Standardise Variable Values With Fuzzy Logic And Correspondence Tables

Costing health economic datasets is an activity that can involve repeated use of lookup tables. This tutorial describes how a module from the costly R package can help you to use a combination of fuzzy logic and correspondence tables to standardise variable values and thus facilitate partial automation of costing algorithms.

This below section renders a vignette article from the costly library. You can use the following links to:

In brief

The steps described and explained in this vignette can also be (more succinctly) accomplished with the following code.

X <- CostlyCountries() 
X <- renew(X, type_1L_chr = "default") 
X <- renew(X, "jw", type_1L_chr = "slot", what_1L_chr = "logic") 
X <- renew(X, T, type_1L_chr = "slot", what_1L_chr = "force")
X <- ratify(X) 

Create project

We begin by creating X, an instance of the CostlyCorrespondences module.

Supply seed dataset

We begin by creating a CostlySeed module instance that includes a dataset containing our variable of interest (in this case, countries). The dataset needs to be paired with a dataset dictionary using the Ready4useDyad module from the ready4use R library. You can supply a custom standards dataset (a tibble), dictionary (a ready4use_dictionary) and the concept represented by our variable of interest using a command of the following format.

# Not run
# A <- CostlySeed(Ready4useDyad_r4 = Ready4useDyad(ds_tb = tibble::tibble(), dictionary_r3 = ready4use_dictionary()), include_chr = c("Country"), label_1L_chr = "Country")

The add_default_country_seed function will perform the previous step using values that pair the world.cities dataset of the maps R library with an appropriate dictionary and specifies countries as the concept we will be standardising.

We can now inspect the first few records from our labelled seed dataset.

renewSlot(A, "Ready4useDyad_r4", type_1L_chr = "label") %>%
exhibitSlot("Ready4useDyad_r4", display_1L_chr = "head", scroll_box_args_ls = list(width = "100%"))
Dataset
City name Country name Population size Latitude coordinate Longitude coordinate Is the nation's capital city
'Abasan al-Jadidah Palestine 5629 31.31 34.34 0
'Abasan al-Kabirah Palestine 18999 31.32 34.35 0
'Abdul Hakim Pakistan 47788 30.55 72.11 0
'Abdullah-as-Salam Kuwait 21817 29.36 47.98 0
'Abud Palestine 2456 32.03 35.07 0
'Abwein Palestine 3434 32.03 35.20 0

We can also inspect the data dictionary contained in A.

exhibitSlot(A, "Ready4useDyad_r4", type_1L_chr = "dict", scroll_box_args_ls = list(width = "100%"))
Data Dictionary
Variable Category Description Class
name City City name character
country.etc Country Country name character
pop Population Population size integer
lat Latitude Latitude coordinate numeric
long Longitude Longitude coordinate numeric
capital Capital Is the nation's capital city integer

We now specify the dictionary category that corresponds to the variable we wish to standardise (“Country”). We need to use the same category name to label the results objects that we generate in subsequent steps.

A@include_chr <- A@label_1L_chr <- "Country"

We now add A to X.

X <- renew(X, A, what_1L_chr = "seed")

Specify standards

We next must specify a dataset that includes the complete list of allowable variable values.

This workflow for this step is similar to that for specifying standards, except that instead of a CostlySeed module we use a CostlyStandards module.

# Not run
# Y <- CostlyStandards(Ready4useDyad_r4 = Ready4useDyad(ds_tb = tibble::tibble(), dictionary_r3 = ready4use_dictionary()))

In many cases using the ISO_3166_1 dataset from the ISOcodes library will be the optimal choice for the standardised form of country names. We can use the add_country_standards function to pair this dataset with its dictionary and create B, a CostlyStandards module instance.

