Enhancing Personalized Decision-Making with the Balanced SPOTIS

Algorithm

Andrii Shekhovtsov

1,2 a

, Jean Dezert

3 b

and Wojciech Sałabun

1,2 c

National Institute of Telecommunications Szachowa 1, 04-894 Warsaw, Poland

West Pomeranian Univ. of Technology

Zołnierska 49, 71-210 Szczecin, Poland

The French Aerospace Lab - ONERA 91120 Palaiseau, France

Keywords:

Multi-Criteria Decision-Making, SPOTIS, Expected Solution Point.

Abstract:

Besides being very useful in solving decision-making problems, classical Multi-Criteria Decision-Making

(MCDM) techniques were designed to consider only proﬁt and cost criteria. However, in some cases, it can

be necessary to include more complex preferences of decision makers to better ﬁt the problem. In such cases,

modern MCDM methods such as Stable Preference Ordering Towards Ideal Solution (SPOTIS) can be used.

The SPOTIS method allows for providing the Expected Solution Point (ESP) as input data for the decision

problem. However, this approach can lead to unsatisfactory results if provided expert preferences are unreli-

able. To solve this problem, we propose a novel Balanced SPOTIS method with an ESP conﬁdence parameter,

which allows us to obtain a solution that is balanced between objectively ideal solutions and subjective expert

preferences. We show how this new approach works in the case study of selecting a used car and provide an

in-depth analysis of the problem using the new ESP conﬁdence parameter for sensitivity analysis. Finally, to

underline the advantages of the proposed approach, we compare it with the Expected Solution Point - Charac-

teristic Objects Method (ESP-COMET).

1 INTRODUCTION

Multi-Criteria Decision Making (MCDM) is a part of

operational research that concentrates on providing

comprehensive tools and algorithms for solving and

analyzing decision-making problems. Such problems

usually involve different criteria and decision alterna-

tives and require some domain knowledge to evaluate

them (Torres et al., 2024). MCDM methods can be

helpful in aiding the expert or a decision maker in the

appropriate and satisfying solution of decision prob-

lems based on the input and preferences provided by

the expert (Shekhovtsov, 2022).

Most of the MCDM methods concentrate on ﬁnd-

ing the optimal solution in the set of decision alter-

natives based on the criteria types and importance

weights. However, this narrows the ability to per-

sonalize the decision-making process, mostly because

most MCDM methods allow only proﬁt (maximiza-

tion) and cost (minimization) criteria types. However,

https://orcid.org/0000-0002-0834-2019

https://orcid.org/0000-0003-3474-9186

https://orcid.org/0000-0001-7076-2519

there are different types of problems in which the type

of ”target” criterion is involved (Jahan et al., 2012).

The target criterion indicates that this criterion should

not be maximized or minimized, but our expected (or

most suitable) value is somewhere between the mini-

mum and maximum values for this criterion.

There are methods designed to operate on target

criteria through the input of the decision maker, such

as Stable Preference Ordering toward the Ideal So-

lution (SPOTIS) (Dezert et al., 2020), Characteris-

tic Objects METhod (COMET) (Shekhovtsov et al.,

2023), and Reference Ideal Method (RIM) (Cables

et al., 2016). While the COMET method requires the

preparation of the pairwise comparison matrix, both

SPOTIS and RIM methods allow the deﬁnition of the

expected (target) solution in the form of the vector of

expected values for the different criteria. For exam-

ple, in material selection decision makers can expect

some speciﬁc value for material’s property, making

this an expected solution value. These methods are

also notable because of their robustness, as they are

resistant to rank reversal by design. Classical MCDM

methods can usually be extended with advanced nor-

malization techniques to include target criteria in the

264

Shekhovtsov, A., Dezert, J. and Sałabun, W.

Enhancing Personalized Decision-Making with the Balanced SPOTIS Algorithm.

DOI: 10.5220/0013119800003890

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2025) - Volume 3, pages 264-271

ISBN: 978-989-758-737-5; ISSN: 2184-433X

problem (Jahan et al., 2012), but the potential and us-

ability of such extensions are rather low and limited

to concrete decision problems.

In this study, we focus on the SPOTIS method,

which is a relatively new decision support method

proposed by Dezert et al. (Dezert et al., 2020).

This method allows the decision maker to provide

the Expected Solution Point (ESP) to personalize the

decision-making process to suit the speciﬁc needs of

the decision maker. However, this approach has some

practical limitations. Changes in ESP can have a great

impact on the ﬁnal ranking, which implies that ESP

provided by inexperienced or not conﬁdent decision

makers can lead to an unsatisfactory solution to the

problem.

