title: Ð ÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°Ñ ÑÐµÐ³ÑÐµÑÑÐ¸Ð¸ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð½ÐµÑÐµÑÐºÐ¸Ñ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Solutions of regression problems using fuzzy sets
Creators: name: ÐÐ¾ÑÐºÐ°ÑÐµÐ², ÐÐ»ÑÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: Ð½ÐµÑÑÑÐºÐ¸Ðµ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð°
Ð½ÐµÑÑÑÐºÐ¸Ðµ ÑÐ¸ÑÐ»Ð°
Ð°Ð½Ð°Ð»Ð¸Ð· Ð´Ð°Ð½Ð½ÑÑ
ÑÐµÐ³ÑÐµÑÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð·
ÑÐ°Ð³Ð¾Ð²ÑÐ¹ Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»Ñ
fuzzy sets
fuzzy numbers
data analisys
regression analisys
stepper motor

description: ÐÐµÑÑÑÐºÐ¸Ðµ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð° ÑÐ²Ð»ÑÑÑÑÑ Ð¾Ð´Ð½Ð¸Ð¼ Ð¸Ð· Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ ÐµÐ¼ÐºÐ¸Ñ ÑÐ¿Ð¾ÑÐ¾Ð±Ð¾Ð² Ð¾Ð¿Ð¸ÑÐ°Ð½Ð¸Ñ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐ½Ð½Ð¾ÑÑÐ¸ Ð´Ð°Ð½Ð½ÑÑ. ÐÑÐ¾Ð¼Ðµ Ð¿ÑÐ¾ÑÐµÐ³Ð¾, Ð² ÑÐ°Ð±Ð¾ÑÐµ ÑÐ¾Ð´ÐµÑÐ¶Ð¸ÑÑÑ Ð¿Ð¾Ð´ÑÐ¾Ð±Ð½ÑÐ¹ Ð¾Ð±Ð·Ð¾Ñ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¾Ð±ÑÐµÐºÑÐ°, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÐµÐ³Ð¾ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐ¸Ð¼ÐµÑÐ° Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð¸ÑÑÐ»ÐµÐ´ÑÑÑÑÑ Ð´Ð°Ð½Ð½ÑÐµ Ð¿Ð¾ ÑÐ¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÑÐ°Ð³Ð¾Ð²ÑÐ¼Ð¸ Ð´Ð²Ð¸Ð³Ð°ÑÐµÐ»ÑÐ¼Ð¸ (Ð¨Ð) Ð² ÑÐµÐ¶Ð¸Ð¼Ðµ Ð´ÑÐ¾Ð±Ð»ÐµÐ½Ð¸Ñ ÑÐ°Ð³Ð°. ÐÑÐ¾Ð±Ð»ÐµÐ½Ð¸Ðµ ÑÐ²Ð»ÑÐµÑÑÑ Ð¸ÑÑÐ¾ÑÐ½Ð¸ÐºÐ¾Ð¼ Ð½ÐµÑÐ¾ÑÐ½Ð¾ÑÑÐ¸, Ð·Ð°ÑÑÑÐ´Ð½ÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¸ Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ. Ð Ð°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÑÑÑÑ Ð´Ð°Ð½Ð½ÑÐµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐµ Ð¿ÑÐ¸ ÑÐ°Ð·Ð»Ð¸ÑÐ½Ð¾Ð¹ Ð´Ð¸ÑÐºÑÐµÑÐ½Ð¾ÑÑÐ¸ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸ Ð¿Ð¾Ð»Ð½Ð¾Ð³Ð¾ ÑÐ°Ð³Ð° (1/8,1/64,1/256). ÐÑÐ´ÐµÐ»ÑÐ½ÑÐ¹ Ð¸Ð½ÑÐµÑÐµÑ ÑÐ°ÐºÐ¶Ðµ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÑÐµÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð»Ð½Ð¾Ð³Ð¾ ÑÐ¾Ð´Ð° Ð¨Ð Ð²Ð¿ÐµÑÐµÐ´ Ð¸ Ð½Ð°Ð·Ð°Ð´ Ð² ÑÐ¾Ð´Ðµ Ð¾Ð´Ð½Ð¾Ð³Ð¾ Ð½ÐµÐ¿ÑÐµÑÑÐ²Ð½Ð¾Ð³Ð¾ Ð·Ð°Ð¼ÐµÑÐ°, ÑÐ°Ðº ÐºÐ°Ðº Ð¸Ð·-Ð·Ð° ÑÐ¿Ð¾Ð¼ÑÐ½ÑÑÐ¾Ð¹ Ð½ÐµÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¨Ð Ð½Ðµ Ð²Ð¾Ð·Ð²ÑÐ°ÑÐ°ÐµÑÑÑ Ð² Ð¸ÑÑÐ¾Ð´Ð½Ð¾Ðµ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ðµ. