Use of the Analytic Hierarchy Process (AHP) method to assess the urban quality of life of seniors

Agnieszka Ptak-Wojciechowska

doi:10.37190/arc240409

Summary

The article presents the application of the AHP method in assessing the quality of life of elderly people in the urban environment. The research methodology and criteria for evaluating urban space in terms of seniors’ needs are discussed. Special attention is paid to practical aspects of using the method in senior-friendly spatial planning.

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2024

4(80)

Agnieszka Ptak-Wojciechowska*

Use of the Analytic Hierarchy Process (AHP) method

to assess the urban quality of life of seniors in terms

of architectural and urban planning aspects

DOI: 10.37190/arc240409

Published in open access. CC BY NC ND license

Abstract

Cities should aim to provide a high quality of life (QoL) for all residents. However, the urban structure often fails to meet the spatial needs of

senior citizens, despite ongoing demographic changes. Furthermore, there is a lack of scientic assessment instruments that could be used to evaluate

the architectural and urban aspects of a city and guide improvements. Although popular urban rankings may be used for urban policy development,

their results are often misinterpreted by their recipients. The use of multi-criteria decision-making (MCDM) methods can facilitate the process of

comparing city areas, increase the transparency of the evaluation, and involve dierent stakeholders in the evaluation process. Machine learning

(ML) could be an interesting extension to commonly used statistical methods. This paper presents the latest research methods on the urban QoL of

seniors, using a multi-criteria analysis of ve neighbourhoods in Poznan as an example. The Analytic Hierarchy Process (AHP) method is discussed

as part of the author’s tool for measuring the perceptual assessment of senior citizens and the expert assessment of architects and urban planners, in

terms of functional and spatial aspects. The AHP method’s eectiveness is demonstrated, and the results can support city authorities, designers, and

researchers. Additionally, this research presents directions for its development using ML methods.

Key words: participatory methods, multi-criteria methods, quality of life in cities, machine learning, ageing societies

Introduction

According to projections, the number of people aged

65 and over worldwide will be around 16% of the popu-

lation in 2050 (United Nations 2022), and the number of

urban dwellers will account for two-thirds of the popula-

tion (United Nations 2020). Climate change and its nega-

tive impacts threaten people’s lives, health and property

(Hoornweg, Sugar, and Trejos Gómez 2011). Cities are

inuential in amplifying the eects of storms, heavy rain-

fall and heat waves (Pörtner et al. 2022), and the shaping

of urban space has an undeniable impact on quality of life

(Wojnarowska 2016). Urban quality of life (QoL) assess-

ment tools (e.g., guidelines, rankings) are considered to

have potential in the context of urban planning and policy

(Lowe et al. 2015). The rationale for addressing the top-

ic was the observation of the inadequacy of urban spaces

to meet the needs of older people and the popularity of

instruments for its evaluation, such as city rankings. The

results of rankings to identify the best places to live attract

the attention of the media and communities, as well as city

authorities around the world, even though most of the tools

were not intended to inuence policy. The current and pop-

ular tools vary considerably, even though they all seem to

touch on the topic of quality of life. The dierences relate

to the commissioning bodies, the methodology, the focus

groups, the target groups of the surveys and the criteria

studied. Cities around the world, but also within one coun-

try, dier signicantly, and yet they are still subject to very

uniform evaluation criteria in rankings. The analysed glob-

al evaluation tools do not take into account that the quality

of life diers depending on the location of residence within

the same city, but for example in other neighbourhoods.

An important motivation in taking up the chosen topic

is the approach that assumes that in assessing the quality

of life in cities, more attention should be paid to subjective

ORCID: 0000-0002-4833-905X. Faculty of Architecture, Poznan

University of Technology, Poland, e-mail: agnieszka.ptak-wojciechowska

@put.poznan.pl

86 Agnieszka Ptak-Wojciechowska

between objective measures of quality of life and subjec-

tive measures is weak, and the author argues for more at-

tention to be paid to subjective indicators of quality of life.

Other researchers present an integrated approach using

GIS (Geographic Information System)

and multi-criteria

decision making/aiding (MCDM/A) methods to assess the

quality of urban open spaces in Milan. The authors pro-

pose criteria and sub-criteria covering features of the built

environment, its organisation and the perception of users.

Data to complete the individual indicators were obtained

from GIS, Open Street Map and Google Maps, as well

as through direct observation (Oppio et al. 2021). Also,

researchers from Poland point out the need to extend so-

cial and economic indicators to include subjective aspects

related to the opinion of the inhabitants and, in addition,

to use geographical research methods (e.g., geo-survey

)

(Czepkiewicz, Jankowski 2015). Quality of life can be

narrowed down to its individual criteria – for example,

accessibility of space. Other authors propose a Decision

Support System (DSS) and a conditioned tool – the on-

line Walkability Explorer (WE) application to support

design and planning for assessing the walkability and

accessibility of a space for pedestrians. The researchers

present a case study in which they discuss the results of

an example application in the Lisbon area (Blečić et al.

2015). Models are proposed to assess the age-friendliness

of cities, such as Best Cities for Successful Aging. This

tool evaluates the spaces of US metropolitan areas against

nine categories and 83 indicators, and aims to highlight

and encourage good practices that improve the quality

of cities and the quality of life of residents (Kubendran,

Soll, and Irving 2017). In turn, the report commissioned

by UNECE and DG EMPL gives numerous examples of

the use of the Active Ageing Index (AAI), its practical in-

strument for identifying areas where appropriate policies

can harness the active potential of older people. The index

is multidimensional, and environmental factors, includ-

ing infrastructure to promote well-being, social cohesion

and digitalisation, among others, are taken into account.