The main contribution of the paper is:

• to propose a Balanced SPOTIS method, which

extends the standard algorithm of the SPOTIS

method with ESP conﬁdence parameter, which al-

lows for balancing between rankings built towards

ideal and expected solutions.

• The usefulness of the method is demonstrated in

the case study of choosing a used car based on

mileage, price, and year of manufacture.

• We demonstrate how to conduct a solution sen-

sitivity analysis with the new method, which can

be used to better understand the problem and the

preferences of the decision maker, providing a

more reliable and informed decision.

• Additionally, we show the comparison with the

ESP-COMET method, as it can handle several

ESP points, making these methods comparable.

The rest of the paper is structured as follows. In

Section 2, we describe some related works on the

topic. In Section 3, we describe the original SPOTIS

method, and in Section 3.3, we describe our proposal

on the extension of this method. Then, in Section 4,

we demonstrate the application of this new method in

a practical case study of choosing a used car in Poland

and we make the analysis of the decision made de-

pending on the conﬁdence factor chosen by the de-

cision maker. Next, in Section 5, we summarize the

research results and propose some possible perspec-

tives.

2 RELATED WORKS

Most popular MCDA methods, such as the Tech-

nique for Order of Preference by Similarity to Ideal

Solution (TOPSIS) and the Analytic Hierarchy Pro-

cess (AHP), suffer from the rank reversal paradox,

which can make the results unreliable in certain cases

(Chakraborty, 2022; Yulistia et al., 2023). This para-

dox typically arises when the set of alternatives is

modiﬁed, causing shifts in the previously established

ranking. In such cases, it can be difﬁcult to determine

which alternative should be ranked higher due to con-

ﬂicting results.

To address the rank-reversal problem, many ex-

tensions of the affected methods have been proposed

(Yulistia et al., 2023). However, it seems more bene-

ﬁcial, in terms of simplicity, to develop methods that

are inherently robust to this issue by design. Methods

such as RIM (Cables et al., 2016) and SPOTIS (Dez-

ert et al., 2020) rely on data normalization and crite-

ria bounds to create decision models that are resistant

to rank reversal. Other approaches, like the COMET

and its extension ESP-COMET (Shekhovtsov et al.,

2023), use fuzzy logic and rule-based systems to

model the full domain of the decision problem.

These methods have demonstrated their applica-

bility and usefulness in practical case studies. For

example, Torres successfully applied the SPOTIS

method for the selection of unmanned aerial ve-

hicle systems (Torres et al., 2024). Furthermore,

Shekhovtsov investigated the possibility of apply-

ing the SPOTIS method to personal decision-making

problems, incorporating the ESP approach within the

SPOTIS framework (Shekhovtsov, 2022).

The RIM was applied by Hsiung et al. in a

case study assessing the risk of COVID-19 in hos-

pital screening procedures (Hsiung et al., 2023). To

address potential uncertainty in the data, the authors

used Single-Valued Trapezoidal Neutrosophic Sets in

combination with the Best-Worth Method (BMW),

followed by the RIM method, to rank the risk models

and identify areas for improvement. Similarly, Patil et

al. (Patil and Majumdar, 2021) sought to identify at-

tributes that inﬂuence the use of two-wheelers in India

and prioritized these attributes using several MCDA

methods, including the RIM method.

The COMET method was applied by (Wi˛eck-

owski and Zwiech, 2021) to select the most energy-

efﬁcient material. In other work, (Kizielewicz and

Dobryakova, 2020) proposed using the COMET

method to assess the performance of NBA players.

They showed that, even with missing data, it is possi-

ble to accurately rank players.

Despite their high applicability, both the COMET

and RIM methods have certain limitations. The

COMET method suffers from the curse of dimension-

ality and requires the creation of a pairwise compari-

son matrix, which can be time consuming. The RIM

method, on the other hand, is easier to use and builds

a ranking towards a reference ideal interval. However,

Enhancing Personalized Decision-Making with the Balanced SPOTIS Algorithm

265

it is not possible to prioritize solutions in the interval

leading to a tie for all alternatives within the reference

interval.

