Research Article | | Peer-Reviewed

Multi-criteria Decision Making Using KEMIRA-Sort Method for Assessing the Suitability of Wild Animals to Promote Sustainable Management of a Wildlife Farm

Received: 17 December 2024     Accepted: 31 December 2024     Published: 14 January 2025
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Abstract

In Burkina Faso, most of the wildlife farms hosting touristic visits, which started out with great enthusiasm, are now closed, highlighting the need for sustainable wildlife farm management. Although also of interest for wildlife farming, most of the study dealing with sustainable animal farm management are focus on livestock farming. This study was motivated by the need to provide an answer to the question of sustainable management of wildlife farming in Burkina Faso. To this end, our aim is to assess the suitability of wild animals to promote sustainable management of an ex-situ wildlife farm, hosting touristic visits. The implementation of a Multi-Criteria Decision Making (MCDM) process enabled us, among other things, to identify the wild animals and the criteria against which their suitability to promote sustainable management has been assessed. Our concern, on the one hand, to enable the stakeholders to easily express their preferences and thus fully adhere to the decision-making process, and on the other hand, to respect the heterogeneous dimensions implied by sustainability led us to choose the KEmeny Median Indicator Ranks Accordance-Sort (KEMIRA-Sort) multi-criteria sorting method. The evaluation phase was guided by the consideration of decision-maker’s preferences for ranking criteria and empirical examples of assigning wild animals to ordered categories of suitability to sustainable management. The complete implementation of the decision-making process enabled us to identify the categories of wild animals according to their suitability to promote sustainable management in the case study of the Wédbila wildlife farm (WWF) in Burkina Faso. More specifically, we showed that the group of wild animals most likely to promote WWF sustainable management was made up of pork-spicy, aulacodes, and red-necked ostrich. These results obtained was in line with empirically estimation of the principle stakeholder playing the role of Decision maker. These relevant results obtained thus validate the effectiveness of the KEMIRA-Sort multi-criteria sorting method. In addition, the flexibility of the proposed approach predisposes it, subject to adaptation, to be used in other sustainable management wildlife farm contexts.

Published in American Journal of Applied Mathematics (Volume 13, Issue 1)
DOI 10.11648/j.ajam.20251301.11
Page(s) 1-12
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

