ELECTRONIC SUPPLEMENTARY INFORMATION (ESI)

Advancing hazard assessment of energy accidents in the natural gas sector with rough set theory and decision rules
Marco Cinelli1,*,^, Matteo Spada2, Miłosz Kadziński3, Grzegorz Miebs3, Peter Burgherr2 
1 Future Resilient Systems (FRS), Swiss Federal Institute of Technology (ETH) Zürich, Singapore-ETH Centre (SEC), Singapore
2 Paul Scherrer Institut (PSI), Laboratory for Energy Systems Analysis, Villigen PSI, Switzerland
3 Institute of Computing Science, Poznań University of Technology, Poznań, Poland
* Corresponding author: Marco Cinelli; email: marco.cinelli@put.poznan.pl  
^ Current address: Environmental Decision Analytics Branch, Land Remediation and Technology Division, Center for Environmental Solutions and Emergency Response, U.S. Environmental Protection Agency (EPA), Cincinnati, Ohio, USA


S.4 SINGLE CLASS-BASED RULES 

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INTERPRETATION OF AN EXAMPLE DECISION RULE
(A1 = 2) & (A5 = 99) & (A2 = 5) => D1 = 1 | D1 = 2 [5, 6, 3,297%, 2,747%, 3,797%, 3,165%, 83,333%][4, 1, 1][{116, 118, 56, 112}, {144}, {162}]
CONDITION PART => DECISION PART [5 - number of alternatives satisfying the condition and decision parts of the rule, 6 - number of alternatives satisfying the condition part of the rule, 3,297 = 6/(cardinality of the entire set of alternatives), 2,747 = 5/(cardinality of the entire set of alternatives), 3,797 = 6/(cardinality of class/class union in the decision part), 3,165 = 5/(cardinality of class/class union in the decision part), 83,333 = 5/6 - certainty][4 alternatives covered in the first class, 2 alternatives covered in the second class, 1 alternative covered in the third class][{116, 118, 56, 112}, {144}, {162}] - indices of the covered alternatives in the respective classes
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==X means Rules for Cl X

==1
(A3 = 33) & (A5 = 2) & (A2 = 6) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{88}, {}, {}]
(A1 = 2) & (A5 = 2) & (A4 = 38) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{4}, {}, {}]
(A3 = 22) & (A5 = 3) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{219}, {}, {}]
(A5 = 4) & (A6 = 99) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{49, 48}, {}, {}]
(A7 = 99) & (A4 = 7) => D1 = 1 [3, 3, 1,2%, 1,2%, 1,863%, 1,863%, 100%][3, 0, 0][{98, 69, 8}, {}, {}]
(A3 = 32) & (A5 = 3) => D1 = 1 [2, 3, 1,2%, 0,8%, 1,863%, 1,242%, 66,667%][2, 1, 0][{33, 104}, {123}, {}]
(A2 = 8) & (A1 = 1) & (A5 = 4) => D1 = 1 [3, 3, 1,2%, 1,2%, 1,863%, 1,863%, 100%][3, 0, 0][{26, 59, 92}, {}, {}]
(A5 = 2) & (A1 = 2) & (A3 = 34) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{231}, {}, {}]
(A1 = 2) & (A3 = 10) & (A4 = 4) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{99}, {}, {}]
(A1 = 1) & (A7 = 3) & (A5 = 5) => D1 = 1 [3, 3, 1,2%, 1,2%, 1,863%, 1,863%, 100%][3, 0, 0][{53, 7, 13}, {}, {}]
(A5 = 8) & (A3 = 34) => D1 = 1 [2, 3, 1,2%, 0,8%, 1,863%, 1,242%, 66,667%][2, 1, 0][{247, 223}, {203}, {}]
(A5 = 38) & (A3 = 10) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{36}, {}, {}]
