SOLUTION UNDER RISK CONDITIONS: LAPLAS CRITERION. MINIMAX AND MAXMIN CRITERION. SAVAGE AND HURWITZ CRITERIA

Аннотация

Decision-making under risk refers to theconsideration of risk indecision-making processes. The Laplace criterion is a method that considers probabilities equal and calculates the average value of each option for each possible situation. The minimax criterion aims to minimize the worst-case scenario under risk. The maxmin criterion is the inverse of the minimax approach. The Savage criterion aims to consider the average and worst-case scenarios in terms of risk in decision-making. The Hurwitz criterion aims to reduce the uncertainty between the average and worst-case scenarios under risk. The approaches presented in thisarticle showwhat methods can beused indecision-making under risk. Keywords: Risk, decision making, Laplace criterion, minimax criterion, maxmin criterion, Savagecriterion, Hurwitz criterion, uncertainty, probabilities, decision making. Introduction . Processes research and optimal management – decision acceptance to do and systems tooptimizescientific fields oriented .​ 1-Process research resources effective distribution for mathematician models , linear programming ,games​ theory andnetworks optimizationsuch as from methods uses . 2-Optimal management systems the most good management strategies determination with He is engaged in his work . main methods Pontryagin's Maximum principle and Bellman's dynamicprogramming . Risk-taking under the circumstances solution acceptance to do , to do a lot in fields including economics , management , engineering​ and other technician in the fields wide This topic is used according to literature various methods and approaches offer it will , this and decision acceptance to do in the process risk-taking how to manage to study help gives . References analysis following criteria based on take Let's go : Laplace criterion , Minimax criterion , Maximin criterion , Savage criterion and Hurwitz criterion .. Laplace criterion risk under the circumstances decision acceptance to do the most simple and wide widespread from the methods Laplace (1814) defined risk as equal distribution hypothesis does and all of circumstances probabilities He considers all​ ​ possible was​ situations for of values average value to calculate and the most high average to value has was option to choose provides . Minimax criterion decision acceptance in doing the most inconvenient thesituation to minimize This approach is aimed at main purpose , decision acceptance doer for the most bad the results the most less to the level von Neumann​ and Morgenstern (1944) in their " page1199 INTERNATIONAL JOURNAL OF ARTIFICIAL INTELLIGENCE ISSN:2692-5206,ImpactFactor:12,23 AmericanAcademicpublishers,volume05,issue04,2025 Journal: https://www.academicpublishers.org/journals/index.php/ijai Theory in the work " Games " minimax approach game theory within current those who have reached.Maxmin criterion minimax approach reverse approach decided​ ​ acceptance doer every one option the most good in the state value This method​ main advantage is that the decision acceptance doer the most good the situation to take strives . Savage criterion decision acceptance in doing average​ and bad situations in consideration to take goal This method ismainly used to determineacceptance theone who does risk level tobalance Savage ( 1950 ) in his method risk relief , average the value maximum to do aimed at strategy 5. Hurwitz criterion risk to minimize aimed at from methods He is a risk taker . relief for average​ and bad situations between the difference tries to alleviate . Gurvitz (1956) in his criterion risk and uncertainty alleviate for working came out . This study aims to explore effective methods for making decisions in risky situations. The study methodology theoretical analysis , mathematics modeling , comparison analysis and experimental analysis own​ inside Research​ ​ during literature analysis through risk under the circumstances decision acceptance to do according to there is scientific sources and methods Laplace , Minimax , Maxmin , Savage​ ​ and Hurwitz criteria such as various approaches analysis will be doneand their risk-taking in management efficiency is studied. In the study mathematician modeling methods using risk under the circumstances decision acceptance to do processes simulation In these processes probability distributions , risk and uncertainties in consideration is taken . Simplex method , graphic method and other modeling methods using decision acceptance to do process optimization opportunities analysis Comparative​ ​ analysis through various methods compared and their efficiency is determined . Experimental analysis methodology theoretical shaped risk under the circumstances solution acceptance to do of the plan to practice implementation to be and the results to study In this process methods using solutions learned , risk - taking management the most effective methods working This is​ methods using risk under the circumstances decision acceptance todoprocess improveand economic efficie