Call for Papers for the 27th International Conference on Intuitionistic Fuzzy Sets is now open!
Conference: 5–6 July 2024, Burgas, Bulgaria • EXTENDED DEADLINE for submissions: 15 APRIL 2024.
Conference: 5–6 July 2024, Burgas, Bulgaria • EXTENDED DEADLINE for submissions: 15 APRIL 2024.
Issue:Modified level operator Nγ1γ2 applied over interval-valued intuitionistic fuzzy sets: Difference between revisions
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[[Category:Publications in 2018 year|{{PAGENAME}}]] | [[Category:Publications in 2018 year|{{PAGENAME}}]] | ||
{{issue/title | {{issue/title | ||
| title = Modified level operator | | title = Modified level operator <math>N_{\gamma_1}^{\gamma_2}</math> applied over interval-valued intuitionistic fuzzy sets | ||
| shortcut = nifs/24/4/29-39 | | shortcut = nifs/24/4/29-39 | ||
}} | }} | ||
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| format = PDF | | format = PDF | ||
| size = 158 Kb | | size = 158 Kb | ||
| abstract = The recently proposed intuitionistic fuzzy level operator | | abstract = The recently proposed intuitionistic fuzzy level operator <math>N_\gamma</math> generates a subset of an intuitionistic fuzzy set <math>A</math>, where the elements of the subset are those elements of <math>A</math>, for which the ratio of their degrees of membership to their degrees of non-membership is greater than or equal to a given constant <math>\gamma > 0</math>. Here we propose a continuation of this idea from the case of intuitionistic fuzzy sets to the case of interval-valued intuitionistic fuzzy sets. This modification requires us to introduce a second constant, i.e. <math>\gamma_1,\gamma_2 > 0</math>. We show that there are twenty possible scenarios for the mutual position of the intervalized level operator <math>N_{\gamma_1}^{\gamma_2}</math> and the element of the interval-valued intuitionistic fuzzy set, and give the respective formulas which calculate in each case the membership and non-membership degrees with which the IVIFS element belongs to the set defined by the operator <math>N_{\gamma_1}^{\gamma_2}</math>. These twenty scenarios are graphically interpreted in the intuitionistic fuzzy interpretational triangle, and the respective formulas have been derived. In conclusion, further ideas of research have been suggested. | ||
membership and non-membership degrees with which the IVIFS element belongs to the set defined by the operator | |||
| keywords = Interval valued intuitionistic fuzzy sets, Intuitionistic fuzzy sets, Level operator, Decision making under uncertainty. | | keywords = Interval valued intuitionistic fuzzy sets, Intuitionistic fuzzy sets, Level operator, Decision making under uncertainty. | ||
| ams = 03E72. | | ams = 03E72. |
Latest revision as of 16:55, 17 December 2018
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