MCDM, Shorting Method, KEMIRA-Sort, Sustainable Management, Wildlife Farm

1. Introduction
Animal breeding farm has more often than not been coupled with tourist visits, which generally entails complex management. To be sustainable, this system combining animal breeding and tourist visits must respect economic, environmental, social and animal reproduction principles. Multi-criteria decision-aid methods are the ideal tools for taking into account the conflicting aspects inherent in decision-making. Also, in the context of agriculture we find successful work combining deterministic and/or uncertain multi-criteria decision making methods to address the sustainability of its management. Particularly in the context of the sustainability of livestock farms, we can note work carried out on several aspects linked to the search for sustainability in the management of the said livestock farm. In contrast to traditional livestock farm management, which focuses on economic profitability alone, thereby generating conflicts with stakeholders given the failure to take into account the environmental components (water, soil, gas emissions, etc.) affected by livestock farm operations, propose a model for the sustainable management of a livestock farm based on a multi-criteria decision making approach to achieve economic, social and environmental objectives. looked at the risks associated with the livestock supply chain. Seventeen risks were identified and ranked according to their importance, using the AHP multi-criteria decision making method, in order to plan and guarantee sustainable management of a livestock farm. Virtual technologies (Artificial Intelligence, Big Data, etc.) and connected objects are known to have a leverage effect in all the business sectors in which they are applied. The sustainable management of animal farms is no exception. point out that the adoption of these new technologies would enable traditional animal breeding farms to become precision breeding farms, where animal health and behavior, among other parameters, would be monitored in real time, thus fostering sustainable animal farm management. On a larger scale, Genovese et al investigate the characteristics of a sustainable business model based on the coexistence of livestock farming and tourism activities. They show that the sustainability and success of such a business model in a mountainous context depends on the proactive intervention of a supra-agricultural dimension, while retaining the specific features of individual farms. It should be noted that the last two works do not mention the use of multi-criteria decision support tools, which could certainly contribute more to giving them a solid theoretical framework that would promote their application to other contexts or study regions of sustainable animal farm management. However, it should be noted that these works, although also of interest for wildlife farming, are more focused on livestock farming. Indeed, as pointed out by speaking specifically of the sustainable management of wild animal farms, an essential element in ensuring sustainable management is the suitability of wild animals to promote sustainable management of the farm in question.
In Burkina Faso, most of the wildlife farms hosting touristic visits, which started out with great enthusiasm, are now closed. This situation highlights the need for sustainable wildlife farm management in Burkina Faso and other countries suffering from this problem.
For a given ex-situ wildlife farm hosting tourist visits, in order to ensure its sustainable management, we propose a methodology for assessing the suitability of wild animals to promote its sustainable management. Specifically, we propose to find orderly categories of the best animals that can promote this sustainable management. Setting up an ex-situ wildlife farm with a view to sustainability requires taking into account criteria relating to profit, reproduction and investment, which are different and conflicting in nature. Concerning the conflicting nature of criteria, note that two criteria are said to be homogeneous when a natural compensation is possible between them (e.g. two economic criteria or two social criteria), otherwise the two criteria are said to be heterogeneous (e.g. a social criterion and an economic criterion or an economic criterion and an environmental criterion). Multiple Criteria Decision Making Methods (MCDM) are better suited to take into account the complexity inherent in a problem. In the context of our sorting problem, several MCDM methods are available (ELECTRE Tri UTADIS KEMIRA-Sort ). Choosing an MCDM sorting method means finding the most efficient one:
1. Achieving a good balance with respect to the number of parameters required for its operation,
2. Respecting the heterogeneity of criteria,
3. Easy to apply.
Looking these criteria for choosing an MCDM method in our context, KEMIRA-Sort method seems the most appropriate for the problem of sustainable wildlife farm management. Unlike the total aggregation method UTADIS , KEMIRA-Sort is a multiple criteria sorting method, avoiding blind compensation between heterogeneous criteria. In addition, it requires few parameters for its implementation, compared with outranking based method as ELECTRE Tri . KEMIRA Sort method is an extension of the multiple criteria choosing method KEMIRA KEMIRA-Sort method has been successfully used for landscape degradation management problems
In the rest of our paper, we describe the case study of the Wédbila wildlife farm, and briefly present the KEMIRA-Sort method. We then apply the KEMIRA-Sort method to categorize the wild animals of the Wédbila wildlife farm according to their suitability to ensure sustainable wildlife farm management. Finally, we conclude our paper with suggestions for future work.
2. Materials and Methods
2.1. Materials
The Wédbila wildlife Farm (WWF), is a project conceived and developed by Lungren since 1954. It is a wildlife farm covering some sixty hectares, where wild animal visits, research and training activities take place, activities to perfect the breeding of wild animals on several parameters such as sexual maturity, gestation time, interval between litters, commercial age, life expectancy, mortality rate, number of pups per litter, cost of care, cost of feed, commercial value and so on. The WWF is located southwest of Ouagadougou, in the commune of Koubri, between latitude 12°03'30.7'' North and longitude 1°25'18.7'' West.
In this study, we propose to assign wild animals to the following ordered categories C1,C2, C3, C4 in order to evaluate their suitability to promote the sustainable management of an ex-situ wildlife farm like that of Wédbila (Burkina Faso). Thus, animals in category C1 will be considered as having the lowest suitability to promote sustainable farm management, and those in category C4 will be considered as having the highest suitability to promote the sustainable management of the wildlife farm. We consider that the more an animal is assigned to a better category, the better it can promote the sustainable management of the wildlife farm.
Table 1 presents the wild animals of the WWF each assigned to a category. In section 3, a justification of the categorization provided by Table 1 is given. Figure 1 presents a plaque of the Wédbila wild farm showing the animals in their habitat.
Table 1. Categorization.

Categories

Alternatives

C1

“ephalophus rufilatus” (X6)

“Sylvicapra grimmia” (X7)

“Geochelone sulcata” (X9)

“Kobus ellipsiprymnus” (X12) psiprymnus” (X12)

“Alcelaphus buselaphus” (X13)

“Hippotragus niger” (X14)

“Lupulella adusta” (X15)

C2

C3

“Phacochoerus africanus” (X2)

“Gazella dorcas” (X3)

“Tragelaphus Seriptus” (X4)

“cricetomys” (X8)

“Gazella rufifrons” (X10)

C4

“Hystrix Cristata” (X1)

“Thryonomys swinderianus” (X5)

“Struthio camelus” (X11)