Twenty-eight countries in the European Union joined the

survey, plus Iceland, Switzerland and Canada (Lamura,

Principi 2019). A methodology for assessing the quality of

life of older adults on a suburban scale is also available, in-

tegrating objective indicators, derived from statistical data,

and subjective indicators, taking into account the opinions

of both experts and older people (Garcia et al. 2017). In

addition, a study based on the Survey of Health, Aging,

and Retirement in Europe (SHARE) is worth mentioning.

The study analysed the direct impact of perceived acces-

sibility on the quality of life of 13,828 Europeans aged 65

and over and the indirect impact after taking into account

aspects related to loneliness, place attachment, marital

status and functional disability (Vitman Schorr, Khalaila

2018). Of interest is the analysis of older people’s sense

Geographic Information System – is used to collect, visualize and

process geographic data, as well as support the decision-making process.

Geosurvey, as one of the forms of conducting online public con-

sultations, is used during the spatial planning process. In this form, re-

spondents provide answers using maps.

indicators regarding residents’ perceptions, and that a com-

plete tool should examine both objective and subjective

aspects (Gawlak, Matuszewska, and Ptak 2021).

The motivation for undertaking the research is the diag-

nosed research gaps. In an analysis of a selection of current

tools for assessing quality of life in cities, it was shown that

global challenges (climate and demographic change) are

overlooked in many of them, and that aspects of the spatial

(architectural-urban) quality of cities and the importance

of perceptual assessment are underestimated. Comparisons

of places to live are global – they apply to entire cities

– and should also be local. Indeed, the study of urban qual-

ity should also include neighbourhood units representing

an intermediate urban scale: larger than a single building

with its immediate surroundings and smaller

than the en-

tire city within its administrative boundaries. Moreover,

seniors use cities locally and their activities are most often

narrowed down to their at and immediate neighbourhood

(Garau, Pavan 2018). Assessment tools are too general and

ambiguous. Rankings should serve as a good example – not

a source of competition. A city ranking system and gover-

nance should be well linked (Ptak-Wojciechowska 2023).

The aim of the research presented in this article was to

formulate guidelines for the denition of an assessment tool

taking into account spatial aspects, expert and perceptual

evaluation, in addition to sustainability principles and so-

cio-cultural context. The guidelines were created on the ba-

sis of a comparative analysis of selected current assessment

tools. It was crucial to select a transparent methodology.

The following research hypothesis was formulated: The

development of tools for assessing urban quality of life

should include participatory methods involving research-

ers, experts and residents. These tools need to take into

account more criteria related to aspects of the shaping of

the spatial structure of cities. In addition, they should be

adapted to the demographic context, local conditions and

global environmental risks.

The research problem related to the inadequacy of ur-

ban spaces and tools for assessing urban quality of life

to current challenges is also presented. The latest meth-

ods and techniques used in urban quality of life research

are then discussed. This is followed by a presentation of

the author’s own research, with particular emphasis on

the selection of a multi-criteria method and the process

of constructing the author’s urban assessment tool. This

is followed by a demonstration of the verication of the

tool, including expert and perception surveys, as well as

the nal ranking of neighbourhoods. The last part includes

a summary, involving recommendations for continuing re-

search using machine learning methods.

State of research

Quality of life is studied both in Poland and internation-

ally in various ways. For example, researchers’ attention

is drawn to the importance of the interrelationship of ob-

jective and subjective measures. Adam Okulicz-Kozaryn

(2013) examines the relationship between Mercer’s

Quality of Living Ranking and survey data from a satis-

faction survey. According to the analysis, the relationship

Use of the Analytic Hierarchy Process (AHP) method to assess the urban quality of life of seniors 87

of safety in the context of the built environment, for which

the starting point was the framework of age-friendly cities

and the quality of life aspect of neighbourhoods (Donder et

al. 2013). There is also interdisciplinary research on the re-

lationship between the health of ageing Australians and ur-

ban sustainability. The authors present a method to explore

the relationship between subjective and objective mea-

sures of built environment characteristics of settlements

(number of buildings, street capacity and connectivity, di-

versity of functions, continuity of elevations, number of

seats) and health for communities of people aged 55 years

and older (Brewer et al. 2014).

Description of original research

The original research was conducted between 2020 and

2023. The study adopted a specic methodology. In the

rst part, the method of logical argumentation was used.

A literature analysis was carried out to be able to identify

the state of the art of the global challenges faced by cit-

ies (climate change, demographics and urbanisation), the

measurement of quality of life in spatial terms, current

tools for assessing urban quality of life and their classi-

cation, in addition to architectural, universal and inclusive

design. This was followed by a quantitative and qualitative

study of the available assessment tools. Statistical tech-

niques and comparative studies were used, as described

in more detail in the dissertation (Ptak-Wojciechowska

2023). A selection of spatial criteria and sub-criteria, ex-

tracted from the analysed existing tools, was then made.

The synthesis was done according to the recommendation

formulated from Miller’s gure that the number of ele-

ments within the model groups should be 7 ± 2 (Miller

1956). The dened criteria and sub-criteria were subject-

ed to expert evaluation by collating and comparing them.

Subsequently, a mathematical multi-criteria method was

applied. The nal stage was quantitative and qualitative

participatory research.

