Models and methods of regression analysis under conditions of fuzzy initial data

Раскін, Лев; Сіра, Оксана; Ivanchykhin, Yuriy

doi:10.15587/1729-4061.2017.107536

Cited by 7 publications

(7 citation statements)

References 21 publications

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“…This system consists of two quite autonomous software subsystems. The first of them is implemented on the basis of the "MS Excel" spreadsheets and it is a subsystem of the FCM analysis which includes the sub systems for entering a cognitive map and obtaining a forecast of the evolving situation [17].…”

Section: Fig 4 the Variance Analysis Of The Results Of The K-means Methods For E9-e10mentioning

confidence: 99%

The synthesis of strategies for the efficient performance of sophisticated technological complexes based on the cognitive simulation modelling

Zaiets¹,

Савчук²,

Shtepa³

et al. 2021

Nauk. visn. nat. hirn. univ.

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Purpose. Improving the productivity and energy efficiency of complex technological complexes through the development and use of scenario-cognitive modeling in control systems. Methodology. Fuzzy cognitive maps, in the form of a weighted oriented graph, were used to develop a scenario-cognitive model. As a result of the conducted research studies, a new strategy of generalization of an expert estimation of mutual influences of concepts on the basis of methods of the cluster analysis is offered. Findings. Based on experimental research and object-oriented analysis of a complex technological complex, a structure of a fuzzy cognitive model is created. A scenario-cognitive model in the form of a weighted oriented graph (fuzzy cognitive map) has been developed, which illustrates a set of connections and the nature of the interaction of expertly determined factors. To solve the problem of impossibility of operative interrogation of experts in case of change in parameters of functioning of difficult technological complexes, expert estimations of values of weight coefficients of mutual influence of concepts are received. Cluster analysis methods were used to group expert assessments and determine a single value as a result of the research. The results of the scenario-cognitive modeling of the enterprise showed that production shutdowns and abnormal situations related to the failure of electrical equipment, deviations of the technological regime and the quality of wastewater treatment have a significant impact on the dynamics of productivity, energy efficiency and efficient use of equipment. Originality. The new scenario-cognitive model developed for forecasting the situation in the absence of accurate quantitative information consists in creating a fuzzy cognitive map, for modeling which many parameters of complex technological complexes are expertly determined. Using the developed methodology, a degree of interaction of these parameters is found, which allows determining dynamics of change in target criteria of functioning under various management strategies. Practical value. On the basis of the created scenario-cognitive model, software has been developed which allowed analyzing dynamics of change in productivity, energy efficiency and efficiency of use of the equipment under possible scenarios of functioning of difficult technological complexes is developed.

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Section: Fig 4 the Variance Analysis Of The Results Of The K-means Methods For E9-e10mentioning

confidence: 99%

The synthesis of strategies for the efficient performance of sophisticated technological complexes based on the cognitive simulation modelling

Zaiets¹,

Савчук²,

Shtepa³

et al. 2021

Nauk. visn. nat. hirn. univ.

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“…Directions for the further research are associated with the development of techniques for extending the method to cases when the parameters for the problem's objective function and constraints are described in terms of fuzzy [22] or inaccurate [23,24] mathematics. Possible ways to overcome the problems that emerge in this case are proposed in [25][26][27].…”

Section: Discussion Of Results Of Constructing a Methods To Solve A Fractional Nonlinear Optimization Problemmentioning