Figure 1. Plaque of Wédbila wild farm.Plaque of Wédbila wild farm.
2.2. Methods
2.2.1. Keys Steps of KEMIRA-Sort Method
In what follows, we adopt the following notations
1. Xk, k1,2,,P designates an alternative.
2. We assume that have Q criteria divided into G groups G1, G2,,GG. Of Course the relation (1) holds:
i=1GGi=Q,(1)
Where Gi represents the cardinal of Gi.
1. The pair (i,j) designates the criterion j of the group Gi.
2. The variable Xi,jk denotes the performance of the alternative Xk with respect to the criteria j of the group Gi.
3. The variable xi,jk denotes the normalized performance of Xk obtained by using the relation (2):
Xi,jk=Xi,jk-minkXi,jkmaxkXi,jk-minkXi,jk.(2)
1. The variable wi,j denotes the weight of criterion (i,j).
2. The variable C1,C2,,CM represent the ordered categories of alternative assignment, with C1 being the worst and CM being the best.
3. The variables αil, l1,,M-1, i1,,G denotes the performance thresholds associated with respect to group of criteria G1, G2,,GG
The main steps in implementing the KEMIRA Sort method are described below.
1. Identification of alternatives.
2. Developing relevant criteria to evaluate the alternatives.
3. Grouping criteria into homogeneous groups.
4. Ranking of criteria by the decision-maker in each sub-group Gi in descending order from the most preferred to the least preferred. So the relations (3), (4) and (5) hold:
i,1>̃1,2>̃>̃i,Gi,   i1,,G, (3)
wi,1wi,2wi,Gi             i1,,G,(4)
j=1Giwi,j=1,    i1,,G, (5)
where i,j>̃(i,l) means that the criterion i,j is at least as important as the criterion i,l.
1. Increasing functions. Wi (weighted averages) are calculated by applying the formula (6):
WiXk=j=1niwi,j×xi,jk.(6)
2. Ask the Decision Maker (DM) to give the parameters 𝑝 (a percentage) of the formula (7) to calculate the thresholds αil of increasing functions Wi:
αilp=p×maxkWiXk, 0<αi1p<<αiM-1p<1.(7)
3. Apply the assignment process (8) to the categories, following the steps below (𝑠𝑡𝑒𝑝 1 to 𝑠𝑡𝑒𝑝 𝑀):
step 1: if  i1,2,,G, WiXk αi1p, assign Xk  to C1;step 2:  if   i1,2,,G, WiXkαi2p,  and notXk C1, assign Xk  to C2;tep 3:  if   i1,2,,G, WiXkαi3p,  and notXk  C1  and  notXk  C2, assign Xk  to C3step M: if Xk does not satisfy the step 1 to step M-1,  assign Xk  to CM(8)
4. Solving the mathematical programming problem (9):
maxwi,jfopt=l=1Ml×Cls.t. wi,1wi,2wi,Gi  i1,,G,j=1Giwi,j=1,    i1,,G, assignment process  8.(9)
At the optimum, alternatives or actions are assigned to their best categories.
2.2.2. KEMIRA-Sort Algorithm
Table 2 describes the KEMIRA-Sort algorithm used to solve mathematical programming problem (9).
Table 2. KEMIRA-Sort algorithm. KEMIRA-Sort algorithm. KEMIRA-Sort algorithm.

1: Fix algorithm parameters:

2: 10-3ϵ10-1, the initial iteration t=0, the maximum of iterations maxiter,

3: Thresholds: 0<αi1p<<αiM-1p<1.

4: Randomly choose an initial weights vector satisfying the conditions (5) and (4):

5: w0=(w1,10,,w1,G10;w2,10,,w2,G20;;wG,10,,wG,GG0)

6: Randomly choose a vector direction w:

7: Increment the number of iterations: t = t + 1

8: Compute the vector wt=w0+ϵ×w

9: if w1 does not meet the restrictions (5) and (4) then

10: apply the corrections proposed by Krylovas et al.

:

11: for i,j

12: if wi,jt<0 then

13: change: wi,jt=0.

14: end if

15: if wi,jt<wi,j+1t then

16: change: wi,jt=wi,j+1t

17: end if

18: if si=j=1Giwi,jt1 then

19: change: wi,j1=wi,j1si

20: end if

21: end for

22: end if

23: Compute the  WiXk as in (6) using w0 values and run the condition (8).

24: Compute the value of the objective function fopt0 as indicated in (9)

25: if t>maxiter then

26: stop the algorithm

27: else

28: Compute  WiXk as in (6) using wt values and execute the condition (8).

29: Compute the value of the current objective function foptt as indicated in (9).

30: if foptt>fopt0 then

31: change: fopt0=foptt, w0=wt and go to step 7 of the algorithm

32: else

33: go to step 4 of the algorithm.