Literature research, criteria for the selection of tools

The subject of the study were publicly available evalua-

tion instruments, both international and Polish. Documents

that meet the specied eligibility have been selected on the

basis of literature and keyword research as well as rec-

ommendations of experts in the eld of design for seniors

(who are both researchers and practicing architects), as

well as creators of other comparative analyses. Eligibility

was related to the scope of the study (including quality of

life in cities, age-friendliness and spatial indicators) and

the characteristics of the indicators included (Fig. 1).

Comparative analysis of tools

The comparative research included an analysis of 24

tools created in the years 2007–2021, such as: rankings

(selecting the best locations to live), guides (measuring

accessibility for seniors), other Polish instruments (taking

into account surveys and assessing the quality of life using

a set of indicators), as well as assessment models proposed

by the researchers. The set of assessment tools consists of

three international guides and one Polish guideline, 13 in-

ternational rankings, and two Polish and ve other Polish

tools (Table 1), as well as 14 models proposed by scientists

(Table 2) (Ptak-Wojciechowska 2023).

Comparative research revealed that in most Polish as-

sessment tools and rankings, aspects related to the aging

of societies were not taken into account in detail. Issues

related to population ageing have been given special at-

tention in the guides created to study the accessibility of

cities for the elderly and in two rankings “Best Cities for

Successful Aging” and “Active Ageing Index” on similar

topics, as well as in the Polish study “Jak się żyje osobom

starszym w Polsce” [How do older people live in Poland].

In 16 tools, on the other hand, the aspect of demographic

change was included, among other things, by providing

information on life expectancy and taking into account

dierent age ranges when analysing the results. Despite

environmental threats, water and climate aspects were not

included in the assessment at all in the Polish and foreign

guides. Indicators assessing climate aspects were included

in 5% in international rankings, 6% in Polish rankings and

1% in other Polish tools, and water-related metrics – only

in 3% in international rankings, in 1% in Polish rankings

and 0.6% in other Polish tools (detailed data can be found

in Ptak-Wojciechowska 2023).

Fig. 1. Criteria for the selection of representative tools (elaborated by A. Ptak-Wojciechowska)

Il. 1. Kryteria wyboru narzędzi reprezentatywnych (oprac. A. Ptak-Wojciechowska)

88 Agnieszka Ptak-Wojciechowska

Tool No. Name Contracting Authority Source

International guides

1.1 Global Age – friendly Cities – A Guide World Health Organisation

(World Health Organization

2007)

1.2

Measuring the age-friendliness of cities.

A guide to using core indicators

World Health Organisation

(World Health Organization

2015)

1.3

Age-friendly rural

and remote communities: a guide

Federal/Provincial/Territorial

Ministers Responsible for Seniors

(Federal/Provincial/Territorial

Ministers Responsible

for Seniors 2007)

Polish guides 1.4

System wsparcia osób starszych

w środowisku zamieszkania – przegląd

sytuacji, propozycja modelu. Synteza

[A system of support for the elderly

in a residential environment

– an overview of the situation and

a proposal for a model. Synthesis]

Rzecznik Praw Obywatelskich

(RPO)

(Błędowski et al. 2016)

International

rankings

2.1 EIU’s Global Liveability Index The Economist Intelligence Unit

(The Economist Intelligence

Unit 2019)

2.2 Mercer’s Quality of Living Ranking Mercer (Mercer 2019)

2.3 Monocle’s Quality of Living Survey Monocle (Monocle 2019)

2.4 Deutsche Bank Liveability Survey Deutsche Bank AG/London (Reid, Nicol, and Allen 2019)

2.5 Euro Health Consumer Index Health Consumer Powerhouse (Björnberg, Phang 2019)

2.6 IMD Smart City Index

IMD World Competitiveness

Center’s Smart City Observatory

Singapore University of

Technology and Design (SUTD)

(IMD World… 2019)

2.7 Best Cities for Successful Aging

Milken Institute Center for the

Future of Aging Milken Institute

Research Department

(Kubendran, Soll,

and Irving 2017)

2.8 Human Development Report

United Nations; Human

Development Report Office

(United Nations Development

Programme 2019)

2.9 Quality of life (well-being of Europeans) Eurostat (Eurostat 2017)

2.10

The European Quality of Life Survey (EQLS)

Eurofound (Eurofound 2017)

2.11 How’s Life? 2020 Measuring Well-being OECD

(Organisation for Economic

Cooperation and Development

2020)

2.12

Quality of life in cities. Perception survey

in 79 European cities

European Commission (European Commission… 2013)

2.13 Active Ageing Index

UNECE + DG EMPL

(European Commission)

(Lamura, Principi 2019)

Polish rankings

2.14

Ranking jakości życia. Wymiary szczęścia

[Quality of life ranking. Dimensions

of happiness]

POLITYKA and the AGH

University of Science

and Technology

(Polityka and Akademia

Górniczo-Hutnicza 2018)

2.15

Uciekające metropolie. Ranking 100

polskich miast [Runaway metropolises.