We can inspect the first few cases of the labelled version of the dataset in B.

renewSlot(B, "Ready4useDyad_r4", type_1L_chr = "label") %>% 
  exhibitSlot("Ready4useDyad_r4", display_1L_chr = "head", scroll_box_args_ls = list(width = "100%"))
Dataset
Alpabetical country code (two letters) Alpabetical country code (three letters) Numeric country code Country name Country name (official) Country name (common alternative)
AW ABW 533 Aruba NA NA
AF AFG 004 Afghanistan Islamic Republic of Afghanistan NA
AO AGO 024 Angola Republic of Angola NA
AI AIA 660 Anguilla NA NA
AX ALA 248 Åland Islands NA NA
AL ALB 008 Albania Republic of Albania NA

We can also inspect the data dictionary contained in B.

exhibitSlot(B, "Ready4useDyad_r4", type_1L_chr = "dict", scroll_box_args_ls = list(width = "100%"))
Data Dictionary
Variable Category Description Class
Alpha_2 A2 Alpabetical country code (two letters) character
Alpha_3 A3 Alpabetical country code (three letters) character
Numeric N Numeric country code character
Name Country Country name character
Official_name Official Country name (official) character
Common_name Common Country name (common alternative) character

We can now specifying both the concept (from the “Category” column of the data dictionary) that specifies allowable values for our target variable and all concepts we plan to use for fuzzy logic matching (described below).

B@label_1L_chr <- "Country"
B@include_chr <- c("Country", "Official","Common","A3","A2")

We now add B to X.

X <- renew(X, B, what_1L_chr = "standards")

Compare variable of interest values from seed and standards dataset.

To identify any disparities between the variable of interest in our seed and standards datasets we can use the ratify method. Supplying the value “identity” ensures that the output will differ from input only in the slot reserved for results.

X <- ratify(X, new_val_xx = "identity")

We can now identify the values from our seed dataset variable of interest that were not in our standard values.

X@results_ls$Country_Output_Validation$Invalid_Values

We can also identify standard values that were not present in the seed dataset variable of interest.

X@results_ls$Country_Output_Validation$Absent_Values
#>  [1] "Åland Islands"                                "Antarctica"                                   "Bolivia, Plurinational State of"              "Bonaire, Sint Eustatius and Saba"            
#>  [5] "Bouvet Island"                                "British Indian Ocean Territory"               "Brunei Darussalam"                            "Cabo Verde"                                  
#>  [9] "Christmas Island"                             "Cocos (Keeling) Islands"                      "Congo, The Democratic Republic of the"        "Côte d'Ivoire"                               
#> [13] "Curaçao"                                      "Czechia"                                      "Eswatini"                                     "Falkland Islands (Malvinas)"                 
#> [17] "French Southern Territories"                  "Guernsey"                                     "Heard Island and McDonald Islands"            "Holy See (Vatican City State)"               
#> [21] "Hong Kong"                                    "Iran, Islamic Republic of"                    "Korea, Democratic People's Republic of"       "Korea, Republic of"                          
#> [25] "Lao People's Democratic Republic"             "Macao"                                        "Micronesia, Federated States of"              "Moldova, Republic of"                        
#> [29] "Palestine, State of"                          "Réunion"                                      "Russian Federation"                           "Saint Barthélemy"                            
#> [33] "Saint Helena, Ascension and Tristan da Cunha" "Saint Martin (French part)"                   "Saint Vincent and the Grenadines"             "Sint Maarten (Dutch part)"                   
#> [37] "South Georgia and the South Sandwich Islands" "Syrian Arab Republic"                         "Taiwan, Province of China"                    "Tanzania, United Republic of"                
#> [41] "Timor-Leste"                                  "Turks and Caicos Islands"                     "United Kingdom"                               "United States"                               
#> [45] "United States Minor Outlying Islands"         "Venezuela, Bolivarian Republic of"            "Viet Nam"                                     "Virgin Islands, British"                     
#> [49] "Virgin Islands, U.S."

Standardise variable values

We can explore the extent to which we can use fuzzy logic to reconcile some of these discrepancies. To identify the types of fuzzy logic algorithms we could use, run the following command to explore the relevant part of the documentation from the stringdist library.

# Not run
# help("stringdist-metrics", package=stringdist)

In this case, we have chosen the Jaro, or Jaro-Winkler distance method (“jw”).