34: end if

35: end if

3. Results
3.1. Wild Animals Selected for the Wédbila Wildlfe Farm (WWF)
The structuring phase allows us to identified fifteen (15) wild animals (alternatives) listed as follows:
1. A couple of pork - spicy (Hystrix Cristata: X1)
2. A couple of warthogs (Phacochoerus africanus: X2)
3. A couple of dorcas gazelle (Gazella Dorcas: X3)
4. A couple of Guib Harnache´ (Tragelaphus Seriptus: X4)
5. A family of aulacodes (Thryonomys swinderianus: X5)
6. A couple of flanked duiker (cephalophus rufilatus: X6)
7. A couple of Grimm’s duiker (Sylvicapra grimmia: X7)
8. A family of Gambia rats (cricetomys: X8)
9. A couple of ring-necked tortoise (Geochelone sulcate: X9)
10. A couple of red-fronted gazelle (Gazella rufifrons: X10)
11. A couple of red-necked ostrich (Struthio camelus: X11)
12. A couple of defassa cobe (ellipsiprymnus: X12)
13. A couple of hartebeest major (Alcelaphus buselaphus: X13)
14. A couple of black hippotrague (Hippotragus niger: X14)
15. A couple of striped jackal (Lupulella adusta: X15)
Figure 1 give some pictures of these wild animals.
3.2. Choice of Evaluation Criteria
The criteria for evaluating the alternatives were identified in common agreement with the manager of the WWF, who has long experience in farm management and who also played the role of decision- maker. This enabled us to select fourteen criteria divided into three groups summarized in Table 3.
1. The group 1, named aspects of reproduction is made up of seven criteria.
2. The group 2, named investment aspects is made up of four criteria.
3. The group 3, called economic aspects, is made up of three criteria.
In each group, the criteria were ranked from best to worst
Table 3. Group 1, Group 2 and Group 3 of criteria.Group 1, Group 2 and Group 3 of criteria.Group 1, Group 2 and Group 3 of criteria.

Criteria

Indicators

Objective

(1, 1)

life expectancy (in years)

maximize

(1, 2)

the number of babies per year

maximize

(1, 3)

sexual maturity (in days)

minimize

(1, 4)

commercial age (in days)

minimize

(1, 5)

gestation time (in days)

minimize

(1, 6)

interval between litters (in days)

minimize

(1, 7)

mortality rate (as a percentage)

minimize

(2, 1)

annual feed cost (in CFA)

minimize

(2, 2)

annual cost of care (in CFA)

minimize

(2, 3)

housing construction costs (in CFA)

minimize

(2, 4)

cost of materials for daily use (in CFA)

minimize

(3, 1)

3-year rate of return (in CFA) maximize

maximize

(3, 2)

training demand (scale from 1 to 15) maximize

maximize

(3, 3)

gains on visits per year (scale from 1 to 15) maximize

maximize

3.3. WWF Evaluation Matrix
The evaluation of each alternative w.r.t. the 14 criteria (see Table 4) was carried out using documents from the literature review on wild animals data from daily animal monitoring and the WWF archives.
Table 4. Evaluation matrix.

Alternatives

Criteria

(1, 1)

(1, 2)

(1, 3)

(1, 4)

(1, 5)

(1, 6)

(1, 7)

(2, 1)

(2, 2)

(2, 3)

(2, 4)

(3, 1)

(3, 2)

(3, 3)

X1

20

3.6

720

150

48

150

0.03

111600

4800

500000

60000

3600000

15

8

X2

21

2

1260

180

175

360

0.05

257000

24590

450000

75000

1250000

15

7

X3

12

1

720

180

180

360

0.03

60000

16990

600000

35500

3000000

10

10

X4

12

1.5

720

180

180

240

0.05

65000

3865

600000

41500

4800000

10

8

X5

6

24

180

90

90

180

0.05

174960

2100

137750

58000

10800000

15

6

X6

15

1

720

180

210

360

0.03

45000

3090

600000

43500

2700000

5

9

X7

14

2

480

180

210

270

0.03

239040

3090

1568500

43500

2700000

5

9

X8

8

96

180

180

32

60

0.05

4363200

2100

100000

44000

10800000

10

5

X9

50

24

180

180

32

360

0.05

900000

5400

1066500

43500

4500000

5

4

X10

14

1

540

180

189

360

0.03

14400

16990

1568500

35500

3000000

10

10

X11

40

8

1440

45

42

360

0.01

219000

10000

838250

35500

74000000

5

15

X12

18

1

1050

270

240

360

0.05

720000

60000

802750

42500

7500000

5

14

X13

19

1

810

720

245

360

0.03

720000

60000

802750

42500

15000000

5

11

X14

20

1

1800

270

270

360

0.03

912500

80000

802750

42500

25000000

5

13

X15

16

6

240

60

60

365

0.05

146000

6000

1022750

42500

4800000

5

12

objective

max

max

min

min

min

min

min

min

min

min

min

max

max

max

The data were then normalized using relation (2) and the normalized evaluation matrix presented in Table 5 (with all the criteria to be maximized).
Table 5. Normalized evaluation matrix. Normalized evaluation matrix. Normalized evaluation matrix.

