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The Inclusion-Exclusion Principle for IF-States | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 3، دوره 11، شماره 2، تیر 2014، صفحه 17-25 اصل مقاله (345.54 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1488 | ||
نویسندگان | ||
L. C. Ciungu ![]() | ||
1Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419, USA | ||
2Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovskeho 40, Banska Bystrica, Slovakia | ||
چکیده | ||
Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events. In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events. Finally, we give some applications of this principle by extending some results regarding the classical probabilities to the case of the IF-states. | ||
کلیدواژهها | ||
IF-set؛ IF-event؛ IFS-probability؛ IF-state؛ Inclusion-exclusion principle؛ Boole inequality؛ Bonferroni inequality؛ L ukasiewicz connectives | ||
مراجع | ||
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