP, hence changes the rank of the criterion under study as seen in Table 13 and Fig. 5. For instance, in case 1, the linguistic preference rating of decision maker 1, ‘VH’ (0.7, 0.9, 1) of C7 is replaced with ‘VL’ (0, 0.1, 0.3) while maintaining that of the other criteria

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Author's personal copy E. Afful-Dadzie et al. Table 12 Inputs for sensitivity analysis

Case Scenario 1

Scenario 2

Scenario 3

Scenario 4

Scenario 5

(Changes made in Wjt), J= C1, C2, …, C9, t=1,2,3,4 Case 1

Wc7 = (0, 0.1, 0.3), Wc1-Wc6, Wc8-Wc9

Case 2

Wc4 = (0, 0.1, 0.3), Wc1-Wc3, Wc5-Wc9

Case 3

Wc6 = (0, 0.1, 0.3), Wc1-Wc5, Wc7-Wc9

Case 4

Wc8 = (0, 0.1, 0.3), Wc1-Wc7, Wc9

Case 5

Wc7 = (0.1, 0.3, 0.5), Wc1-Wc6, Wc8-Wc9

Case 6

Wc4 = (0.1, 0.3, 0.5), Wc1-Wc3, Wc5-Wc9

Case 7

Wc6 = (0.1, 0.3, 0.5), Wc1-Wc5, Wc7-Wc9

Case 8

Wc8 = (0.1, 0.3, 0.5), Wc1-Wc7, Wc9

Case 9

Wc7 = (0.3, 0.5, 0.7), Wc1-Wc6, Wc8-Wc9

Case 10

Wc4 = (0.3, 0.5, 0.7), Wc1-Wc3, Wc5-Wc9

Case 11

Wc6 = (0.3, 0.5, 0.7), Wc1-Wc5, Wc7-Wc9

Case 12

Wc8 = (0.3, 0.5, 0.7), Wc1-Wc7, Wc9

Case 13

Wc7 = (0.5, 0.7, 0.9), Wc1-Wc6, Wc8-Wc9

Case 14

Wc4 = (0.5, 0.7, 0.9), Wc1-Wc3, Wc5-Wc9

Case 15

Wc6 = (0.5, 0.7, 0.9), Wc1-Wc5, Wc7-Wc9

Case 16

Wc8 = (0.5, 0.7, 0.9), Wc1-Wc7, Wc9

Case 17

Wc7 = (0.7, 0.9, 1.0), Wc1-Wc6, Wc8-Wc9

Case 18

Wc4 = (0.7, 0.9, 1.0), Wc1-Wc3, Wc5-Wc9

Case 19

Wc6 = (0.7, 0.9, 1.0), Wc1-Wc5, Wc7-Wc9

Case 20

Wc8 = (0.7, 0.9, 1.0), Wc1-Wc7, Wc9

including major criteria not under consideration. In cases 2 and 4, the linguistic preference ratings of decision maker 1, ‘VH’ (0.7, 0.9, 1) of C4 and C8 are replaced with ‘VL’ (0, 0.1, 0.3) while that of all other criteria remains unchanged. In case 3 the linguistic preference rating of decision maker 1, ‘H’ (0.5, 0.7, 0.9) of C6 is replaced with ‘VL’ (0, 0.1, 0.3) while also maintaining that of the other criteria at their original settings. These four set of cases constitute scenario 1. In scenario 2, the same format is applied for cases 5, 6, 7 and 8 as in scenario 1 with the linguistic preference rating of criteria C7, C4, C6 and C8 changed to ‘L’ (0.1, 0.3, 0.5) respectively while all other criteria remain unchanged. Scenario 3 (cases 9-12), scenario 4 (cases 13-16) and scenario 5(cases 17-20) change original linguistic preference rating to ‘M’, ‘H’ and ‘VH’ respectively for the major criteria under study. Table 12 indicates the all the 20 cases performed. The effect of the various cases on the criteria weights are indicated in Table 13 and Fig. 5 below where ‘c1’ stands for case 1 as is ‘c2’ for case 2 and so on. A change in the linguistic preference rating of a major criterion by a decision maker for the criteria under study results in some few changes in the ranking of the criteria. C7 remains the first ranked criterion through the cases except for scenario 1 (c1), scenario 2 (c1) and scenario 3 (c1) where the criterion is ranked 4, 3, and 2 respectively as shown in Table 13 and Fig. 5. C4 remains the second ranked criterion except for scenario 1 (c1, c2), scenario 2 (c1, c2) and scenario 3 (c1) where some changes occurred. The same conclusion applies to C6 and C8 as seen in Table 13 and Fig. 5 below. Whether the changes in the BNP and ranking of the criteria will have a rippling effect on the ranking and selection of the alternatives is therefore analysed using the new BNPs