Alternatives

Criteria

(1, 1)

(1, 2)

(1, 3)

(1, 4)

(1, 5)

(1, 6)

(1, 7)

(2, 1)

(2, 2)

(2, 3)

(2, 4)

(3, 1)

(3, 2)

(3, 3)

X1

0.318

0.027

0.666

0.844

0.932

0.704

0.5

0.977

0.965

0.7276

0.379

0.032

1.

0.363

X2

0.340

0.010

0.333

0.8

0.399

0.016

0.

0.944

0.711

0.761

0

0.

1.

0.272

X3

0.136

0.

0.666

0.8

0.378

0.016

0.5

0.989

0.808

0.659

1

0.024

0.5

0.545

X4

0.136

0.005

0.666

0.8

0.378

0.409

0.

0.988

0.977

0.659

0.848

0.048

0.5

0.363

X5

0.

0.242

1.

0.933

0.756

0.606

0.

0.963

1.

0.974

0.430

0.131

1.

0.181

X6

0.204

0.

0.666

0.8

0.252

0.016

0.5

0.992

0.987

0.659

0.797

0.019

0.

0.454

X7

0.181

0.010

0.814

0.8

0.252

0.311

0.5

0.992

0.987

0.659

0.797

0.019

0.

0.454

X8

0.045

1.

1.

0.8

1.

1.

0.

0.

1.

1.

0.784

0.131

0.5

0.090

X9

1

0.242

1.

0.8

1.

0.016

0.

0.796

0.957

0.341

0.797

0.044

0.

0.

X10

0.181

0.

0.777

0.8

0.340

0.016

0.5

1.

0.808

0.

1.

0.024

0.5

0.545

X11

0.772

0.073

0.222

1.

0.957

0.016

1.

0.952

0.898

0.497

1.

1.

0.

1.

X12

0.272

0.

0.462

0.666

0.126

0.016

0.

0.837

0.256

0.521

0.822

0.085

0.

0.909

X13

0.295

0.

0.611

0.

0.105

0.016

0.5

0.837

0.256

0.521

0.822

0.189

0.

0.636

X14

0.318

0.

0.

0.666

0.

0.016

0.5

0.793

0.

0.521

0.822

0.326

0.

0.818

X15

0.227

0.052

0.962

0.977

0.882

0.

0.

0.969

0.949

0.371

0.822

0.048

0.

0.727

objective

max

max

max

max

max

max

max

max

max

max

max

max

max

max

3.4. Empirical Assignment of Alternatives
Recall that we wanted to assign the wild animals (alternatives) according to four ordered categories: the C4 category for the best wild animals promoting sustainable management of the wildlife farm; the C1category for the worst animals; and two intermediate C2 and C3 categories for animals that do not belong to either the C1 or C4 categories. In order to guide the analyst in the choice of parameters for implementing KEMIRA-Sort method, we (playing the role of analyst) asked the decision-maker to give us examples of category assignments based on his experience. Empirically, the decision-maker was able to provide us with assignment examples as summarized in Table 6. Note that while the decision-maker was sure about his examples of assignment to the best category C4 and to the worst category C1, he was more hesitant about assigning alternatives to the intermediate categories C2 and C3. Consequently, according to the decision-maker, the examples of assignment to category C2 could just as well correspond to those of category C3.
Table 6. Examples of empirical assignment. Examples of empirical assignment. Examples of empirical assignment.

Alternatives

Assignment categories

X6, X7,X9

C1

C2

X3, X8,X10

C3

X1, X2,X5

C4

3.5. Running KEMIRA-sort Algorithm
3.5.1. Setting Parameters
We have implemented KEMIRA-Sort algorithm in python language. The parameters of the KEMIRA-Sort algorithm have been chosen in such a way as to match the results in Table 6 as closely as possible. This enabled us to set the performance threshold values αilp as presented in Table 7 and Table 8, and the following parameters:
The maximum number of iterations is set at 100000 (maxiter = 100000).
The parameter 𝑝 varies over the set 𝑝 ∈ {40%; 45%; 60%} and can be used to create tiers of three (03) thresholds as a function of 𝑝 as stated in relation (7).
The value of 𝜖 is set to 𝜖 = 0.01
KEMIRA-Sort algorithm begins by randomly choose a vector:
w0=(w1,10,,w1,G10;w2,10,,w2,G20;;wG,10,,wG,GG0)
satisfying relations (4) and (5).
Here w0 = (0.19, 0.17, 0.17, 0.16, 0.14, 0.1, 0.07; 0.4, 0.35, 0.14, 0.11; 0.61, 0.35, 0.04) is the initial weights vector for starting iteration.
3.5.2. Results with the Initial Values of Parameters
With the values of parameters as set in section 3.5.1, KEMIRA-sort algorithm implemented in python gave the result summarized in the Table 7 and Table 8.
In the first part of Table 7:
The columns WiXk=j=1niwi,j×xi,jk, i 1,2,,G give us the average performance of the alternatives in relation to each group of criteria;
Considering columns C1,C2, C3, C4, the number 1 (respectively 0) in the Table 6 indicates that the alternative is assigned (respectively not assigned) to the corresponding category.
In the second part of the Table 7:
the different performance thresholds for the different criteria groups are represented. Each group of criteria Gi, is assigned three thresholds α1lp, α2lp, α3lp, l 1,2,3.
The initial weights vector w0 satisfying the relations (4) and (5) allowed the algorithm to find the first assignment of alternatives to categories and the value of the objective function fopt0=26.
Table 7. Result with the initial values.