Our proposed method, Balanced SPOTIS, ad-

dresses these issues. Although it remains as easy to

use and understand as the original SPOTIS method, it

allows the incorporation of both Ideal Solution Points

(ISP) and Expected Solution Points (ESP), along with

the ability to adjust the importance of ESP using a

conﬁdence parameter α. This approach not only en-

ables the preference of ESP over ISP to some ex-

tent but also offers analytical advantages, providing

deeper insights into the decision problem and prefer-

ences of decision makers.

3 METHODOLOGY

3.1 Stable Preference Ordering

Towards Ideal Solution (SPOTIS)

The SPOTIS method is a MCDA method proposed

by (Dezert et al., 2020). This method uses reference

objects to evaluate decision alternatives. However, in

contrast to other methods, which usually deduce ref-

erence objects based on the data in the decision ma-

trix, the SPOTIS method requires them to be deﬁned

by the decision-maker.

To apply the SPOTIS method, the decision maker

must ﬁrst deﬁne the data boundaries that will form

reference objects for alternative evaluation. For each

criterion C

( j ∈ {1, 2,.. .,N}) the maximum S

max

and

minimum S

min

bounds must be deﬁned. Next, the ISP

∗

= {S

∗

,. ..S

∗

,. ..S

∗

} is selected as S

∗

= S

max

for

the proﬁt criterion and as S

∗

= S

min

for the cost crite-

rion. The decision matrix is deﬁned as S = (S

i j

)

M×N

where S

i j

is the attribute value of the i-th alternative

for the j-th criterion C

The algorithm of the SPOTIS method presented in

(Dezert et al., 2020) is as follows:

Step 1. Calculation of the normalized distances to

ISP (1).

i j

∗

) =

i j

− S

∗

max

− S

min

(1)

Step 2. Calculation of the weighted normalized dis-

tances from ISP d(A

∗

) ∈ [0,1], according to (2).

d(A

∗

) =

∑

j=1

i j

∗

) (2)

Step 3. Determine the ﬁnal ranking by ordering the

alternatives by the values d(A

∗

). The better alter-

natives have smaller values of d(A

∗

The interesting features of this method are its sim-

plicity, its robustness to the rank reversal paradox, and

also its ability to use the so-called Expected Solution

Point (ESP), which allows the deﬁnition of an out-

come expected by the decision maker and builds the

ranking toward this point instead of the ISP. In order

to use the SPOTIS method with selected ESP S

one

should apply the normal SPOTIS procedure, substi-

tuting values of Ideal Solution Point S

∗

to values of

ESP S

. The decision maker should choose the val-

ues of S

to ﬁt the given decision problem. How-

ever, it is essential to ensure that the chosen ESP is

within the scope of the problem, i.e., S

must satisfy

min

≤ S

max

for every j.

3.2 Expected Solution Point COMET

The Expected Solution Point COMET was devel-

oped to address the dimensionality curse present in

the COMET method (Shekhovtsov et al., 2023). To

overcome this challenge, the ESP-COMET method

was introduced as an alternative approach to build-

ing the pairwise comparison matrix in the original

COMET method. In this approach, the expert or de-

cision maker ﬁrst deﬁnes one or more Expected So-

lution Points (ESPs) based on their preferences and

domain expertise. Each ESP vector contains N val-

ues, where N represents the number of criteria in the

decision problem.

The short version of the algorithm is deﬁned as

follows.

Step 1. Deﬁne the criteria for the decision problem

and assign fuzzy numbers to represent each criterion.

Deﬁne ESP points which should be used to build the

pairwise comparison matrix.

Step 2. Use the Cartesian product of fuzzy numbers

to create a set of Characteristic Objects representing

all possible combinations.

Step 3. Use the deﬁned Expected Solution Points to

identify pairwise comparison matrix, rather than us-

ing manual comparisons. The preference values for

the Characteristic Objects then deﬁned based on the

identiﬁed matrix.

Step 4. Convert each characteristic object and its

preference value into a fuzzy rule.

Step 5. Use the fuzzy rule base and Mamdani’s infer-

ence method to evaluate and rank alternatives. Alter-

natives with a higher preference value are better.

The complete algorithm of the ESP-COMET

method is presented in (Shekhovtsov et al., 2023),

while implementation of the method can be found

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

266

and used in pymcdm Python library (Kizielewicz et al.,

2023).

3.3 Proposed Approach

The SPOTIS method is quite effective and can be

helpful even in complex decision-making problems.

If ESP is used in the SPOTIS method it can also be

useful in the case of personalized decision-making,

where the target criteria appear in the problem (Jahan

et al., 2012; Shekhovtsov, 2022). However, this ap-

proach has some limitations because the selection of

ESP has a critical impact on the ﬁnal ranking, which

can lead to unsatisfactory outcome.