(A3 = 10) & (A6 = 3) & (A4 = 4) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{101, 27}, {}, {}]
(A4 = 5) & (A6 = 99) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{94, 16}, {}, {}]
(A3 = 32) & (A4 = 2) & (A5 = 99) => D1 = 1 [20, 28, 11,2%, 8%, 17,391%, 12,422%, 71,429%][20, 5, 3][{34, 198, 73, 11, 79, 111, 80, 18, 19, 83, 52, 181, 55, 24, 185, 186, 187, 60, 61, 189}, {194, 151, 138, 157, 127}, {164, 172, 240}]
(A6 = 2) & (A5 = 3) => D1 = 1 [4, 4, 1,6%, 1,6%, 2,484%, 2,484%, 100%][4, 0, 0][{21, 9, 41, 250}, {}, {}]
(A2 = 8) & (A1 = 1) & (A4 = 2) & (A5 = 99) => D1 = 1 [17, 19, 7,6%, 6,8%, 11,801%, 10,559%, 89,474%][17, 2, 0][{3, 67, 37, 38, 198, 73, 42, 11, 79, 111, 80, 83, 52, 55, 61, 93, 189}, {194, 151}, {}]
(A3 = 32) & (A1 = 2) & (A4 = 4) => D1 = 1 [3, 3, 1,2%, 1,2%, 1,863%, 1,863%, 100%][3, 0, 0][{102, 182, 87}, {}, {}]
(A1 = 1) & (A3 = 34) & (A4 = 4) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{226, 39}, {}, {}]
(A5 = 4) & (A6 = 3) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{71, 72}, {}, {}]
(A5 = 5) & (A6 = 3) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{75, 44}, {}, {}]
(A1 = 2) & (A3 = 34) & (A4 = 2) & (A5 = 99) => D1 = 1 [6, 9, 3,6%, 2,4%, 5,59%, 3,727%, 66,667%][6, 1, 2][{230, 40, 232, 43, 237, 207}, {205}, {244, 176}]
(A1 = 2) & (A6 = 99) & (A4 = 12) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{227, 204}, {}, {}]
(A5 = 17) & (A1 = 2) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{65, 32}, {}, {}]
(A4 = 17) & (A6 = 99) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{23}, {}, {}]
(A1 = 1) & (A5 = 2) & (A6 = 99) & (A4 = 4) & (A2 = 5) => D1 = 1 [3, 3, 1,2%, 1,2%, 1,863%, 1,863%, 100%][3, 0, 0][{51, 78, 96}, {}, {}]
(A1 = 1) & (A3 = 10) & (A4 = 2) & (A5 = 3) => D1 = 1 [3, 4, 1,6%, 1,2%, 2,484%, 1,863%, 75%][3, 1, 0][{50, 46, 63}, {135}, {}]
(A4 = 40) & (A1 = 1) & (A3 = 10) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{241}, {}, {}]
(A4 = 1) & (A5 = 99) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{195}, {}, {}]
(A1 = 2) & (A5 = 99) & (A4 = 4) => D1 = 1 [4, 4, 1,6%, 1,6%, 2,484%, 2,484%, 100%][4, 0, 0][{199, 200, 217, 91}, {}, {}]
(A4 = 8) & (A1 = 2) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{105}, {}, {}]
(A4 = 2) & (A6 = 3) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{109}, {}, {}]
(A1 = 1) & (A4 = 1) & (A6 = 4) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{85, 234}, {}, {}]
(A1 = 1) & (A4 = 1) & (A5 = 2) & (A6 = 99) => D1 = 1 [3, 3, 1,2%, 1,2%, 1,863%, 1,863%, 100%][3, 0, 0][{97, 193, 5}, {}, {}]
(A2 = 2) & (A4 = 38) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{90}, {}, {}]
(A1 = 1) & (A3 = 10) & (A5 = 99) & (A2 = 5) => D1 = 1 [11, 15, 6%, 4,4%, 9,317%, 6,832%, 73,333%][11, 1, 3][{1, 68, 84, 100, 214, 74, 107, 28, 29, 14, 64}, {134}, {171, 158, 159}]
(A1 = 2) & (A5 = 2) & (A4 = 3) & (A2 = 5) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{197, 246}, {}, {}]
(A2 = 8) & (A1 = 1) & (A4 = 38) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{54}, {}, {}]
(A3 = 32) & (A4 = 40) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{106}, {}, {}]