W1Xk

W2Xk

W3Xk

C1

C2

C3

C4

X1

0.549

0.872

0.384

0

0

1

0

X2

0.308

0.733

0.360

0

1

0

0

X3

0.356

0.881

0.211

0

0

0

1

X4

0.362

0.923

0.219

0

0

0

1

X5

0.527

0.918

0.437

0

0

0

1

X6

0.352

0.922

0.030

1

0

0

0

X7

0.404

0.812

0.030

1

0

0

0

X8

0.716

0.576

0.258

1

0

0

0

X9

0.670

0.789

0.027

1

0

0

0

X10

0.379

0.793

0.211

1

0

0

0

X11

0.562

0.875

0.65

0

0

0

1

X12

0.256

0.588

0.088

1

0

0

0

X13

0.211

0.588

0.140

1

0

0

0

X14

0.203

0.480

0.231

1

0

0

0

X15

0.495

0.862

0.058

1

0

0

0

α1l40%,

0.2864

0.3692

0.26

α2l45%,

0.3222

0.4153

0.2925

α3l60%,

0.4296

0.5538

0.39

3.5.3. Final Iteration Results
The results become stable at the hundred thousandth iteration, with the optimum of the objective function, fopt100000, always equal to 34 and an execution time of around 65 seconds.
The final weights vector
w100000=0.21, 0.2, 0.19, 0.18, 0.14, 0.06, 0.02; 0.375, 0.365, 0.230, 0.028; 0.530, 0.448, 0.020
satisfying the relations (4) and (5) computed by the algorithm allowed to find the final assignment of alternatives to categories and the value of the objective function fopt100000=34.
So after the hundred thousandth iterations, the categorization results no longer change, giving the result summarized in Table 8.
Table 8. Final iteration Results.