Ranking of 100 Polish cities]

Klub Jagielloński (Wałachowski, Król 2019)

Other Polish

appraisal

instruments

3.1

Jakość życia w Polsce. Edycja 2017

[Quality of life in Poland. 2017 Edition]

Główny Urząd Statystyczny (GUS) (Bendowska et al. 2017)

3.2

Zadowolenie z życia

[Life satisfaction]

Centrum Badania Opinii

Społecznej (CBOS)

(Centrum Badania Opinii

Społecznej 2020)

3.3

Diagnoza społeczna 2015. Warunki

i jakość życia Polaków

[Social Diagnosis 2015. Conditions

and quality of life of Poles]

Rada Monitoringu Społecznego (Czapiński, Panek 2015)

3.4

Jakość życia mieszkańców Łodzi

i jej przestrzenne zróżnicowanie

[Quality of life of Lodz’s inhabitants

and its spatial diversity]

Urząd Miasta Łodzi (Rokicka 2013)

3.5

Jak się żyje osobom starszym w Polsce

[How do older people live in Poland]

Główny Urząd Statystyczny (GUS)

(Główny Urząd Statystyczny

2012)

Table 1. Summary of current assessment tools analysed:

foreign and Polish guides, international and Polish rankings and other Polish assessment tools (elaborated by A. Ptak-Wojciechowska)

Tabela 1. Zestawienie analizowanych aktualnych narzędzi oceny:

wytycznych zagranicznych i polskich, rankingów międzynarodowych i polskich oraz innych polskich narzędzi oceny (oprac. A. Ptak-Wojciechowska)

Use of the Analytic Hierarchy Process (AHP) method to assess the urban quality of life of seniors 89

Multicriteria methods

On the basis of the comparative analysis, it was noted

that the available tools often use a non-transparent meth-

odology (without indicating the specic sources on the ba-

sis of which the own set of evaluation criteria is created;

without providing data on the number and characteristics

of experts participating in the study; without specifying

how the weights and the aggregate index were calculated)

and that the perspectives of dierent stakeholders (such

as experts and seniors) were not combined. Therefore,

a search was started for a method that would be transpar-

ent and would allow for including various aspects in the

assessment. It was decided to use multi-criteria methods

widely used in decision-making (Afshari, Vatanparast, and

Ćoćkalo 2016). The number of available multi-criteria de-

cision support methods is signicant (over 200), and their

diversity means that the selection of the method itself is

a multi-criteria problem (Trzaskalik 2014).

Method selection

The use of various multi-criteria methods was consid-

ered, both with the help of an expert (a university pro-

fessor and practitioner whose specialization is the use

of multi-criteria decision support methods in urban mo-

bility management) and the Multiple Criteria Decision

Analysis Methods Selection Software (MCDA-MSS

)

tool for matching multi-criteria methods to a specic de-

cision problem (Cinelli et al. 2021). Initially, the AHP

and ELECTRE-III-H methods (the so-called Electre with

sub-criteria) were taken into account together with the

expert, while the algorithm resulted in the recommenda-

tion of the MCHP-PROMETHEE method. The practical

aspect, related to the selection of a less complicated and

more understandable method for decision-makers, experts

in the discipline of architecture and urban planning, nal-

ly conrmed the eectiveness of the AHP method (Saaty

1986). The individual stages of the procedure are present-

ed in the diagram (Fig. 2).

A tool using many questions (concerning, among others, the type

of problem, the way of ordering, the set of evaluation criteria and its

structure, or the way of measuring the performance of the variant) en-

abling step-by-step rejection of a method that does not meet the criteria

– ultimately leading to the recommendation of methods that meet all

selected assumptions.

Table 2. Set of scientific studies analysed

(elaborated by A. Ptak-Wojciechowska)

Tabela 2. Zestaw analizowanych opracowań naukowych

(oprac. A. Ptak-Wojciechowska)

No. Title Source

Developing a checklist for assessing

urban design qualities

of residential complexes

in new peripheral parts

of Iranian cities:

A case study of Kerman, Iran

(Abousaeidi,

Hakimian 2020)

Urban design assessment tools:

A model for exploring atmospheres

and situations

(Abusaada, Elshater

2020)

Responsive environments:

A manual for designers

(Bentley et al. 2005)

Socially sustainable suburbia:

Linking neighbourhood

characteristics to health outcomes

in an ageing population

(Brewer et al. 2014)

Towards an urban quality framework:

Determining critical measures

for different geographical scales

to attract and retain talent in cities

(Esmaeilpoorarabi,

Yigitcanlar,

and Guaralda 2016)

Assessment of and improvement

strategies for the housing of healthy

elderly: Improving quality of life

(Feng et al. 2018)

Evaluating Urban Quality:

Indicators and Assessment Tools

for Smart Sustainable Cities

(Garau, Pavan 2018)

Assessment of an urban sustainability

and life quality index for elderly

(Garcia et al. 2017)

City planning and population health:

A global challenge

(Giles-Corti et al.

2016)

Developing and testing a framework

for the assessment of neighbourhood

liveability in two contrasting countries:

Iran and Estonia

(Maleki et al. 2015)

Assessing urban quality: A proposal for

a MCDA evaluation framework

(Oppio, Bottero, and

Arcidiacono 2022)

How to assess urban quality:

A spatial multicriteria

decision analysis approach

(Oppio et al. 2021)

Model for Assessment

of Public Space Quality

in Town Centers

(Wojnarowska 2016)

Neighbourhood sustainability

assessment: Evaluating residential

development sustainability

in a developing country context

(Yigitcanlar,

Kamruzzaman,

and Teriman 2015)

Fig. 2. Tool development process – on a diagram of how multi-criteria decision methods work

(elaborated by A. Ptak-Wojciechowska based on: Kobryń 2014)