To address this issue, we propose the improve-

ment of the SPOTIS method named Balanced SPO-

TIS (B-SPOTIS), as well as a sensitive analysis algo-

rithm that can be used to comprehensively analyze the

decision problem. This hybrid approach allows users

to deﬁne the level of conﬁdence (or trust) in ESP, al-

lowing them to perform a ﬁner analysis of the deci-

sion problem.

The application of the proposed B-SPOTIS

method requires the deﬁnition of the criteria bounds

min

and S

max

for all criteria C

and the ESP values

. Next, the decision maker should choose which

criteria values are preferred if they are smaller and

which are preferred if they are larger than ESP. Based

on this information, it is necessary to deﬁne the Ideal

Solution Point S

∗

as S

min

if the decision maker prefers

the values smaller than ESP or as S

max

if larger values

are preferred than ESP for the jth criterion. Next, it is

required to choose the value of the conﬁdence param-

eter of the ESP α ∈ [0,1], which regulates the trust of

the decision maker to the provided values.

When all values are deﬁned, the B-SPOTIS proce-

dure can be applied in three steps as follows:

1. Apply the standard SPOTIS algorithm to calculate

the weighted normalized distances d(A

) from

ESP S

. Those values will allow one to choose

the closest alternative to ESP.

2. Apply the standard SPOTIS algorithm to calculate

the weighted normalized distances d(A

∗

) from

the ISP S

∗

. Those values will allow one to choose

the closest alternative to the ISP.

3. Calculate the ﬁnal compromise (i.e. balanced)

distances P

= d(A

∗

,α) for each alternative

using the convex combination of d(A

∗

) and

d(A

) given in (3):

= α · d(A

) + (1 − α) · d(A

∗

) (3)

Manipulation of the ESP conﬁdence parameter α

can be useful to provide certain information on which

alternatives are closer to the objectively chosen Ideal

Solution and which are closer to the subjectively se-

lected Expected Solution. This type of analysis can

be useful to get a different perspective on the problem

and the preferences chosen, which can help to make

more deliberate and informed decisions.

4 EXPERIMENTS AND RESULTS

4.1 Case Study

To demonstrate the application of the Balanced SPO-

TIS, we present the case study of choosing a used car

in Poland. In Table 1, we present the primary crite-

ria involved in the decision problem. The criterion

describes the mileage of the car in thousands of

kilometers; criterion C

is a price and is deﬁned in

thousands of Polish złoty (PLN), as the data were col-

lected from the Polish Web pages. The last criterion,

, is a production year.

For this example, we consider eight decision al-

ternatives in which the criteria data are within the

range of minimum and maximum criteria values (S

min

and S

max

) deﬁned by the decision maker. The impor-

tance weights of the criteria presented in Table 1 were

identiﬁed by the decision maker using the RANking

COMparison method (RANCOM), which creates nu-

merical weights based on the importance established

by the expert (Wi˛eckowski et al., 2023).

Table 1: Criteria description.

Name Unit w

Type S

min

max

Mileage k km 0.33 Min 70 360

Price k PLN 0.56 Min 35 70

Year Year 0.11 Max 2013 2018

The data collected are presented in Table 2. The

alternatives A

- A

were established based on adver-

tisements for one speciﬁc car model, but from differ-

ent advertisements. We also include the ESP S

de-

ﬁned by the decision maker, as well as the Ideal So-

lution Point S

∗

deﬁned based on the types and limits

of criteria (see Table 1). It can be seen that both ESP

and ISP set the criterion C

(production year) to 2018,

and none of the alternatives considered can satisfy this

value. However, ESP and ISP differ in terms of car

price and mileage, which presents subjective prefer-

ences of the decision maker and an objective ideal so-

lution.

We then calculate three preference vectors and

three ranking using the standard algorithm of the

SPOTIS method with regard to the Ideal Solution

Point (ranking P

(∗)

and ranking R

(∗)

), with regard to

Enhancing Personalized Decision-Making with the Balanced SPOTIS Algorithm

267

Table 2: Alternatives data (A

) with ESP S

and ISP S

∗

94.0 69.9 2017

297.0 42.0 2013

205.0 68.9 2015

360.0 36.9 2014

86.0 59.9 2017

79.6 63.8 2017

113.0 56.9 2015

171.0 58.0 2016

110.0 45.0 2018

∗

70.0 35.0 2018

the Expected Solution Point (P

(+)

and R

(+)

) and us-

ing the proposed Balanced SPOTIS algorithm with

the conﬁdence parameter ESP α set to 0.5 (P

(0.5)

and

(0.5)

). Those preferences and rankings for all alter-

natives are presented in Table 3. Keep in mind that

both SPOTIS and Balanced SPOTIS evaluate alterna-

tives in terms of distance to the Ideal or Expected So-

lution. Therefore, smaller values of P

indicate better

alternatives.