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Author's personal copy A fuzzy TOPSIS framework for selecting fragile states for support facility Table 13 Result of sensitivity analysis: ranking of criteria Original Scenario 1 = VL

Scenario 2 = L

Scenario 3 = M

Scenario 4 = H

Scenario 5 = VH

c1 c2 c3 c4

c5 c6 c7 c8

c9 c10 c11 c12 c13 c14 c15 c16 c17 c18 c19 c20

C1 8

8

8

8

8

8

8

8

8

8

8

8

8

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8

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8

C2 7

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7

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C3 5

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C4 2

1

6

2

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1

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1

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C5 5

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C6 3

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C7 1

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1

3

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1

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1

C8 4

3

3

3

7

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3

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6

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3

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3

C9 9

9

9

9

9

9

9

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9

9

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9

9

9

9

9

9

9

9

9

9

Fig. 5 Plot of result of sensitivity analysis on criteria

in weighting the normalized fuzzy decision matrix of Table 9 for all the 4 scenarios and 20 cases. Results of the alternative rankings are shown in Table 14 and Fig. 6. Alternatives A8, A7 and A3 which ranked 1, 2 and 3 respectively remained unchanged for all the scenarios and cases. All other alternatives also remained the same. The implication of this result is that assuming the preference rating of a decision maker for a perceived major criterion is incorrect, influenced or has a mistake, it does not have a rippling effect on the alternative ranking and selection. In effect, we can confidently say (based on the input for the case-study), the best and worst alternative decisions are relatively insensitive to changes in the major criteria.

6 Comparison with fuzzy VIKOR and AHP methods This section compares the fuzzy TOPSIS results from the study with two other popular MCDM methods, specifically the multi-criteria optimization and compromise solution which

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Author's personal copy E. Afful-Dadzie et al. Table 14 Result of sensitivity analysis: Ranking of alternatives Original Scenario 1 = VL

Scenario 2 = L

Scenario 3 = M

Scenario 4 = H

Scenario 5 = VH

c1 c2 c3 c4

c5 c6 c7 c8

c9 c10 c11 c12 c13 c14 c15 c16 c17 c18 c19 c20

A1 5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

A2 8

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8

8

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A3 3

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A4 4

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A5 6

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A6 7

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A8 1

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1

Fig. 6 Plot of result of sensitivity analysis on alternatives

originally translates to VlseKriterijumska Optimizacija I Kompromisno Resenje’, in Serbian language and the fuzzy Analytical Hierarchy Process. Fuzzy TOPSIS, VIKOR and AHP are widely employed for various selection and ranking solutions. In reference to Fuzzy TOPSIS and Fuzzy VIKOR, both arrive at a scalar (crisp) value in their ranking by considering the best and worst fuzzy values in their calculation (Deng et al. 2000; Shih et al. 2007). Hence as seen in Table 15, the ranking of the alternatives for both the fuzzy TOPSIS and fuzzy VIKOR methods (based on the numerical example in this paper) yielded the same ranking order. It must be noted however that in Fuzzy VIKOR unlike TOPSIS, the smaller the value of the best compromise solution, the better the alternative. Fuzzy TOPSIS and Fuzzy VIKOR are both found also to be theoretically robust (Deng et al. 2000). In particular comparison to AHP, Fuzzy TOPSIS method is generally seen to outperform Fuzzy AHP especially in cases of group decision-making, accommodating changes to alternatives and criteria and the number of criteria and alternatives it can support in a decision making process (Junior 2014). In general Fuzzy TOPSIS is computationally simpler than VIKOR and AHP. This and many other strengths of TOPSIS outlined above informed its choice for this study.