X <- renew(X, "jw", type_1L_chr = "slot", what_1L_chr = "logic") 
X <- ratify(X, new_val_xx = NULL)

This method will replace every previously invalid seed dataset variable value with the best available match identified by the selected fuzzy logic algorithm.

X@results_ls$Country_Output_Validation$Invalid_Values
#> character(0)

However, some of the replacements will be spurious as can be seen by inspecting the record of the replacements made.

X@results_ls$Country_Output_Correspondences
#> # A tibble: 41 × 2
#>    old_nms_chr               new_nms_chr                          
#>    <chr>                     <chr>                                
#>  1 Azores                    Timor-Leste                          
#>  2 Bolivia                   Bolivia, Plurinational State of      
#>  3 British Virgin Islands    Virgin Islands, British              
#>  4 Brunei                    Brunei Darussalam                    
#>  5 Canary Islands            Åland Islands                        
#>  6 Cape Verde                Cabo Verde                           
#>  7 Congo Democratic Republic Congo, The Democratic Republic of the
#>  8 Czech Republic            Czechia                              
#>  9 East Timor                Eswatini                             
#> 10 Easter Island             Christmas Island                     
#> # ℹ 31 more rows

For each of the incorrect correspondences, we will need to manually specify correct values. We can do this using the ready4show_correspondences sub-module.

# Not run
# a <- ready4show::renew.ready4show_correspondences(ready4show::ready4show_correspondences(), 
#         old_nms_chr = c("old_name_1", "old_name_2", "etc...."), new_nms_chr = c("new_name_1", "new_name_2", "etc...."))

The make_country_correspondences can be used as a shortcut for creating the alternative correspondences for this specific example.

We can inspect the values of this correspondence table.

exhibit(a, scroll_box_args_ls = list(width = "100%"))
Old name New name
Azores Portugal
Canary Islands Spain
Easter Island Chile
East Timor Timor-Leste
Ivory Coast Côte d'Ivoire
Kosovo Kosovo
Madeira Portugal
Netherlands Antilles Bonaire, Sint Eustatius and Saba
Sicily Italy
Vatican City Holy See (Vatican City State)

When the ratify method was used to apply the fuzzy logic algorithm in a previous step, X was modified so that this logic is by default switched off for future calls to ratify. If we had created a new correspondence table that specified replacements for all invalid values, this would not be a problem. However, in this example we are only specifying correspondences where the fuzzy logic algorithm failed, so we need to again supply our desired fuzzy logic value.

X <- renew(X, "jw", type_1L_chr = "slot", what_1L_chr = "logic") 

We now rerun our ratify method (which in this example will combine fuzzy logic with lookups from the manually created correspondences table).

X <- ratify(X, new_val_xx = a)

We once again inspect results.

Our correspondences table looks better.

X@results_ls$Country_Output_Correspondences
#> # A tibble: 41 × 2
#>    old_nms_chr               new_nms_chr                          
#>    <chr>                     <chr>                                
#>  1 Azores                    Portugal                             
#>  2 Bolivia                   Bolivia, Plurinational State of      
#>  3 British Virgin Islands    Virgin Islands, British              
#>  4 Brunei                    Brunei Darussalam                    
#>  5 Canary Islands            Spain                                
#>  6 Cape Verde                Cabo Verde                           
#>  7 Congo Democratic Republic Congo, The Democratic Republic of the
#>  8 Czech Republic            Czechia                              
#>  9 East Timor                Timor-Leste                          
#> 10 Easter Island             Chile                                
#> # ℹ 31 more rows

There is still a value that is not included in our standards.

X@results_ls$Country_Output_Validation$Invalid_Values
#> [1] "Kosovo"

We can rerun the ratify method to force the removal of any record that is not included in our standards dataset.

X <- renew(X, T, type_1L_chr = "slot", what_1L_chr = "force") 
X <- ratify(X, new_val_xx = "identity")

No invalid values remain.

X@results_ls$Country_Output_Validation$Invalid_Values
#> character(0)

However, there are also a some values from our standards dataset that are not represented in the results dataset values.