To analyze the results presented in Table 3, we

will concentrate on the ﬁrst three ranking positions.

As we can see, in the case of ranking R

(∗)

built to-

wards ISP, the best alternatives are A

, A

and A

however, in the case of both R

(+)

and R

(0.5)

rankings,

the order of the best alternatives is A

, A

and A

Two alternatives, A

and A

, are especially interest-

ing for our analysis. It can be seen that A

is closest

to ESP and A

is closest to ISP and if we analyze pref-

erences obtained using the Balanced SPOTIS method

with α = 0.5 (see P

(0.5)

) we can see that these two al-

ternatives performed very similar (A

got 0.3632 and

0.3626), therefore this can be seen as a tie from a

certain point of view. However, the decision maker

decided that for his case, alternative A

is the best,

showing that in addition to being closer to ISP than

ESP, it can be a good solution for the personalized

decision-making process.

We also add the resulted preference values for the

ESP S

and ISP S

∗

vectors in Table 3. It can be seen

that in the ranking built towards ISP, the ESP pref-

erence is 0.2055, and for the ranking built towards

ESP, the ISP preference is the same value (0.2055).

However, in the results of the Balanced SPOTIS with

α = 0.5, both ESP and ISP received a preference value

equal to 0.1028. This property is derived from the lin-

ear behavior of the SPOTIS algorithm and is proved

as follows.

Theorem. In the case of using α = 0.5 ESP, ISP and

all the alternatives places between them will be eval-

uated equally.

Table 3: Preferences P

and rankings R

for ESP (+),

ISP (∗) and Balanced SPOTIS with α = 0.5 algorithms.

(∗)

(+)

(0.5)

(∗)

(+)

(0.5)

0.6077 0.4386 0.5232 7 6 7

0.4803 0.3708 0.4256 4 5 4

0.7620 0.5565 0.6593 8 8 8

0.4484 0.5021 0.4752 2 7 6

0.4386 0.2877 0.3632 1 2 2

0.4937 0.3574 0.4256 5 4 5

0.4653 0.2598 0.3626 3 1 1

0.5269 0.3214 0.4242 6 3 3

0.2055 0.0000 0.1028 - - -

∗

0.0000 0.2055 0.1028 - - -

Proof. Consider N > 2 criteria C

( j = 1,2,.. ., N)

with their importance weights w

≥ 0

( j = 1,2,. .., N), and an alternative A

with its

score vector S

= [S

,. .. ,S

i j

,. .. ,S

]. Suppose that

for any criterion C

the condition S

∗

≤ S

i j

≤ S

∗

satisﬁed, where S

∗

is the j-th component of ISP point

and S

is the j-th component of ESP point, which

can be written more concisely as S

∗

≤ S

. The

distance of A

to ISP and the distance of A

to ESP

are respectively given by

d(A

∗

) =

∑

j=1

i j

− S

∗

(4)

d(A

) =

∑

j=1

i j

− S

(5)

where δ

≜ |S

max

− S

min

The Balanced SPOTIS solution is given by

= α · d(A

) + (1 − α) · d(A

∗

) (6)

and for α = 1/2 we get

∑

j=1

i j

− S

∑

j=1

i j

− S

∗

(7)

∑

j=1

i j

− S

| + |S

i j

− S

∗

(8)

Because we have the inequality S

∗

≤ S

i j

≤ S

∗

sat-

isﬁed, we get |S

i j

− S

| = S

− S

i j

and |S

i j

− S

∗

| =

i j

− S

∗

. Therefore |S

i j

− S

| + |S

i j

− S

∗

| = S

−

∗

, whence for any alternative A

we always have

∑

j=1

−S

∗

, which is actually independent

of the alternative scores S

i j

. In this very particular bal-

anced case where S

∗

≤ S

with α = 1/2 none of

the alternatives can be preferred and we have a total

uncertain situation showing indifference between all

the alternatives. The similar remark holds for the case

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

268

where the condition S

≤ S

i j

≤ S

for j = 1, 2,. .., N

is satisﬁed (i.e. S

≤ S

∗

holds) because we will

get P

∑

j=1

∗

−S

This behavior implies that there is no possibility

to differentiate or order alternatives between ESP and

ISP when α = 0.5. This reﬂects a situation with full

uncertainty on which alternative should be preferred

as it lies within a range between equally preferred val-

ues. To ensure that this paradox does not interfere

with the results, it is advisable to always investigate

several possible α values or to ensure that there are

no alternatives between Expected and Ideal solutions.

