Open AccessMethod for Ordering Procedures of Dividing States by Procedures with Two and Three Results Taking into Account their Cost and Weight of States
Author(s) -
Д.В. Ефанов,
Валерий Вячеславович Хорошев
Publication year - 2020
Publication title -
trudy spiiran
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.242
H-Index - 9
eISSN - 2078-9599
pISSN - 2078-9181
DOI - 10.15622/sp.2020.19.1.8
Subject(s) - terminology , class (philosophy) , preference , sequence (biology) , binary number , computer science , limit (mathematics) , ternary operation , function (biology) , mathematics , management science , statistics , artificial intelligence , arithmetic , linguistics , mathematical analysis , philosophy , evolutionary biology , biology , genetics , programming language , economics
A method for streamlining state partitioning procedures with two and three outcomes is considered. A terminology and methods of the questionnaire theory were used, and the sequence of partitioning procedures itself was defined as a heterogeneous questionnaire with questions having two or three answers. This class of questionnaires is special and is defined by the authors as a class of binary-ternary questionnaires. This is the simplest class of heterogeneous questionnaires. An increase in number of answers to a question in practice can give an advantage in parameters of the questionnaires, including in the indicator of its effectiveness – the average implementation cost. It is noted that the use of binary-ternary questionnaires in practice can reduce the average time for identifying events on a questionnaire, which is extremely important in those applications of questionnaires in which there is a time limit for identifying events, for example, in critical application systems. A method for optimizing binary-ternary questionnaires is presented, based on the search for the most preferred questions for each subset of identifiable events. The choice of preferred questions is based on establishing a comparison relationship between them. The article describes all possible types of comparison relations between two questions with two answers, two questions with three answers, and also between a question with two answers and a question with three answers. An example of obtaining a mathematical expression for a function that characterizes the preference of questions over each other, as well as a generalized formula for choosing the most preferred question for any heterogeneous questionnaires is given. An algorithm has been formed for the method of ordering questions, which allows one to construct a binary-ternary questionnaire with the lowest implementation cost in polynomial time. An example of a binary-ternary questionnaire optimization by the presented method is given.