Il. 2. Proces tworzenia narzędzia – na schemacie działania metod wielokryterialnego wspomagania decyzji

(oprac. A. Ptak-Wojciechowska na podstawie: Kobryń 2014)

90 Agnieszka Ptak-Wojciechowska

Formulation of criteria and sub-criteria

related to the selection of the variant

A literature analysis of current assessment instruments

and models yielded 2189 metrics. Metrics are understood

as the smallest components for assessing the quality of

life in cities, constituting a component of the sub-crite-

ria. Only those related to the assessment of the spatial

structure aecting quality of life were included. After re-

moving redundancy, 128 relevant metrics were nally ob-

tained. In the course of their analysis, certain relationships

between them were diagnosed – consequently, they were

grouped into sub-criteria

. Metrics that were recurrent

The grouping was performed and veried by at least two people.

in the various reference materials or non-recurrent, but

proposed in signicant tools/studies, or assessed as high-

ly relevant, were taken into account. The reference tools

were in particular the most inuential publications: the

WHO guides Global Age-friendly Cities. A guide (2007)

and Responsive environments. A manual for designers

(Bentley et al. 2005).

In the end, a list of criteria and sub-criteria was created

that was considered the most eective for the study. The

need for both expert and perceptual evaluation was taken

into account, hence each criterion included sub-criteria for

measurement by experts and one sub-criterion each related

to the subjective evaluation of the residents of the neigh-

bourhoods (Fig. 3). The characteristics of each sub-criteri-

on can be found in the dissertation (Ptak-Wojciechowska

2023).

Fig. 3. Formulation of evaluation

criteria and sub-criteria including

expert and perceptual evaluation

(elaborated by

A. Ptak-Wojciechowska)

Il. 3. Sformułowanie kryteriów

i podkryteriów oceny

z uwzględnieniem oceny

eksperckiej i percepcyjnej

(oprac. A. Ptak-Wojciechowska)

Use of the Analytic Hierarchy Process (AHP) method to assess the urban quality of life of seniors 91

Constructing the tool,

ranking the criteria by importance

The next part of the study consisted of making pairwise

comparisons, according to the AHP multi-criteria method

using the AHP-OS program (Goepel 2018) in order to rank

the criteria and sub-criteria by weight. Ten experts were

invited to the study, of which eight nally participated.

The experts were a group of architects (n = 6) and urban

planners (n = 2) – both scientists and practitioners work-

ing actively in the profession. The experts included people

specialising in designing for ageing societies (n = 2) and in

health care (n = 4).

AHP calculation procedure

The initial stage of the calculation procedure for the

AHP method is related to the decomposition of the deci-

sion problem. A hierarchical model is created consisting of

elements such as: overarching goal, criteria, sub-criteria,

decision variants (Fig. 4).

The calculation procedure presented in this article only

concerns the main criteria in order to illustrate the sam-

ple calculations made by the AHP-OS system. It should

be noted that a matrix is constructed at each level of the

AHP model and, as part of the work in AHP-OS, eight

matrices were constructed for the sub-criteria importance

analysis, i.e., there were nine matrices in total. Sample cal-

culations were performed in Google Sheets on the basis

of the individually prepared matrices, the results of which

appeared to coincide with the results of the calculations

in the software by Klaus D. Goepel (2018). However, it

should be emphasised that the specialised tools are more

accurate than the calculations made in Google Sheets, as

obtaining accurate results involves the execution of com-

plex mathematical procedures, and the literature on AHP

shows simplied methods for obtaining similar results

(Stefanów, Prusak 2011). Hence, a slight dierence, e.g.,

in the third digit after the decimal point, is visible in the

results performed by the system and the author of the study

in question.

The rst step was to create a comparison matrix A of

dimensions (n × n) (1), where n is the number of criteria

being compared.

(1)

The matrix consists of criteria compared in pairs (K1–

K8) and scores awarded by experts according to the Saaty

scale. On this scale, the higher number of points awarded

by the expert is associated with the greater importance of

the criterion (Fig. 5).

Fig. 4. Hierarchical structure

of the author’s evaluation model

(elaborated by A. Ptak-

Wojciechowska)

Il. 4. Struktura hierarchiczna

autorskiego modelu oceny

(oprac. A. Ptak-Wojciechowska)

According to the principle of inverse preference applied

here, where the rst criterion compared to the second cri-

terion is more important to a certain extent (expressed on

an accepted point scale), the second criterion compared

to the rst criterion is proportionally less important (and

expressed as a fraction). The experts’ preferences were

explored in the form of a questionnaire, in which they

were asked to indicate an advantage individually for each

pair of criteria. Each expert’s individual responses were

then aggregated using a geometric mean expressed by

a formula:

(2)

Fig. 5. The comparison scale of pairwise

(elaborated by A. Ptak-Wojciechowska based on: Saaty 1986)

Il. 5. Skala porównań Saaty’ego

(oprac. A. Ptak-Wojciechowska na podstawie: Saaty 1986)

= 







1 



 







1  



   









 1

for i, j = 1, 2, …, n

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









(



)











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

= 0.016

CR =

0.016

1.41

= 0.01

CR = 0.01 100% = 1%

































= 









= 1

Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

0.016

CR =

0.016

1.41

0.01

CR = 0.01 100% = 1%



















= 











= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

92 Agnieszka Ptak-Wojciechowska

This resulted in a consolidated a

cons

matrix. The next

step was to transform the pairwise comparison matrix

A into a normalised matrix B = [b

] (Fig. 6). For this pur-

pose, the values of the a

cons were summed in the individ-

ual columns of the matrix A = [a

Then, the elements appearing in the individual columns

of matrix A were divided by the result of the sum from

the previous step (for example, 2.36/9.5912 = 0.2461)

according to formula (3). The individual elements are

there fore equal:

(3)

where: n – number of elements compared in pairs.