Going further with the analysis of the rankings

presented in Table 3 we can check the values of

the Weighted Spearman correlation coefﬁcient r

be-

tween the rankings (Pinto da Costa and Soares, 2005).

The correlation between the rankings R

(∗)

and R

(+)

0.4709, which implies that these rankings are quite

different but not uncorrelated. Then, r

correlation

between R

(0.5)

and R

(∗)

is 0.5873, but for pair R

(0.5)

and R

(+)

we got the value 0.9630. This shows that a

balanced ranking is much closer to the ranking built

toward ESP than ISP. It can be expected that a bal-

anced ranking would have a similar correlation to the

ESP and ISP rankings. However, it is very depen-

dent on the decision problem and the correlation co-

efﬁcient used. In the case of the Weighted Spearman

correlation, R

(0.5)

is closer to R

(+)

due to the similar

heading of the ranking, as this correlation coefﬁcient

puts more weight on the top alternatives.

4.2 Sensitivity Analysis

As mentioned earlier, the ESP conﬁdence parameter,

α, can be used to analyze which alternatives are closer

to the Expected Solution Point (ESP) and which are

closer to the Ideal Solution Point (ISP). This analy-

sis can be performed by gradually changing the value

of α within the range [0, 1], using a chosen step size.

Figure 1 presents the proposed sensitivity analysis al-

gorithm.

Define the decision

problem including:

- Decision matrix

- Criteria weights and bounds

- Ideal Solution Point (ISP)

- Expected Solution Point (ESP)

Compute

ranking

toward ESP

Compute

ranking

toward ISP

Compute Balanced SPOTIS

rankings using different

values of α parameter

Analyze changes

in the rankings

1 2

Figure 1: Flowchart of the sensitivity analysis process.

In the current research, we demonstrate the appli-

cation of this sensitivity analysis framework with step

∆α = 0.1. It is worth mentioning that according to

Equation (3), using α = 0.0 will provide the same re-

sults as ISP SPOTIS, and the use of α = 1.0 is the

same as applying ESP SPOTIS. The results of the cal-

culations are shown in Figure 2.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

(ISP SPOTIS) (ESP SPOTIS)

ESP confidence α

Position in ranking

Figure 2: Changes in alternatives’ positions in ranking for

different values of α parameter.

From the analysis of Figure 2, we can see that

there are not many changes in the ranking, because

the chosen ESP and ISP are similar. However, there

are two interesting cases that we want to discuss in

detail, speciﬁcally alternatives A

and A

. The alter-

native A

at the sixth position for α = 0.0, and the

increase of α improved the positions of the alterna-

tive A

, and in the ranking for α = 1.0, it took the

third position. It is interesting because most of the

alternatives do not change their rankings more than

one position up or down. If we look closer to Ta-

ble 2, this change can easily be explained: while A

performs relatively poorly with regard to ISP because

of the large mileage and price, it is closer to ESP

than some other alternatives because ESP allows for a

higher price and mileage. However, the alternative A

changes its position from seventh in the ranking with

α = 1.0 to second for α = 0.0. At ﬁrst sight, it can be

very strange that this alternative got such a high posi-

tion, performing badly in mileage and year. However,

the most important criterion for the decision-maker is

price, and this alternative has the lowest price among

all alternatives.

To better explain how the ESP conﬁdence fac-

tor α inﬂuences the results of the Balanced SPO-

TIS method, we show in Figure 3 how the prefer-

ence function changes depending on different val-

ues of α. We choose to present the plots only for

α ∈ {0.1,0.5,0.9}, as these three values are most

signiﬁcant in understanding how the ESP conﬁdence

factor inﬂuences preferences. The three subplots of

Figure 3 show the change of preferences for the three

α values based on criteria C

and C

when C

is set to

Enhancing Personalized Decision-Making with the Balanced SPOTIS Algorithm

269

70 140 215 290 360

- Mileage

- Price

α = 0.1

ISP S

ESP S

0.00

0.25

0.50

0.75

1.00

70 140 215 290 360

- Mileage

- Price

α = 0.5

ISP S

ESP S

0.00

0.25

0.50

0.75

1.00

70 140 215 290 360

- Mileage

- Price

α = 0.9

ISP S

ESP S

0.00

0.25

0.50

0.75

1.00

Figure 3: Visualization of the preference function shape for α ∈ {0.1,0.5,0.9}. For all evaluated points C

is set to 2018.