X@results_ls$Country_Output_Validation$Absent_Values
#>  [1] "Åland Islands"                                "Antarctica"                                   "Bouvet Island"                                "British Indian Ocean Territory"              
#>  [5] "Christmas Island"                             "Cocos (Keeling) Islands"                      "Curaçao"                                      "French Southern Territories"                 
#>  [9] "Heard Island and McDonald Islands"            "Hong Kong"                                    "Macao"                                        "Sint Maarten (Dutch part)"                   
#> [13] "South Georgia and the South Sandwich Islands" "United States Minor Outlying Islands"

Whether this is a problem or not depends on the intended purposes of the standardised dataset we are creating. We could choose to rerun the previous steps after making edits to either or both of the standards dataset (e.g. we could delete any superfluous, outdated or incorrect records or use an entirely new standards dataset) and seed dataset (e.g. adding new records or recategorising existing records so that there are corresponding values for every missing standard value). In this case we are going to assume that the above missing values are not a cause for concern for the valid use of our updated dataset for it intended purposes. We can now create a new object Y, using our results dataset’s Ready4useDyad module instance.

Y <- X@results_ls$Country_Output_Lookup

We can inspect the records for cases corresponding to capital cities from our new dataset.

renewSlot(Y,"ds_tb",Y@ds_tb %>% dplyr::filter(capital==1)) %>%
  renew(type_1L_chr = "label") %>%
  exhibit(scroll_box_args_ls = list(width = "100%"))
Dataset
City name Country name Population size Latitude coordinate Longitude coordinate Is the nation's capital city
'Amman Jordan 1303197 31.95 35.93 1
Abu Dhabi United Arab Emirates 619316 24.48 54.37 1
Abuja Nigeria 178462 9.18 7.17 1
Accra Ghana 2029143 5.56 -0.20 1
Adamstown Pitcairn 51 -25.05 -130.10 1
Addis Abeba Ethiopia 2823167 9.03 38.74 1
Agana Guam 1041 13.47 144.75 1
Algiers Algeria 2029936 36.77 3.04 1
Alofi Niue 627 -19.05 -169.92 1
Amsterdam Netherlands 744159 52.37 4.89 1
Andorra la Vella Andorra 20314 42.51 1.51 1
Ankara Turkey 3579706 39.93 32.85 1
Antananarivo Madagascar 1463754 -18.89 47.51 1
Apia Samoa 40805 -13.83 -171.76 1
Asgabat Turkmenistan 823013 37.95 58.38 1
Asmara Eritrea 578860 15.33 38.94 1
Astana Kazakhstan 351343 51.17 71.47 1
Asuncion Paraguay 507574 -25.30 -57.63 1
Athens Greece 725049 37.98 23.73 1
Avarua Cook Islands 13645 -21.20 -159.76 1
Baghdad Iraq 5753612 33.33 44.44 1
Bairiki Kiribati 45982 1.33 172.99 1
Baku Azerbaijan 1118725 40.39 49.86 1
Bamako Mali 1342519 12.65 -7.99 1
Bandar Seri Begawan Brunei Darussalam 67077 4.93 114.95 1
Bangkok Thailand 4935988 13.73 100.50 1