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Author's personal copy A fuzzy TOPSIS framework for selecting fragile states for support facility Table 15 Compared ranking of fuzzy TOPSIS with fuzzy VIKOR results

Alternatives

Fuzzy TOPSIS

Fuzzy VIKOR

Results (CCi )

Rank

Results (Q)

Rank

A1

0.3529

5

0.0794

5

A2

0.3415

8

0.1087

8

A3

0.3759

3

0.0480

3

A4

0.3601

4

0.0774

4

A5

0.3489

6

0.0939

6

A6

0.3487

7

0.1019

7

A7

0.3765

2

0.0315

2

A8

0.3992

1

0.0239

1

7 Implications The donor community continues to seek for new methodologies for improving selection and evaluation methods of developmental aid support facilities. For example, the World Bank’s CPIA and IDA allocation system which incidentally is what the African Development Bank relies upon to select ‘fragile states’, have often been described as complex and difficult to measure performance. To proffer selection and evaluation solutions, this paper provides an effective guiding model for both donors and recipient countries to computationally track progress in an aid allocation and evaluation process. One major contribution of this study is its ability to explicitly model subjectivity which is characteristic of most aid selection and assessment processes. The other implication of the study is that a fair and transparent assessment methodology such as the one proposed advocates for the position by (Rodrik 2004) that resources should be offered to states which have been most effective over a period and not necessarily to those that need it. This position gives confidence to the assessment process and assures all parties involved that eventual awardees merit the selection. For example, it has been noted that the recipient countries for the IDA’s assistance to Africa have mostly been to only Nigeria, Ethiopia, Tanzania, DRC, Uganda and Mozambique (Kararach et al. 2012) at the neglect of more developmentally performing countries. Similarly, (Alexander 2010) also bemoans the situation where assistance to ‘fragile’ states tends to be focused on only few countries that often have powerful lobbying groups. In view of this, the proposed framework would impact on aid selection and evaluation methods making it more transparent.

8 Conclusion The aim of the research was to come out with a fuzzy TOPSIS framework that could be used to evaluate, rank and select ‘fragile’ and or conflict states for support facility. The African Development Bank ‘fragile’ states support facility is used to demonstrate how the framework could prove useful to both donors and recipient countries. The study used the nine criteria selection format by the bank with a custom-made rating scale to propose a model in selecting eligible but deserving countries. The proposed model would not only aid in deepening transparency in the selection process but would also help in determining the most important criteria in the selection process. The model can be used by other aid allocation

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organizations around the world. The study also conducted a sensitivity analysis to ascertain whether the influence of lobbyists and mistakes in the criteria will have an impact on final ranking of alternatives. The result indicates that a change in the linguistic preference ratings of decision makers has no effect on the final ranking and selection of fragile states in this model. The study to rank and select ‘fragile’ states for support facility could have far reaching implications in particular for donors, recipient countries and the academic community in general even as developmental aid to third world countries shrinks in the face of recent economic crises. The fuzzy TOPSIS method was chosen over other MCDM methods for this study because of its simplicity, agility in decision process, strength in modeling group decisions and ability to accommodate changes to alternatives and criteria when the need arises. Acknowledgments This work was supported by Internal Grant Agency of Tomas Bata University IGA/FAI/2014/037 and IGA/FaME/2014/007.

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