2018 for all the evaluated points. The direction of the

criteria and the weights are drawn from Table 1. For

each subplot, the ESP is marked with a red plus sym-

bol and the ISP is marked with a red star symbol for

convenience. The black circles with white numbers

indicate the position of the eight alternatives.

It can be seen that for α = 0.1, the yellow region

of the smallest distances (more preferred solutions) is

placed around ISP, but for α = 0.9, the region with

the most preferred solutions is located around ESP,

which is in agreement with how the ESP conﬁdence

parameter is expected to work. However, in the case

of α = 0.5, it can be observed that there is no yellow

region around ISP or ESP, but a light green region

that determines the equally preferred alternatives be-

tween ESP and ISP, as mentioned earlier in the pa-

per. It is also worth noting that the alternatives A

and

, which were ranked best for both models, are visu-

ally closer to ESP and ISP than the other alternatives.

When A

appears to be close to both ESP and ISP, it

ranked lower than A

and A

due to the lower value of

the criterion C

(year).

4.3 Comparison Between Balanced

SPOTIS and ESP-COMET

To highlight the advantages of the Balanced SPOTIS

method, we also present a comparison with the ESP-

COMET method. This method was chosen because

of the possibility to provide several expected solution

points and build the ranking based on them. How-

ever, the procedure of the ESP-COMET doesn’t pro-

vide the ability to prioritize one or another ESP. An-

other limitation is that there is no possibility to apply

criteria weights in this method.

Equation 9 shows the ranking produced using

the ESP-COMET method (R

(E)

). The ESP-COMET

ranking takes into account both the ESP and ISP

points utilized in the SPOTIS calculations. In the

ESP-COMET ranking, the alternative A

holds the top

position, which is the same as in the SPOTIS ranking

toward ISP. However, the alternative A

, which ranked

second in the ESP-COMET method, is lower in the

other rankings (see Table 3). This is notable since A

has criteria values similar to A

and may be seen as a

better candidate for second place than A

It is important to note that the SPOTIS method in-

corporates the criteria weights of Table 1, while the

ESP-COMET method treats all criteria equally. Given

that Price is the most important criterion, it is reason-

able to expect A

to rank higher and A

lower, as re-

ﬂected in the SPOTIS results. A similar discrepancy

can be observed with A

(E)

= [7 4 8 6 2 5 1 3]

(9)

In addition, in Figure 4, we present a visualization

of the preference function in the ESP-COMET model

for two criteria, with the third criterion held constant.

Note that in the COMET method, more preferred al-

ternatives receive higher preference values, so we re-

versed the colormap for convenience. Brighter, more

yellow regions represent more preferred alternatives.

The orange dots and lines indicate the grid of Charac-

teristic Objects.

70 140 215 290 360

- Mileage

- Price

ESP

0.00

0.25

0.50

0.75

1.00

Figure 4: Visualization of the preference function shape

for ESP-COMET with two ESP selected. For all evaluated

points C

is set to 2018.

The region between two ESPs (or an ESP and ISP)

in Figure 4 is particularly interesting. It shows that, in

ICAART 2025 - 17th International Conference on Agents and Artiﬁcial Intelligence

270

addition to the highly preferred yellow region, there

are two areas with slightly lower preference values.

This situation may seem counterintuitive. While hav-

ing all alternatives between the ISP and ESP receive

the same preference values, as observed in Balanced

SPOTIS with α = 0.5, seems more intuitive to us,

the differing preferences in this area can be harder

to justify. With B-SPOTIS, it is possible to eval-

uate multiple values of α, which is not possible in

ESP-COMET. Consequently, when decision-makers

encounter cases where two very similar alternatives

within the expected/ideal value range have different

preference values, it can lead to confusion.