Example calculation:

The matrix has normalized.

In order to determine the weights of the evaluated cri-

teria, the arithmetic mean in each row of the normalized

matrix B was calculated according to the formula:

(4)

Example calculation:

Fig. 6. Consolidated matrix A,

transformed into

normalised matrix B

(elaborated by A. Ptak-

Wojciechowska)

Il. 6. Macierz skonsolidowana A

przekształcona

w macierz znormalizowaną B

(oprac. A. Ptak-Wojciechowska)

In the case of pairwise comparisons by experts, it is pos-

sible that the principle of transitivity of preferences is vio-

lated. If the expert considers the rst criterion more import-

ant than the second and the second criterion more important

than the third, he cannot at the same time consider the rst

criterion less important than the third. The AHP method

allows the consistency of pairwise comparisons to be veri-

ed. For this purpose, it is necessary to determine the max-

imum eigenvalue of the A matrix. In the present study λ

max

was determined according to the formula (Cabała 2018):

(5)

The measures used to assess the consistency of pairwise

comparisons are:

– consistency index (CI) increasing with increasing in-

consistencies in estimates calculated according to the for-

mula:

(6)

where:

max

– maximum eigenvalue of the matrix,

RI – random index dependent on the degree of the ma-

trix n (see Table 3),

n – matrix degree.

Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

= 0.016

CR =

0.016

1.41

= 0.01

CR = 0.01 100% = 1%



















= 











Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

= 0.016

CR =

0.016

1.41

= 0.01

CR = 0.01 100% = 1%



















= 











Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

= 0.016

CR =

0.016

1.41

= 0.01

CR = 0.01 100% = 1%



















= 















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012





(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012



max



∑

()









=1

Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

0.016

CR =

0.016

1.41

0.01

CR = 0.01 100% = 1%



















= 











Use of the Analytic Hierarchy Process (AHP) method to assess the urban quality of life of seniors 93

The consistency ratio (CR) which is the ratio of the ma-

trix consistency index (CI) to the random index (RI) de-

pending on the degree of this matrix is calculated accord-

ing to the formula:

(7)

Taking into account the maximum value of the matrix

(λ

max

= 8.11) a consistency index has been determined:

And nally, the consistency ratio was calculated:

The calculations presented show that CR < 10% and

therefore pairwise comparisons of the evaluation criteria

are consistent.

It should be emphasised that, thanks to the AHP-OS

system, the expert is automatically informed when his/her

individual answers are inconsistent, so he/she can correct

them at any stage during the completion of the survey.

The result of this part of the survey was the weights giv-

en to the individual criteria and sub-criteria and the calcu-

lation of global priorities

. The K1: Accessibility of urban

area for ageing population criterion was indicated as the

most important (0.202), then K7: Aordability of housing

for older people (0.193) and K6: Adaptability for seniors

aging in place (0.150). The K8 criterion received the low-

est weight: Quality of multisensory experience of the built

environment (0.059). The share of individual criteria in

percentages is presented in Figure 7.

Tool verification

The stage following the creation of a decision hierarchy

using the AHP method and assigning weights to criteria

and sub-criteria was the verication of the tool. Due to the

argument raised in the literature regarding the validity of

assessing urban quality within the boundaries of neigh-

bouring units instead of within the boundaries of entire

cities, the following variants were indicated: the neigh-

bourhoods of the city of Poznań most frequently inhab-

ited by seniors: Rataje, Piątkowo, Św. Łazarz, Grunwald

Południe, Chartowo (Fig. 8).

The global priority presents the average dominance of each of the

(smallest) elements (sub-criteria) over the others in relation to the objective

of the hierarchy; it is the product of the weights for criterion and sub-criterion.

The experts received a research questionnaire consist-

ing of two parts: a table and a legend with a description of

each of the sub-criteria. The table included variants, i.e.,

selected neighbourhoods in the city of Poznań, as well as

their assessment criteria and sub-criteria – all excluding

the sub-criteria concerning the perception of seniors. The

experts were asked to enter a rating for the individual vari-

ants, on a scale of 0–10. The rating was to be assigned to

the neighbourhoods in the individual criteria based on their

own knowledge and experience and the attached support-

ing materials in the form of maps and photos. The group

of experts consisted of eight researchers and practitioners:

architects specializing in designing for the disabled and se-

niors (n = 1), health care (n = 1), as well as in both of these

areas (n = 2), also – architects/historians/urban planners

(n = 2) and architects/urban planners (n = 2).

In parallel with the expert study, a questionnaire survey

was conducted on the perceptual assessment of architec-

ture and urban planning in Poznan according to senior citi-

zens. The survey design underwent a four-stage validation

process. At the rst stage, the survey questionnaire was

analysed and rened on the basis of expert consultation

with a senior citizen. At the second stage, the questionnaire

was further evaluated by a psychologist and a pilot study

was conducted among older people on its readability. At

the third, it received expert approval. The nal stage was

the positive approval of the questionnaire by the Research

Ethics Committee for Studies Involving Humans at Poznan

University of Technology. The survey was anonymous and

took place in stationary and online forms. Ultimately, 198

questionnaires with responses from seniors were taken for

the survey. Seniors were qualied for the survey on the

basis of the age criterion: 60 years and over.