W1Xk

 W2Xk

 W3Xk

C1

C2

C3

C4

X1

0.533

0.898

0.473

0

0

0

1

X2

0.337

0.789

0.454

0

0

1

0

X3

0.363

0.847

0.248

0

0

1

0

X4

0.377

0.904

0.257

0

0

1

0

X5

0.548

0.963

0.522

0

0

0

1

X6

0.359

0.908

0.019

1

0

0

0

X7

0.403

0.739

0.019

1

0

0

0

X8

0.743

0.618

0.295

0

0

1

0

X9

0.733

0.750

0.023

1

0

0

0

X10

0.388

0.699

0.248

0

0

1

0

X11

0.554

0.829

0.551

0

0

0

1

X12

0.283

0.552

0.064

1

0

0

0

X13

0.203

0.552

0.113

1

0

0

0

X14

0.197

0.441

0.189

1

0

0

0

X15

0.540

0.820

0.040

1

0

0

0

α1l40%,

0.2972

0.3852

0.2204

α2l45%,

0.3343

0.4333

0.2479

α3l60%,

0.4458

0.5778

0.3306

4. Discussion
We find that, among the feasible solution of our mathematical programming problem (9), the ones with the best economic function value is given by the objective function value fopt100000=34. The optimal value of the economic function thus identified, is the one enables us to obtain a best categorization, presented in Table 8, associated to the set of weights
w100000= 0.21, 0.2, 0.19, 0.18, 0.14, 0.06, 0.02; 0.375, 0.365, 0.230, 0.028; 0.530, 0.448, 0.020
which is a solution of the mathematical programming problem (9).
As shown the results presented in Table 1, a best choices of the KEMIRA-Sort algorithm parameters allows us to have alternatives assigned to categories such a way to respect as much as possible all the empirical assignment examples given by the decision-maker (see Table 6). More specifically, the final assignment given by KEMIRA-Sort method, showed that:
“Ephalophus rufilatus” (X6), “Sylvicapra grimmia” (X7), “Geochelone sulcata” (X9), “Kobus
Ellipsiprymnus” (X12), “Alcelaphus buselaphus” (X13), “Hippotragus niger” (X14), “Lupulella adusta” (X15) are assigned to the worst category C1;
No alternatives assigned to category C2;
“Phacochoerus africanus” (X2), “Gazella dorcas” (X3), “Tragelaphus Seriptus” (X4), “cricetomys” (X8), “Gazella rufifrons” (X10), are assigned to C3 category;
“Hystrix Cristata” (X1), “Thryonomys swinderianus” (X5), “Struthio camelus” (X11) are assigned to the best category C4;
Two animals have been added among the best categoties C3 and C4 (comparing with examples of empirical assignment to categories of Table 6) which are respectively the “Tragelaphus Seriptus”(X4) and the “Struthio camelus”(X11).
Empirically:
Most of this result reflects the estimate given by the manager (playing the role of decision- maker) of the Wédbila Demonstration Farm (WDF) at the very start of our study, and this validate our findings. Note that using examples of empirical assignment to categories allowed us to elicit indirectly the performance thresholds, α1lp, α2lp, α3lp, l 1,2,3, of KEMIRA-Sort method. This way of eliciting parameters has already been successfully tested by Zheng et al. , Kadziński and Ciomek .
The information given by the decision-maker relative to weights elicitation was not rich (i.e. imprecise). Indeed, in each group, he had to give a ranking of criteria according to their importance i,1>̃1,2>̃>̃i,Gi,   i1,,G; i.e. we only have information on the ranking order of the criteria in each group, which is usually an information easy to provide by the DM. As a result, the set of weights to be investigated as a solution for the mathematical programming problem (9) was very large. This can result in a long algorithm execution time in case of large data dimension to find a suitable weights vector as solution for the mathematical programming problem (9).
Assessing the suitability of wild animal species for sustainable farm management is a new concept, as reported in . To the best of our knowledge, we have yet to see such an evaluation carried out by any other method. In the future, we plan to carry out such an evaluation using other methods, and compare the results in order to consolidate the evaluation approach we have proposed.
5. Conclusions
For sustainable management of a wildlife farm, the choice of animals is of prime importance. Evaluating alternatives (animals) based on criteria, using the KEMIRA-Sort method, enabled us to identify “Phacochoerus africanus” (X2), “Gazella dorcas” (X3), “Tragelaphus Seriptus” (X4), “cricetomys” (X8), “Gazella rufifrons” (X10), “Hystrix Cristata” (X1), “Thryonomys swinderianus” (X5), “Struthio camelus” (X11) as the most appropriate for the sustainable management of the Wédbila Wildlife Farm (WWF). Most of this result reflects the estimate given by the manager of the WWF at the very start of our study, and this supports our findings. Furthermore, to demonstrate the credibility of our results, we plan to apply the KEMIRA-Sort method to other contexts of sustainable livestock farm management, and to compare it with other multiple criteria sorting methods.
Abbreviations

CDPF

Centre de Développement et de Production Faunique

KEMIRA

KEmeny Median Indicator Ranks Accordance

MCDM

Multi-Criteria Decision Making

WWF

Wédbila wildlfe farm

Acknowledgments
We would like to thank the center for the development of wildlife production for providing us with the data required to complete this work (in French: Centre de Développement et de Production Faunique (CDPF)).
Author Contributions
Gilbert Tapsoba: Data curation, Software, Writing – original draft
Stéphane Aimé Metchebon Takougang: Conceptualization, Data curation, Methodology, Supervision, Writing – original draft
Désiré Ouédraogo: Data curation, Validation
Data Availability Statement
The data supporting the outcome of this research work has been reported in this manuscript.
Conflicts of Interest
The authors declare no conflicts of interest.
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    Tapsoba, G., Takougang, S. A. M., Ouédraogo, D. (2025). Multi-criteria Decision Making Using KEMIRA-Sort Method for Assessing the Suitability of Wild Animals to Promote Sustainable Management of a Wildlife Farm. American Journal of Applied Mathematics, 13(1), 1-12. https://doi.org/10.11648/j.ajam.20251301.11

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    Tapsoba, G.; Takougang, S. A. M.; Ouédraogo, D. Multi-criteria Decision Making Using KEMIRA-Sort Method for Assessing the Suitability of Wild Animals to Promote Sustainable Management of a Wildlife Farm. Am. J. Appl. Math. 2025, 13(1), 1-12. doi: 10.11648/j.ajam.20251301.11

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    Tapsoba G, Takougang SAM, Ouédraogo D. Multi-criteria Decision Making Using KEMIRA-Sort Method for Assessing the Suitability of Wild Animals to Promote Sustainable Management of a Wildlife Farm. Am J Appl Math. 2025;13(1):1-12. doi: 10.11648/j.ajam.20251301.11