5 CONCLUSIONS

In this paper, we proposed a Balanced SPOTIS

method, which can be helpful for personalized

decision-making and analysis of the decision prob-

lem. The usefulness of the proposed approach was

demonstrated in the case study of choosing a used

car, where the decision maker provided the ESP but

preferred the alternative, which was the best in the

ISP ranking. ESP trust (or conﬁdence) parameter

α can be very useful in such situations when it is

necessary to perform a sensitivity analysis, investi-

gating the decision problem from different perspec-

tives. It can also be useful in cases where we do not

have too much conﬁdence in the preferences provided

by the expert. We also performed a comparison be-

tween the Balanced SPOTIS and ESP-COMET meth-

ods, highlighting certain drawbacks of ESP-COMET.

Although ESP-COMET allows for the inclusion of

any number of ESPs, it faces issues such as the curse

of dimensionality and lacks a weighting mechanism,

leading to equal treatment of all criteria.

This work opens some interesting future research

directions. The Balanced SPOTIS method can be ex-

tended further to address the issue of aggregating sev-

eral ESP or expert preferences to provide a compre-

hensive compromise solution. We also want to fur-

ther investigate the properties of the proposed method

and compare its performance with different MCDM

methods in more real-life case studies. In the future,

we also plan to extend B-SPOTIS to handle imprecise

data.

ACKNOWLEDGMENTS

The work was supported by the National Science Cen-

tre 2021/41/B/HS4/01296.

REFERENCES

Cables, E., Lamata, M. T., and Verdegay, J. L. (2016). RIM-

reference ideal method in multicriteria decision mak-

ing. Inf. Sci., 337:1–10.

Chakraborty, S. (2022). TOPSIS and Modiﬁed TOP-

SIS: A comparative analysis. Decision Analytics J.,

2:100021.

Dezert, J., Tchamova, A., Han, D., and Tacnet, J.-M.

(2020). The SPOTIS rank reversal free method for

multi-criteria decision-making support. In In Proc. of

Fusion 2020 Int. Conf., pages 1–8. IEEE.

Hsiung, M.-C., Tung, T.-H., Lo, H.-W., Hou, Y.-S., Ma,

J. C., and Liou, J. J. (2023). A hybrid model to as-

sess the risk of COVID-19 in hospital screening pro-

cedures under uncertain information. Int. J. of Disas-

ter Risk Reduction, 96:103911.

Jahan, A., Bahraminasab, M., and Edwards, K. L. (2012).

A target-based normalization technique for materials

selection. Materials & Design, 35:647–654.

Kizielewicz, B. and Dobryakova, L. (2020). MCDA based

approach to sports players’ evaluation under incom-

plete knowledge. Proc. Comp. Sci., 176:3524–3535.

Kizielewicz, B., Shekhovtsov, A., and Sałabun, W.

(2023). pymcdm—the universal library for solving

multi-criteria decision-making problems. SoftwareX,

22:101368.

Patil, M. and Majumdar, B. B. (2021). Prioritizing key

attributes inﬂuencing electric two-wheeler usage: a

multi criteria decision making (MCDM) approach–

A case study of Hyderabad, India. Case Studies on

Transport Policy, 9(2):913–929.

Pinto da Costa, J. and Soares, C. (2005). A weighted rank

measure of correlation. Australian & New Zealand J.

of Statistics, 47(4):515–529.

Shekhovtsov, A. (2022). Decision-making process cus-

tomization by using expected solution point. Proc.

Comp. Sci., 207:4556–4564.

Shekhovtsov, A., Kizielewicz, B., and Sałabun, W. (2023).

Advancing individual decision-making: An extension

of the characteristic objects method using expected so-

lution point. Inf. Sci., 647:119456.

Torres, P. S., Gomes, C. F. S., and Santos, M. D. (2024).

Selection of unmanned aerial vehicle systems for bor-

der monitoring using the MPSI-SPOTIS method. J. of

Def. Analytics and Log., 8(1):80–104.

Wi˛eckowski, J., Kizielewicz, B., Shekhovtsov, A., and

Sałabun, W. (2023). RANCOM: A novel approach

to identifying criteria relevance based on inaccuracy

expert judgments. Eng. Appl. of AI, 122:106114.

Wi˛eckowski, J. and Zwiech, P. (2021). Can weighting meth-

ods provide similar results in MCDA problems? Se-

lection of energetic materials study case. Proc. Comp.

Sci., 192:4592–4601.

Yulistia, Ermatita, Samsuryadi, and Abdiansah (2023). New

AHP Improvement using COMET Method Character-

istic to Eliminate Rank Reversal Phenomenon. Int. J.

of Adv. Comp. Sci. and Appl., 14(11).

Enhancing Personalized Decision-Making with the Balanced SPOTIS Algorithm

271