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¸Ð²ÐµÐ´ÐµÐ½ Ð¼ÐµÑÐ¾Ð´ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð½ÐµÑÑÑÐºÐ¸Ñ Ð´Ð°Ð½Ð½ÑÑ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐµÑÐºÐ¸Ñ, Ð¾ÑÐ½Ð¾ÑÑÑÐ¸ÑÑÑ Ðº ÐºÐ¾Ð½ÐºÑÐµÑÐ½Ð¾Ð¼Ñ ÐºÐ»Ð°ÑÑÑ. ÐÐ²ÐµÐ´ÐµÐ½Ð° Ð¼ÐµÑÑÐ¸ÐºÐ° ÑÑÐµÐ¿ÐµÐ½Ð¸ ÑÑÐµÑÐ° ÑÐ¿ÐµÑÐ¸ÑÐ¸ÐºÐ¸ Ð´Ð°Ð½Ð½ÑÑ. ÐÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½ ÑÐ¿Ð¾ÑÐ¾Ð± Ð¿ÑÐ¾Ð³Ð½Ð¾Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð¾Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Ð²Ð°Ð»Ð° Ð¨Ð Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ»Ð°ÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐµÐ³ÑÐµÑÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð°, Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð½ÑÑ Ðº Ð½ÐµÑÑÑÐºÐ¸Ð¼ Ð´Ð°Ð½Ð½ÑÐ¼. ÐÑÐ¸Ð²ÐµÐ´ÐµÐ½ ÑÐ¿Ð¾ÑÐ¾Ð± Ð°Ð½Ð°Ð»Ð¸Ð·Ð° ÑÑÐµÐ¿ÐµÐ½Ð¸ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ° Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸Ñ Ð²Ð½ÑÑÑÐµÐ½Ð½ÐµÐ¹ Ð¸ Ð²Ð½ÐµÑÐ½ÐµÐ¹ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½ÑÑ Ð¾ÑÐµÐ½Ð¾Ðº Ð¸Ð· Ð½ÐµÑÑÑÐºÐ¾Ð³Ð¾ ÑÐ¸ÑÐ»Ð° Ñ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐ¸Ð¼ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸ÐµÐ¼ Ð¼ÐµÑÑ ÐÐ°ÐºÐºÐ°ÑÐ° Ð´Ð»Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐ²Ð¸Ð½Ð°.
description: Fuzzy sets are one of the most capacious ways to describe data uncertainty. Among other things, the work provides a detailed overview of this mathematical object, as well as the features of its practical application. As a practical example, the work investigates stepper motor (SM) control data in pitch crushing mode. Pitch crushing is a source of inaccuracy, making research and prediction difficult. Data obtained at different discretization of full step processing (1/8,1/64,1/256) are examined. Comparison of the total forward and backward travel of the drive during one continuous measurement is also of particular interest, since the drive does not return to the initial position due to the mentioned inaccuracy. In this work, a method of constructing fuzzy data based on crisp class-specific data is presented. A metric for the degree of data specificity is introduced. A method of predicting the position of the shaft of the SM using classical regression analysis methods applied to fuzzy data is presented. A method of analyzing the degree of uncertainty of the result by obtaining internal and external interval estimates from a fuzzy number and then calculating the Jaccard measure for the obtained tween is presented.