Bangui Central African Republic 547668 4.36 18.56 1
Banjul Gambia 34388 13.46 -16.60 1
Basse-Terre Guadeloupe 11298 16.00 -61.72 1
Basseterre Saint Kitts and Nevis 12883 17.31 -62.73 1
Bayrut Lebanon 1273440 33.88 35.50 1
Beijing China 7602069 39.93 116.40 1
Belgrade Serbia 1113589 44.83 20.50 1
Belmopan Belize 14590 17.25 -88.79 1
Berlin Germany 3378275 52.52 13.38 1
Bern Switzerland 120596 46.95 7.44 1
Biskek Kyrgyzstan 915625 42.87 74.57 1
Bissau Guinea-Bissau 404119 11.87 -15.60 1
Bogota Colombia 7235084 4.63 -74.09 1
Brasilia Brazil 2260541 -15.78 -47.91 1
Bratislava Slovakia 422452 48.16 17.13 1
Brazzaville Congo 1326975 -4.25 15.26 1
Bridgetown Barbados 98725 13.11 -59.61 1
Brussels Belgium 1031925 50.83 4.33 1
Bucharest Romania 1862930 44.44 26.10 1
Budapest Hungary 1700019 47.51 19.08 1
Buenos Aires Argentina 11595183 -34.61 -58.37 1
Bujumbura Burundi 336561 -3.37 29.35 1
Cairo Egypt 7836243 30.06 31.25 1
Canberra Australia 324736 -35.31 149.13 1
Caracas Venezuela, Bolivarian Republic of 1808937 10.54 -66.93 1
Castries Saint Lucia 12904 14.03 -60.98 1
Cayenne French Guiana 62926 4.92 -52.34 1
Charlotte Amalie Virgin Islands, U.S. 10415 18.35 -64.94 1
Chisinau Moldova, Republic of 623671 47.03 28.83 1
Cockburn Town Turks and Caicos Islands 174 21.46 -71.14 1
Colombo Sri Lanka 649496 6.93 79.85 1
Conakry Guinea 1970382 9.55 -13.67 1
Copenhagen Denmark 1091978 55.68 12.57 1
Dakar Senegal 2406598 14.72 -17.48 1
Damascus Syrian Arab Republic 1580909 33.50 36.32 1
Dhaka Bangladesh 6724976 23.70 90.39 1
Dili Timor-Leste 163305 -8.57 125.58 1
Dodoma Tanzania, United Republic of 188150 -6.17 35.74 1
Doha Qatar 351381 25.30 51.51 1
Douglas Isle of Man 25621 54.15 -4.48 1
Dublin Ireland 1030431 53.33 -6.25 1
Dushanbe Tajikistan 538456 38.57 68.78 1
Dzaoudzi Mayotte 14558 -12.77 45.25 1
Fakaofo Tokelau 267 -9.38 -171.22 1
Fort-de-France Martinique 89233 14.60 -61.08 1
Freetown Sierra Leone 818709 8.49 -13.24 1
Gaborone Botswana 214412 -24.65 25.91 1
George Town Cayman Islands 30570 19.28 -81.39 1
Georgetown Guyana 236878 6.79 -58.16 1
Gibraltar Gibraltar 26404 36.14 -5.35 1
Guatemala Guatemala 1010253 14.63 -90.55 1
Ha Noi Viet Nam 1452055 21.03 105.84 1
Hamilton Bermuda 889 32.30 -64.79 1
Harare Zimbabwe 1575127 -17.82 31.05 1
Havanna Cuba 2163132 23.13 -82.39 1
Helsinki Finland 558341 60.17 24.94 1
Honiara Solomon Islands 57410 -9.43 159.91 1
Islamabad Pakistan 794431 33.72 73.06 1
Jakarta Indonesia 8556798 -6.18 106.83 1
Jamestown Saint Helena, Ascension and Tristan da Cunha 603 -15.92 -5.71 1
Jerusalem Israel 731731 31.78 35.22 1
Jibuti Djibouti 633884 11.56 43.15 1
Kabul Afghanistan 3120963 34.53 69.17 1
Kampala Uganda 1403619 0.32 32.58 1
Kathmandu Nepal 822930 27.71 85.31 1
Khartoum Sudan 2090001 15.58 32.52 1
Kiev Ukraine 2491404 50.43 30.52 1
Kigali Rwanda 800003 -1.94 30.06 1
Kingston Jamaica 585300 17.99 -76.80 1
