A Concise Introduction to HyperFuzzy, HyperNeutrosophic, HyperPlithogenic, HyperSoft, and HyperRough Sets with Practical Examples
Takaaki Fujita Β· Florentin Smarandache
Infinite Study
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Π‘ΡΡΠ°Π½ΠΈΡΠ°
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ΠΡΠΏΡΡΠ°Π²Π° ΡΡΠ»ΠΎΠ²Π΅
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reportΠΡΠ΅Π½Π΅ ΠΈ ΡΠ΅ΡΠ΅Π½Π·ΠΈΡΠ΅ Π½ΠΈΡΡ Π²Π΅ΡΠΈΡΠΈΠΊΠΎΠ²Π°Π½Π΅ Β Π‘Π°Π·Π½Π°ΡΡΠ΅ Π²ΠΈΡΠ΅
Π ΠΎΠ²ΠΎΡ Π΅-ΠΊΡΠΈΠ·ΠΈ
Various set concepts are widely recognized for effectively addressing uncertainty, including fuzzy sets, neutrosophic sets, plithogenic sets, rough sets, and soft sets. These concepts have been further extended through hyperstructures (based on powersets) and superhyperstructures (based on n-th powersets, which are sets with repeated power set structures). These extensions are commonly referred to as HyperUncertain, SuperUncertain, and SuperHyperUncertain Sets/Logics/Probabilities/Statistics, and they were introduced by Smarandache in 2016-2017 as parts of HyperStructures, SuperStructures, and SuperHyperStructures respectively. This paper recalls these concepts along with concrete examples.
ΠΡΠ΅Π½ΠΈΡΠ΅ ΠΎΠ²Ρ Π΅-ΠΊΡΠΈΠ³Ρ
ΠΠ°Π²ΠΈΡΠ΅ Π½Π°ΠΌ ΡΠ²ΠΎΡΠ΅ ΠΌΠΈΡΡΠ΅ΡΠ΅.
ΠΠ½ΡΠΎΡΠΌΠ°ΡΠΈΡΠ΅ ΠΎ ΡΠΈΡΠ°ΡΡ
ΠΠ°ΠΌΠ΅ΡΠ½ΠΈ ΡΠ΅Π»Π΅ΡΠΎΠ½ΠΈ ΠΈ ΡΠ°Π±Π»Π΅ΡΠΈ
ΠΠ½ΡΡΠ°Π»ΠΈΡΠ°ΡΡΠ΅ Π°ΠΏΠ»ΠΈΠΊΠ°ΡΠΈΡΡ Google Play ΠΊΡΠΈΠ³Π΅ Π·Π° Android ΠΈ iPad/iPhone. ΠΡΡΠΎΠΌΠ°ΡΡΠΊΠΈ ΡΠ΅ ΡΠΈΠ½Ρ
ΡΠΎΠ½ΠΈΠ·ΡΡΠ΅ ΡΠ° Π½Π°Π»ΠΎΠ³ΠΎΠΌ ΠΈ ΠΎΠΌΠΎΠ³ΡΡΠ°Π²Π° Π²Π°ΠΌ Π΄Π° ΡΠΈΡΠ°ΡΠ΅ ΠΎΠ½Π»Π°ΡΠ½ ΠΈ ΠΎΡΠ»Π°ΡΠ½ Π³Π΄Π΅ Π³ΠΎΠ΄ Π΄Π° ΡΠ΅ Π½Π°Π»Π°Π·ΠΈΡΠ΅.
ΠΠ°ΠΏΡΠΎΠΏΠΎΠ²ΠΈ ΠΈ ΡΠ°ΡΡΠ½Π°ΡΠΈ
ΠΠΎΠΆΠ΅ΡΠ΅ Π΄Π° ΡΠ»ΡΡΠ°ΡΠ΅ Π°ΡΠ΄ΠΈΠΎ-ΠΊΡΠΈΠ³Π΅ ΠΊΡΠΏΡΠ΅Π½Π΅ Π½Π° Google Play-Ρ ΠΏΠΎΠΌΠΎΡΡ Π²Π΅Π±-ΠΏΡΠ΅Π³Π»Π΅Π΄Π°ΡΠ° Π½Π° ΡΠ°ΡΡΠ½Π°ΡΡ.
Π-ΡΠΈΡΠ°ΡΠΈ ΠΈ Π΄ΡΡΠ³ΠΈ ΡΡΠ΅ΡΠ°ΡΠΈ
ΠΠ° Π±ΠΈΡΡΠ΅ ΡΠΈΡΠ°Π»ΠΈ Π½Π° ΡΡΠ΅ΡΠ°ΡΠΈΠΌΠ° ΠΊΠΎΡΠ΅ ΠΊΠΎΡΠΈΡΡΠ΅ Π΅-ΠΌΠ°ΡΡΠΈΠ»ΠΎ, ΠΊΠ°ΠΎ ΡΡΠΎ ΡΡ Kobo Π΅-ΡΠΈΡΠ°ΡΠΈ, ΡΡΠ΅Π±Π° Π΄Π° ΠΏΡΠ΅ΡΠ·ΠΌΠ΅ΡΠ΅ ΡΠ°ΡΠ» ΠΈ ΠΏΡΠ΅Π½Π΅ΡΠ΅ΡΠ΅ Π³Π° Π½Π° ΡΡΠ΅ΡΠ°Ρ. ΠΡΠ°ΡΠΈΡΠ΅ Π΄Π΅ΡΠ°ΡΠ½Π° ΡΠΏΡΡΡΡΠ²Π° ΠΈΠ· ΡΠ΅Π½ΡΡΠ° Π·Π° ΠΏΠΎΠΌΠΎΡ Π΄Π° Π±ΠΈΡΡΠ΅ ΠΏΡΠ΅Π½Π΅Π»ΠΈ ΡΠ°ΡΠ»ΠΎΠ²Π΅ Ρ ΠΏΠΎΠ΄ΡΠΆΠ°Π½Π΅ Π΅-ΡΠΈΡΠ°ΡΠ΅.