The nal stage of verication was the generation of

the nal ranking of neighbourhoods based on expert and

senior citizen assessments. It should be noted that in the

present study, the stage characteristic of the AHP method,

involving pairwise comparison of options, was abandon-

ed, as in the case of the publication by Edmundas K. Za-

vadskas et al. (2014) and the work of Helder Costa (2017).

The motivation for this decision was the need to combine

expert and perceptual evaluation. In the survey, the senior

citizens commented only on the neighbourhoods they lived

in, while the experts evaluated all ve locations. In addi-

tion, two dierent ordinal scales were included in the sur-

vey. A Likert scale (ratings 1–5), more readable for older

respondents, and a broader scale (ratings 0–10) giving the

experts more freedom of expression. Although it would

have been permissible to translate the aggregated and

standardised scores into pairwise comparisons on Saaty’s

(1986) scale, due to the subjectivity of such a translation

related to the establishment of a class range, the scores

were left as scores.

n 1 2 3 4 5 6 7 8 9 10

Random

index

0 0 0.52 0.89 1.11 1.25 1.35 1.40 1.45 1.49

Table 3. The value of the random index RI (elaborated by A. Ptak-Wojciechowska based on: Saaty 2004)

Tabela 3. Wartość indeksu losowego RI (oprac. A. Ptak-Wojciechowska na podstawie: Saaty 2004)

Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

= 0.016

CR =

0.016

1.41

= 0.01

CR = 0.01 100% = 1%



















= 











Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

0.016

CR =

0.016

1.41

0.01

CR = 0.01 100% = 1%



















= 











Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

0.016

CR =

0.016

1.41

0.01

CR = 0.01 100% = 1%



















= 











Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

= 0.016

CR =

0.016

1.41

= 0.01

CR = 0.01 100% = 1%



















= 











94 Agnieszka Ptak-Wojciechowska

Fig. 7. View after the weights

have been completed by experts

in the AHP-OS programme

(elaborated by

A. Ptak-Wojciechowska)

Il. 7. Widok po uzupełnieniu wag

przez ekspertów w programie

AHP-OS

(oprac. A. Ptak-Wojciechowska)

Fig. 8. Selected variants, i.e., the neighbourhoods in Poznań most populated by senior citizens (elaborated by A. Ptak-Wojciechowska)

Il. 8. Wybrane warianty, czyli osiedla Poznania najliczniej zamieszkane przez seniorów (oprac. A. Ptak-Wojciechowska)

Use of the Analytic Hierarchy Process (AHP) method to assess the urban quality of life of seniors 95

In order to nally rank the variants (neighbourhoods),

a matrix was created consisting of the scores assigned to

each sub-criterion C

in the rows and the variants A

(alter-

natives) in the columns.

The ratings were then normalised according to the for-

mula (Mathew, Sahu and Upadhyay 2017):

(8)

where: x

max

= the maximum possible value of the variant

assessment in a given line (in the case of expert assess-

ments, the maximum value of the rating is 10, and in the

case of senior ratings – 5).

The next stage was to calculate the sum of the products

of weights (global priorities) of the sub-criteria and their

individual normalized values for each neighbourhood, as

well as to rank the preferences in order to obtain the nal

ranking of areas. The nal ranking of preference (P

) is

created on the basis of the weighted sum model according

to the formula:

(9)

where:

– weight of the sub-criterion C

– normalized variant evaluation A

for a given

sub-criterion C

Based on the results obtained during the study of the

eciency of the author’s tool for assessing spatial aspects

aecting the quality of life of seniors, it turned out that the

highest position in the ranking was given to the Grunwald

Południe neighbourhood, and the lowest – to Chartowo

(Fig. 9).

The Grunwald Południe neighbourhood received the

best rating among all the surveyed areas only in terms of

adaptability for seniors aging in place and environmental

friendliness of space. It also scored high in terms of acces-

sibility of space, friendliness of function and urban form,

and legibility of space, which ultimately contributed to

taking rst place in the ranking. But this neighbourhood

fared worst in terms of aordability (cf. Fig. 10).

Conclusions and summary

Based on research, it has been shown that current tools

for assessing urban quality of life are not suciently

adapted to global challenges such as ageing populations,

urbanisation and climate change, and their assessment is

not comprehensive enough. The author’s set of criteria

and sub-criteria proposed in this paper makes it possible

to ll this gap. Current assessment instruments do not take

into account the importance of spatial scale, even though

quality of life can vary within the boundaries of a single

city. The method described in this paper therefore covers

a smaller spatial scale, close to the area of the auxiliary

units – known as neighbourhoods. The research results ob-

tained allowed the research hypothesis to be conrmed.

Signicant results include assigning weight to criteria

according to experts’ opinions, determining the percep-

tual quality of spatial aspects by older people and spatial

quality by experts for ve neighbourhoods in Poznań, and

formulating guidelines for a tool for assessing the spatial

quality of cities, including dening the decision problem

and variants, dening a coherent family of criteria and the

way they are measured, selecting a transparent method,

and verifying eciency through pilot studies. The meth-

od proposed in this article complements existing scientic

tools and models. This is because it makes it possible to

take into account both the global context (universal criteria

created on the basis of international quality of life studies)

and local conditions (measurement of sub-areas instead of

the entire city), and furthermore includes an evaluation of

the quality of space in the expert assessment and the level

of satisfaction with it in the seniors’ perceptual assessment.

