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Operators over intuitionistic fuzzy sets: Difference between revisions

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In May 1983 the modal operators [[necessity and possibility]] were defined. In October 1983 the topological operators [[closure and interior]] followed. Later, the relations between the modal and the topological operators were studied and published<ref>[[Krassimir Atanassov|Atanassov, K.]], ''More on intuitionistic fuzzy sets'', Fuzzy Sets and Systems, 33, 1989, No. 1, 37-46</ref>.
In May 1983 the modal operators [[necessity and possibility]] were defined. In October 1983 the topological operators [[closure and interior]] followed. Later, the relations between the modal and the topological operators were studied and published<ref>[[Krassimir Atanassov|Atanassov, K.]], ''More on intuitionistic fuzzy sets'', Fuzzy Sets and Systems, 33, 1989, No. 1, 37-46</ref>.
; References:
* [http://upcommons.upc.edu/revistes/bitstream/2099/3593/1/vol8-1-Atanasov.pdf A theorem for basis operators over intuitionistic fuzzy sets], Krassimir Atanassov, 2001


== Modal type operators ==
== Modal type operators ==

Revision as of 23:47, 16 March 2011

Different operators were defined over intuitionistic fuzzy sets throughout the years.

In May 1983 the modal operators necessity and possibility were defined. In October 1983 the topological operators closure and interior followed. Later, the relations between the modal and the topological operators were studied and published[1].

References


Modal type operators

Necessity and possibility

Operator Dα

Operator Fα,β

Operator Gα,β

Operators Hα,β , H*α,β , Jα,β and J*α,β

Operator Xa,b,c,d,e,f

Topological operators

References

Closure and interior

Level operators

Operators ! and ?

Operators Pα,β and Qα,β

References

  1. ↑ Atanassov, K., More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33, 1989, No. 1, 37-46
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