(A1 = 1) & (A3 = 2) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{77}, {}, {}]
(A4 = 17) & (A1 = 2) & (A6 = 2) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{45}, {}, {}]
(A1 = 1) & (A5 = 2) & (A3 = 99) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{114}, {}, {}]
(A7 = 3) & (A5 = 4) & (A4 = 12) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{70}, {}, {}]
(A1 = 1) & (A3 = 33) & (A6 = 99) => D1 = 1 [5, 6, 2,4%, 2%, 3,727%, 3,106%, 83,333%][5, 1, 0][{81, 3, 67, 56, 25}, {126}, {}]
(A1 = 2) & (A3 = 10) & (A5 = 99) => D1 = 1 [5, 7, 2,8%, 2%, 4,348%, 3,106%, 71,429%][5, 1, 1][{113, 116, 118, 215, 47}, {145}, {161}]
(A3 = 16) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{17}, {}, {}]
(A3 = 24) & (A1 = 2) & (A7 = 99) & (A5 = 3) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{76}, {}, {}]
(A3 = 19) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{35}, {}, {}]
(A5 = 2) & (A1 = 2) & (A4 = 12) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{212}, {}, {}]
(A1 = 1) & (A3 = 26) => D1 = 1 [3, 3, 1,2%, 1,2%, 1,863%, 1,863%, 100%][3, 0, 0][{210, 20, 58}, {}, {}]
(A4 = 40) & (A6 = 3) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{196, 86}, {}, {}]
(A2 = 8) & (A5 = 2) & (A3 = 10) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{103}, {}, {}]
(A4 = 2) & (A3 = 99) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{89, 15}, {}, {}]
(A2 = 4) & (A1 = 1) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{110}, {}, {}]
(A1 = 1) & (A6 = 2) & (A7 = 99) & (A5 = 5) & (A2 = 5) => D1 = 1 [5, 5, 2%, 2%, 3,106%, 3,106%, 100%][5, 0, 0][{2, 6, 30, 62, 31}, {}, {}]
(A3 = 29) & (A5 = 99) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{208}, {}, {}]
(A1 = 1) & (A5 = 2) & (A6 = 3) & (A4 = 12) => D1 = 1 [2, 2, 0,8%, 0,8%, 1,242%, 1,242%, 100%][2, 0, 0][{115, 95}, {}, {}]
(A2 = 2) & (A6 = 3) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{10}, {}, {}]
(A3 = 32) & (A6 = 2) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{184}, {}, {}]
(A3 = 32) & (A1 = 1) & (A6 = 3) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{12}, {}, {}]
(A5 = 3) & (A2 = 5) & (A3 = 29) => D1 = 1 [1, 1, 0,4%, 0,4%, 0,621%, 0,621%, 100%][1, 0, 0][{249}, {}, {}]

==2
(A3 = 33) & (A5 = 3) & (A2 = 6) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {248}, {}]
(A5 = 4) & (A4 = 39) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {154}, {}]
(A4 = 1) & (A1 = 2) & (A5 = 2) & (A2 = 6) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {137}, {}]
(A2 = 8) & (A1 = 2) & (A4 = 38) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {221}, {}]
(A5 = 2) & (A6 = 99) & (A4 = 12) => D1 = 2 [2, 2, 0,8%, 0,8%, 3,774%, 3,774%, 100%][0, 2, 0][{}, {120, 128}, {}]
(A1 = 1) & (A5 = 3) & (A2 = 6) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {130}, {}]
(A2 = 8) & (A3 = 10) & (A6 = 2) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {148}, {}]
(A7 = 3) & (A5 = 4) & (A4 = 7) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {133}, {}]
(A1 = 2) & (A4 = 2) & (A3 = 13) => D1 = 2 [2, 2, 0,8%, 0,8%, 3,774%, 3,774%, 100%][0, 2, 0][{}, {242, 213}, {}]