Kingston Norfolk Island 890 -29.03 168.05 1
Kingstown Saint Vincent and the Grenadines 18160 13.16 -61.23 1
Kinshasa Congo, The Democratic Republic of the 8096254 -4.31 15.32 1
Koror Palau 11458 7.35 134.51 1
Kuala Lumpur Malaysia 1482359 3.16 101.71 1
Libreville Gabon 591356 0.39 9.45 1
Lilongwe Malawi 683477 -13.97 33.80 1
Lima Peru 7857121 -12.07 -77.05 1
Lisbon Portugal 508209 38.72 -9.14 1
Ljubljana Slovenia 254188 46.06 14.51 1
Lome Togo 737751 6.17 1.35 1
London United Kingdom 7489022 51.52 -0.10 1
Longyearbyen Svalbard and Jan Mayen 1263 78.21 15.61 1
Luanda Angola 2875277 -8.82 13.24 1
Lusaka Zambia 1306577 -15.42 28.29 1
Luxemburg Luxembourg 76380 49.62 6.12 1
Madrid Spain 3146804 40.42 -3.71 1
Malabo Equatorial Guinea 161409 3.74 8.79 1
Male Maldives 87154 4.17 73.50 1
Managua Nicaragua 990417 12.15 -86.27 1
Manama Bahrain 147894 26.21 50.58 1
Manila Philippines 10546511 14.62 120.97 1
Maputo Mozambique 1220167 -25.95 32.57 1
Maseru Lesotho 116268 -29.31 27.49 1
Mata'utu Wallis and Futuna 1310 -13.28 -176.13 1
Mbabane Eswatini 78740 -26.32 31.14 1
Mexico City Mexico 8659409 19.43 -99.14 1
Minsk Belarus 1747482 53.91 27.55 1
Mogadishu Somalia 2723378 2.05 45.33 1
Monaco-Ville Monaco 975 43.74 7.42 1
Monrovia Liberia 954458 6.31 -10.80 1
Montevideo Uruguay 1271664 -34.87 -56.17 1
Moroni Comoros 43704 -11.74 43.23 1
Moscow Russian Federation 10472629 55.75 37.62 1
Muscat Oman 24122 23.61 58.54 1
N'Djamena Chad 737281 12.11 15.05 1
Nairobi Kenya 2864667 -1.29 36.82 1
Nassau Bahamas 231519 25.06 -77.33 1
Ni Dilli India 321883 28.60 77.22 1
Niamey Niger 801297 13.52 2.12 1
Nicosia Cyprus 202488 35.16 33.38 1
Nicosia Cyprus 42372 35.18 33.37 1
Nouakchott Mauritania 731242 18.09 -15.98 1
Noumea New Caledonia 94751 -22.27 166.44 1
Nuku'alofa Tonga 23733 -21.14 -175.22 1
Nuuk Greenland 15243 64.18 -51.73 1
Oranjestad Aruba 30710 12.53 -70.03 1
Oslo Norway 821445 59.91 10.75 1
Ottawa Canada 885542 45.42 -75.71 1
Ouagadougou Burkina Faso 1119775 12.37 -1.53 1
Pago Pago American Samoa 4180 -14.24 -170.72 1
Palikir Micronesia, Federated States of 4552 6.92 158.16 1
Panama Panama 406070 8.97 -79.53 1
Papeete French Polynesia 26400 -17.52 -149.56 1
Paramaribo Suriname 224925 5.85 -55.20 1
Paris France 2141839 48.86 2.34 1
Phnum Penh Cambodia 1673131 11.57 104.92 1
Port Louis Mauritius 156760 -20.17 57.51 1
Port Moresby Papua New Guinea 289861 -9.48 147.18 1
Port Stanley Falkland Islands (Malvinas) 2269 -51.70 -57.82 1
Port of Spain Trinidad and Tobago 49764 10.66 -61.51 1
Port-au-Prince Haiti 1277104 18.54 -72.34 1
Porto Novo Benin 238199 6.48 2.63 1
Prague Czechia 1168374 50.08 14.43 1
Praia Cabo Verde 117342 14.93 -23.54 1
Pretoria South Africa 1687779 -25.73 28.22 1
Pyongyang Korea, Democratic People's Republic of 2992272 39.02 125.75 1
Quito Ecuador 1399814 -0.19 -78.50 1
Rabat Morocco 1688738 34.02 -6.84 1
Rangoon Myanmar 4572948 16.79 96.15 1