Based on the process of verifying the eciency of the

tool, several potential limitations can be diagnosed, such

as: the choice of urban areas of the city (some of the select-

ed areas turned out to be so heterogeneous in their bound-

aries that they made it signicantly dicult for the experts

to assess them reliably), the detail of the questions in the

neighbourhood assessment questionnaire for the experts

(the characterisation of the individual sub-criteria devel-

oped on the basis of indicators from the current assessment

tools analysed earlier turned out to be too general for the

experts), and the fact that the expert surveys were conduct-

ed individually instead of in the form of a group discussion

Fig. 9. Ranking of

neighbourhoods in terms of

the friendliness of architectural

and urban spaces for seniors

(elaborated by

A. Ptak-Wojciechowska)

Il. 9. Ranking osiedli Poznania

pod względem przyjazności

przestrzeni architektoniczno-

-urbanistycznej seniorom

(oprac. A. Ptak-Wojciechowska)





= ∑



̅





=1

Wzory w artykule

= 









1 



 



1/



1  



   

1/



1/



 1

for , = 1, 2, … , 

























… 













 











2.36

9.5912

= 0.2461



















(0.1905 + 0.2461 + 0.2178 + 0.1988 + 0.2002 + 0.2190 + 0.1354 + 0.2016) = 0.2012









()











CI =









CR =

100%

CI =

(

8.11 8

)

(

8 1

)

0.016

CR =

0.016

1.41

0.01

CR = 0.01 100% = 1%



















= 











96 Agnieszka Ptak-Wojciechowska

Fig. 10. Rankings of

neighbourhoods in terms of their

senior citizen-friendliness

in various aspects (elaborated by

A. Ptak-Wojciechowska)

Il. 10. Rankingi osiedli Poznania

pod względem ich przyjazności

seniorom z uwzględnieniem

poszczególnych aspektów

(oprac. A. Ptak-Wojciechowska)

(due to the interdisciplinary nature and diversity of the

questions, the assessment could have been conducted in

a working group and the result worked out in the form of

a discussion between the experts).

The data obtained from the seniors’ perception survey

not only served to supplement the perception sub-criteria

for the assessment tool under development. The ways in

which they were used and visualised are shown in the dis-

sertation; the statistical analysis and visualisation of the

survey results were performed using Microsoft Excel and

the statistical package Statistica (Ptak-Wojciechowska

2023).

An interesting alternative to statistical testing is articial

intelligence. The author is currently working on the use of

machine learning (decision trees and rules) to analyse the

results obtained from perceptual surveys conducted among

seniors and questionnaire surveys of expert assessment.

Analyses are performed using the WEKA programme,

among others. In addition, research into the quality of life

in cities is being continued through ongoing projects using

data mining. Their aim is to automate the extraction of ob-

jective information from available data sources (e.g., Open

Street Map) to supplement expert and perceptual evalua-

tions. These concern the distance of important functions

from the place of residence of seniors and the location of

small architecture in the context of the needs and mobility

of older people.

Translated by

Agnieszka Ptak-Wojciechowska

Acknowledgements

The described research was carried out as part of the doctoral disserta-

tion conducted under the supervision of Prof. Agata Gawlak.

I would like to thank the Supervisor, the experts who shared their special-

ist knowledge, and all the Seniors involved and their Representatives for

their participation in the research.

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Streszczenie

Wykorzystanie metody Analytic Hierarchy Process (AHP) do oceny jakości życia osób starszych w miastach

pod względem aspektów architektoniczno-urbanistycznych

Miasta powinny zapewniać wysoką jakość życia wszystkim mieszkańcom. Mimo zachodzących zmian demogracznych tkanka urbanistyczna

odpowiada w sposób niewystarczający na potrzeby przestrzenne seniorów. Brakuje ponadto naukowych instrumentów oceny, które mogłyby posłu-

żyć za wsparcie w ocenie aspektów architektoniczno-urbanistycznych miasta, a w konsekwencji także w ich poprawie. Chociaż popularne rankingi

miejskie mogą być wykorzystywane w rozwoju polityki miejskiej, ich wyniki są często nieprawidłowo interpretowane przez odbiorców. Zastosowanie

metod wielokryterialnego wspomagania decyzji może ułatwić proces porównywania obszarów miasta, zwiększyć transparentność ewaluacji oraz

zaangażować różnych interesariuszy w proces oceny. Uczenie maszynowe natomiast może stanowić interesujące rozszerzenie dla stosowanych po-

wszechnie metod statystycznych. W artykule zaprezentowano najnowsze metody w badaniach nad miejską jakością życia seniorów na przykładzie

wielokryterialnej analizy pięciu osiedli miasta Poznania. Omówiono wykorzystanie metody analytic hierarchy process (AHP) jako części autorskiego

narzędzia do oceny percepcyjnej przez starszych mieszkańców, a także oceny eksperckiej przez architektów i urbanistów pod względem aspektów

funkcjonalno-przestrzennych. Dowiedziono skuteczności metody AHP – rezultaty mogą stanowić wsparcie dla władz miasta, projektantów i badaczy.

Przedstawiono ponadto kierunki rozwoju niniejszych badań z zastosowaniem metod uczenia maszynowego.

Słowa kluczowe: metody partycypacyjne, metody wielokryterialne, jakość życia w miastach, uczelnie maszynowe, starzejące się społeczeństwo