(A4 = 40) & (A1 = 2) & (A5 = 2) & (A6 = 99) & (A2 = 5) => D1 = 2 [2, 3, 1,2%, 0,8%, 5,66%, 3,774%, 66,667%][1, 2, 0][{66}, {129, 233}, {}]
(A1 = 2) & (A3 = 11) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {156}, {}]
(A1 = 2) & (A4 = 99) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {153}, {}]
(A1 = 1) & (A4 = 1) & (A3 = 10) & (A6 = 3) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {136}, {}]
(A3 = 32) & (A7 = 2) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {141}, {}]
(A3 = 13) & (A6 = 2) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {202}, {}]
(A4 = 1) & (A1 = 2) & (A3 = 29) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {121}, {}]
(A3 = 33) & (A4 = 1) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {152}, {}]
(A2 = 8) & (A4 = 3) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {236}, {}]
(A2 = 8) & (A4 = 8) & (A8 = 99) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {124}, {}]
(A3 = 32) & (A1 = 1) & (A4 = 4) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {132}, {}]
(A7 = 2) & (A8 = 99) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {119}, {}]
(A4 = 1) & (A1 = 2) & (A6 = 2) & (A2 = 5) => D1 = 2 [2, 2, 0,8%, 0,8%, 3,774%, 3,774%, 100%][0, 2, 0][{}, {155, 144}, {}]
(A3 = 32) & (A4 = 1) & (A6 = 3) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {142}, {}]
(A3 = 33) & (A1 = 2) & (A5 = 99) => D1 = 2 [3, 4, 1,6%, 1,2%, 7,547%, 5,66%, 75%][1, 3, 0][{183}, {139, 125, 191}, {}]
(A2 = 8) & (A6 = 3) & (A4 = 4) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {143}, {}]
(A4 = 5) & (A1 = 2) => D1 = 2 [1, 1, 0,4%, 0,4%, 1,887%, 1,887%, 100%][0, 1, 0][{}, {147}, {}]

==3
(A5 = 8) & (A3 = 10) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {228}]
(A2 = 1) & (A4 = 1) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {174}]
(A1 = 1) & (A4 = 2) & (A2 = 6) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {165}]
(A4 = 1) & (A1 = 2) & (A5 = 2) & (A2 = 5) => D1 = 3 [2, 2, 0,8%, 0,8%, 5,556%, 5,556%, 100%][0, 0, 2][{}, {}, {225, 167}]
(A1 = 1) & (A4 = 17) & (A5 = 2) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {179}]
(A2 = 9) & (A3 = 13) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {190}]
(A6 = 4) & (A1 = 2) => D1 = 3 [2, 2, 0,8%, 0,8%, 5,556%, 5,556%, 100%][0, 0, 2][{}, {}, {180, 235}]
(A2 = 4) & (A5 = 3) => D1 = 3 [2, 2, 0,8%, 0,8%, 5,556%, 5,556%, 100%][0, 0, 2][{}, {}, {168, 192}]
(A4 = 17) & (A1 = 2) & (A6 = 3) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {175}]
(A1 = 1) & (A4 = 2) & (A3 = 11) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {220}]
(A5 = 2) & (A3 = 6) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {218}]
(A3 = 32) & (A5 = 8) & (A1 = 2) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {166}]
(A1 = 1) & (A4 = 3) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {177}]
(A1 = 2) & (A3 = 10) & (A5 = 3) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {178}]
(A1 = 1) & (A3 = 14) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {206}]
(A6 = 5) & (A7 = 2) => D1 = 3 [1, 1, 0,4%, 0,4%, 2,778%, 2,778%, 100%][0, 0, 1][{}, {}, {162}]