Reykjavik Iceland 114576 64.14 -21.92 1
Riga Latvia 738386 56.97 24.13 1
Rita Marshall Islands 21270 7.12 171.06 1
Riyadh Saudi Arabia 4328067 24.65 46.77 1
Road Town Virgin Islands, British 8613 18.43 -64.63 1
Rome Italy 2561181 41.89 12.50 1
Roseau Dominica 16577 15.30 -61.39 1
Saint George's Grenada 4315 12.06 -61.74 1
Saint Helier Jersey 28910 49.19 -2.11 1
Saint John's Antigua and Barbuda 25321 17.11 -61.85 1
Saint Peter Port Guernsey 16702 49.47 -2.55 1
Saint-Denis Réunion 137787 -20.87 55.46 1
Saint-Pierre Saint Pierre and Miquelon 6254 46.79 -56.18 1
San Jose Costa Rica 32187 10.97 -85.13 1
San Jose Costa Rica 339588 9.93 -84.08 1
San Juan Puerto Rico 417154 18.44 -66.13 1
San Marino San Marino 4624 43.94 12.43 1
San Salvador El Salvador 534409 13.69 -89.19 1
San'a Yemen 1921589 15.38 44.21 1
Santiago Chile 4893495 -33.46 -70.64 1
Santo Domingo Dominican Republic 2253437 18.48 -69.91 1
Sao Tome Sao Tome and Principe 63772 0.37 6.73 1
Sarajevo Bosnia and Herzegovina 737350 43.85 18.38 1
Singapore Singapore 3601745 1.30 103.85 1
Skopje North Macedonia 477493 42.00 21.47 1
Sofia Bulgaria 1166143 42.69 23.31 1
Seoul Korea, Republic of 10409345 37.56 126.99 1
Stockholm Sweden 1260712 59.33 18.07 1
Sucre Bolivia, Plurinational State of 232669 -19.06 -65.26 1
Susupe Northern Mariana Islands 2402 15.14 145.70 1
Taipei Taiwan, Province of China 2491662 25.02 121.45 1
Tallinn Estonia 392386 59.44 24.74 1
Tashkent Uzbekistan 1967879 41.31 69.30 1
Tbilisi Georgia 1038343 41.72 44.79 1
Tegucigalpa Honduras 872403 14.09 -87.22 1
Tehran Iran, Islamic Republic of 7160094 35.67 51.43 1
The Valley Anguilla 1435 18.22 -63.05 1
Thimphu Bhutan 74175 27.48 89.70 1
Tirana Albania 380403 41.33 19.82 1
Tokyo Japan 8372440 35.67 139.77 1
Torshavn Faroe Islands 13313 62.03 -6.80 1
Tripoli Libya 1164634 32.87 13.18 1
Tunis Tunisia 693294 36.84 10.22 1
Ulaanbaatar Mongolia 862842 47.93 106.91 1
Vaduz Liechtenstein 5248 47.14 9.53 1
Vaiaku Tuvalu 4835 -8.52 179.20 1
Valletta Malta 6748 35.91 14.52 1
Vatican City Holy See (Vatican City State) 767 41.90 12.46 1
Victoria Seychelles 22611 -4.62 55.45 1
Vienna Austria 1570976 48.22 16.37 1
Vientiane Lao People's Democratic Republic 199863 17.97 102.61 1
Vila Vanuatu 37141 -17.74 168.31 1
Vilnius Lithuania 542014 54.70 25.27 1
Warsaw Poland 1634441 52.26 21.02 1
Washington United States 548359 38.91 -77.02 1
Wellington New Zealand 182254 -41.28 174.78 1
Willemstad Bonaire, Sint Eustatius and Saba 98339 12.10 -68.93 1
Windhoek Namibia 277349 -22.56 17.09 1
Yamoussoukro Côte d'Ivoire 200103 6.82 -5.28 1
Yaounde Cameroon 1344617 3.87 11.52 1
Yaren Nauru 4587 -0.55 166.91 1
Yerevan Armenia 1090537 40.17 44.52 1
Zagreb Croatia 700717 45.80 15.97 1
al-'Ayun Western Sahara 188084 27.16 -13.20 1
al-Kuwayt Kuwait 63596 29.38 47.99 1
Last modified February 3, 2024: partially aliased reorganisation (05709d2)