Krite rij minimalnoyi dispersiyi Rozglyanemo situaciyu koli osoba sho prijmaye rishennya zacikavlena ne stilki u maksimizaciyi funkciyi korisnosti stilki u stabilnosti rishen yih yakomoga bilshoyi nezalezhnosti vid staniv Vvedemo poznachennya u x s displaystyle u x s funkciya rishen viznachena na X S displaystyle X times S de X displaystyle X mnozhina alternativ S displaystyle S mnozhina staniv a p x s displaystyle p x s jmovirnisna mira situaciyi f x s g displaystyle mathcal f x s mathcal g D x s S u x s E x 2 p x s d s x X displaystyle D x int s in S u x s E x 2 p x s ds forall x in X 1 de E x s S u x s p x s d s displaystyle E x int s in S u x s p x s ds U skinchenno vimirnomu vipadku yaksho U u k j M N displaystyle mathbf U u kj M times N matricya rishen a P p k j M N displaystyle mathbf P p kj M times N stohastichna matricya to 1 zapisuyetsya tak D x k j 1 N u k j E x k 2 p x j k 1 M displaystyle D x k sum limits j 1 N u kj E x k 2 p xj forall k overline 1 M 2 de E x k s S u x s p x s d s displaystyle E x k int s in S u x s p x s ds Mnozhina optimalnih alternativ za kriteriyem minimalnoyi dispersiyi formuyetsya tak X M V arg min x X D x displaystyle X MV arg min x in X D x 3 X M V arg min x k k 1 M D x displaystyle X MV arg min x k k overline 1 M D x 4 Priklad red U 4 1 5 4 6 7 8 3 9 1 2 4 displaystyle mathbf U begin bmatrix 4 amp 1 amp 5 amp 4 6 amp 7 amp 8 amp 3 9 amp 1 amp 2 amp 4 end bmatrix nbsp P 0 1 0 3 0 6 0 0 2 0 5 0 0 3 0 6 0 2 0 2 0 displaystyle mathbf P begin bmatrix 0 1 amp 0 3 amp 0 6 amp 0 0 2 amp 0 5 amp 0 amp 0 3 0 6 amp 0 2 amp 0 2 amp 0 end bmatrix nbsp E x 1 4 0 1 1 0 3 5 0 6 4 0 3 7 displaystyle E x 1 4 cdot 0 1 1 cdot 0 3 5 cdot 0 6 4 cdot 0 3 7 nbsp E x 2 6 0 2 7 0 5 8 0 3 0 3 5 6 displaystyle E x 2 6 cdot 0 2 7 cdot 0 5 8 cdot 0 3 cdot 0 3 5 6 nbsp E x 3 9 0 6 1 0 2 2 0 2 4 0 6 displaystyle E x 3 9 cdot 0 6 1 cdot 0 2 2 cdot 0 2 4 cdot 0 6 nbsp D x 1 4 3 7 2 0 1 1 3 7 2 0 3 5 3 7 2 0 6 4 3 7 2 0 3 21 displaystyle D x 1 4 3 7 2 cdot 0 1 1 3 7 2 cdot 0 3 5 3 7 2 cdot 0 6 4 3 7 2 cdot 0 3 21 nbsp D x 2 6 6 5 2 0 2 7 6 5 2 0 5 8 6 5 2 0 3 6 5 2 0 3 3 04 displaystyle D x 2 6 6 5 2 cdot 0 2 7 6 5 2 cdot 0 5 8 6 5 2 cdot 0 3 6 5 2 cdot 0 3 3 04 nbsp D x 3 9 6 2 0 6 1 6 2 0 2 2 6 2 0 2 4 6 2 0 13 6 displaystyle D x 3 9 6 2 cdot 0 6 1 6 2 cdot 0 2 2 6 2 cdot 0 2 4 6 2 cdot 0 13 6 nbsp X M V arg min x k k 1 M D x arg min x k k 1 M 3 21 3 04 13 6 x 2 displaystyle X MV arg min x k k overline 1 M D x arg min x k k overline 1 M 3 21 3 04 13 6 x 2 nbsp Div takozh red Kriterij Bajyesa Laplasa Kriterij Valda Kriterij Sevidzha Kriterij Gurvica Kriterij Germejyera Kriterij dobutkiv Kriterij Hodzha Lemana Kriterij maksimalnoyi imovirnosti Procesno oriyentovane upravlinnya vitratami Metod analizu iyerarhij Bayesova jmovirnist Causal decision theory en Choice Modelling en Constraint satisfaction en Decision field theory en Uhvalennya rishen Decision making software en Evidential decision theory en Teoriya igor Judge Advisor System JAS en Kelly criterion en Morfologichnij analiz vinahidnictvo Multi criteria decision making en Neuroscience of free will en Doslidzhennya operacij Optimalne rishennya Klas skladnosti PP Teoriya socialnogo viboru Racionalnist Rationality and power en Recognition primed decision en Zadacha pro perebirlivu molodicyu Stochastic dominance en Zadacha pro dva konverti Two moment decision models en Modalnij kriterij Cya stattya ne mistit posilan na dzherela Vi mozhete dopomogti polipshiti cyu stattyu dodavshi posilannya na nadijni avtoritetni dzherela Material bez dzherel mozhe buti piddano sumnivu ta vilucheno lipen 2022 Otrimano z https uk wikipedia org w index php title Kriterij minimalnoyi dispersiyi amp oldid 38375615