confidence: 99%

Construction of the fractional-nonlinear optimization method

Раскін

Сіра

2019

EEJET

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Запропоновано метод розв'язання задачі дрібно-нелінійної оптимізації. Показано, що саме до такої математичної моделі зводяться численні задачі управління запасами, раціонального розподілу обмежених ресурсів, відшукання оптимальних шляхів на графі, раціональної організації перевезень, управління динамічними системами та інші задачі у випадках, коли вихідні дані задачі описані в термінах теорії ймовірностей або нечіткої математики. Проведено аналіз відомих методів вирішення задач дрібно-нелінійної оптимізації. Найбільш продуктивний з них заснований на ітераційної процедурі послідовного поліпшення початкового рішення задачі. При цьому на кожному кроці вирішується задача математичного програмування. Метод сходиться, якщо область допустимих рішень компактна. Очевидний недолік методу -неконтрольована швидкість збіжності. В роботі запропонований метод розв'язання задачі, ідея якого перегукується з відомим методом дрібно-лінійної оптимізації. Запропонована технологія перетворює вихідну задачу з дрібно-раціональним критерієм до звичайної задачі математичного програмування. Головне достоїнство методу і його відмінність від відомих полягає в тому, що метод реалізується з використанням однокрокової процедури отримання рішення. При цьому розмірність задачі не є обмежуючим фактором. Вимоги до математичної моделі задачі, які звужують область можливих додатків розробленої методики: 1) компоненти цільової функції повинні бути сепарабельними функціями; 2) показники ступеня всіх нелінійних доданків компонентних функцій повинні бути однаковими. Інша важлива перевага методу полягає в можливості його використання для вирішення задачі безумовної та умовної оптимізації. Розглянуто приклади Ключові слова: оптимізація дрібно-нелінійної функції, лінійні обмеження, однокрокова процедура, точне розв'язання

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“…Moreover, situations when this uncertainty is described in terms of fuzzy [18] or inaccurate [23] mathematics are the most interesting and important in theoretical and practical respects. Possible approaches to solving the problem in these cases are proposed in [24][25][26].…”

Section: Discussion Of the Results Of Solving The Set Of Tasks Of Formentioning

confidence: 99%

Dynamic Problem of Formation of Securities Portfolio Under Uncertainty Conditions

Раскін

Сіра

Katkova

2019

EUREKA: Physics and Engineering

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The analysis of known methods for solving the problem of forming a portfolio of securities in the face of uncertainty is carried out. Traditionally, the problem is solved under the assumption that for each type of asset, the values of the main statistical characteristics of the random value of their profitability (mathematical expectation and variance) are known. At the same time, the variance of portfolio returns, which is minimized, is used as a criterion for portfolio optimization. Two alternative approaches to solving the formulated problem are proposed. The first of them provides a decision on the criterion of the probability that the random total portfolio return will not be lower than the given. It is assumed that the random return for each type of asset is distributed normally and the statistical characteristics of the respective densities are known. The original problem is reduced to the problem of maximizing the quadratic fractional criterion in the presence of linear constraints. To solve this non-standard optimization problem, a special iterative algorithm is proposed that implements the procedure for sequential improvement of the plan. The method converges and the computational procedure for obtaining a solution can be stopped by any of the standard criteria. The second approach considers the possibility of solving the problem under the assumption that the distribution densities of random asset returns are not known, however, based on the results of preliminary statistical processing of the initial data, estimates of the values of the main numerical characteristics for each of the assets are obtained. To solve the problem, a new mathematical apparatus is used-continuous linear programming, which is a generalization of ordinary linear programming to the case when the task variables are continuous. This method, in the considered problem, is based on solving an auxiliary problem: finding the worst-case distribution density of a random total portfolio return at which this total return does not reach an acceptable threshold with maximum probability. Now the main minimax problem is being solved: the formation of the best portfolio in the worst conditions. The resulting computational scheme leads to the problem of quadratic mathematical programming in the presence of linear constraints. Next, a method is proposed for solving the problem of forming a portfolio of securities, taking into account the real dynamics of the value of assets. The problem that arises in this case is formulated and solved in terms of the general theory of control, using the Riccati equation.

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Models and methods of regression analysis under conditions of fuzzy initial data

Cited by 7 publications

References 21 publications

The synthesis of strategies for the efficient performance of sophisticated technological complexes based on the cognitive simulation modelling

The synthesis of strategies for the efficient performance of sophisticated technological complexes based on the cognitive simulation modelling

Construction of the fractional-nonlinear optimization method

Dynamic Problem of Formation of Securities Portfolio Under Uncertainty Conditions

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