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  • @article{10.11648/j.ajam.20251301.11,
      author = {Gilbert Tapsoba and Stéphane Aimé Metchebon Takougang and Désiré Ouédraogo},
      title = {Multi-criteria Decision Making Using KEMIRA-Sort Method for Assessing the Suitability of Wild Animals to Promote Sustainable Management of a Wildlife Farm},
      journal = {American Journal of Applied Mathematics},
      volume = {13},
      number = {1},
      pages = {1-12},
      doi = {10.11648/j.ajam.20251301.11},
      url = {https://doi.org/10.11648/j.ajam.20251301.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20251301.11},
      abstract = {In Burkina Faso, most of the wildlife farms hosting touristic visits, which started out with great enthusiasm, are now closed, highlighting the need for sustainable wildlife farm management. Although also of interest for wildlife farming, most of the study dealing with sustainable animal farm management are focus on livestock farming. This study was motivated by the need to provide an answer to the question of sustainable management of wildlife farming in Burkina Faso. To this end, our aim is to assess the suitability of wild animals to promote sustainable management of an ex-situ wildlife farm, hosting touristic visits. The implementation of a Multi-Criteria Decision Making (MCDM) process enabled us, among other things, to identify the wild animals and the criteria against which their suitability to promote sustainable management has been assessed. Our concern, on the one hand, to enable the stakeholders to easily express their preferences and thus fully adhere to the decision-making process, and on the other hand, to respect the heterogeneous dimensions implied by sustainability led us to choose the KEmeny Median Indicator Ranks Accordance-Sort (KEMIRA-Sort) multi-criteria sorting method. The evaluation phase was guided by the consideration of decision-maker’s preferences for ranking criteria and empirical examples of assigning wild animals to ordered categories of suitability to sustainable management. The complete implementation of the decision-making process enabled us to identify the categories of wild animals according to their suitability to promote sustainable management in the case study of the Wédbila wildlife farm (WWF) in Burkina Faso. More specifically, we showed that the group of wild animals most likely to promote WWF sustainable management was made up of pork-spicy, aulacodes, and red-necked ostrich. These results obtained was in line with empirically estimation of the principle stakeholder playing the role of Decision maker. These relevant results obtained thus validate the effectiveness of the KEMIRA-Sort multi-criteria sorting method. In addition, the flexibility of the proposed approach predisposes it, subject to adaptation, to be used in other sustainable management wildlife farm contexts.},
     year = {2025}
    }
    

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  • TY  - JOUR
    T1  - Multi-criteria Decision Making Using KEMIRA-Sort Method for Assessing the Suitability of Wild Animals to Promote Sustainable Management of a Wildlife Farm
    AU  - Gilbert Tapsoba
    AU  - Stéphane Aimé Metchebon Takougang
    AU  - Désiré Ouédraogo
    Y1  - 2025/01/14
    PY  - 2025
    N1  - https://doi.org/10.11648/j.ajam.20251301.11
    DO  - 10.11648/j.ajam.20251301.11
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 1
    EP  - 12
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20251301.11
    AB  - In Burkina Faso, most of the wildlife farms hosting touristic visits, which started out with great enthusiasm, are now closed, highlighting the need for sustainable wildlife farm management. Although also of interest for wildlife farming, most of the study dealing with sustainable animal farm management are focus on livestock farming. This study was motivated by the need to provide an answer to the question of sustainable management of wildlife farming in Burkina Faso. To this end, our aim is to assess the suitability of wild animals to promote sustainable management of an ex-situ wildlife farm, hosting touristic visits. The implementation of a Multi-Criteria Decision Making (MCDM) process enabled us, among other things, to identify the wild animals and the criteria against which their suitability to promote sustainable management has been assessed. Our concern, on the one hand, to enable the stakeholders to easily express their preferences and thus fully adhere to the decision-making process, and on the other hand, to respect the heterogeneous dimensions implied by sustainability led us to choose the KEmeny Median Indicator Ranks Accordance-Sort (KEMIRA-Sort) multi-criteria sorting method. The evaluation phase was guided by the consideration of decision-maker’s preferences for ranking criteria and empirical examples of assigning wild animals to ordered categories of suitability to sustainable management. The complete implementation of the decision-making process enabled us to identify the categories of wild animals according to their suitability to promote sustainable management in the case study of the Wédbila wildlife farm (WWF) in Burkina Faso. More specifically, we showed that the group of wild animals most likely to promote WWF sustainable management was made up of pork-spicy, aulacodes, and red-necked ostrich. These results obtained was in line with empirically estimation of the principle stakeholder playing the role of Decision maker. These relevant results obtained thus validate the effectiveness of the KEMIRA-Sort multi-criteria sorting method. In addition, the flexibility of the proposed approach predisposes it, subject to adaptation, to be used in other sustainable management wildlife farm contexts.
    VL  - 13
    IS  - 1
    ER  - 

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