Лепский Александр Евгеньевич

Measuring External Conflict in Dempster-Shafer Theory Based on Kantorovich Problems

2026 · ARTICLE · en

In the paper, we consider three possible types of external conflict in Dempster-Shafer theory and propose its measurement based on functionals evaluating intersection, inclusion and distance between random sets. All proposed functionals can be viewed as extensions of known functionals like Jaccard metric, Jaccard index, and Dice coefficient from usual sets to random sets based on the solutions of the Kantorovich problems.

Нечеткие модели анализа данных и принятия решений. 2-е изд.

2026 · BOOK · ru

В учебном пособии рассмотрены такие основные разделы теории нечетких множеств, как нечеткие отношения, нечеткие числа, нечеткий логический вывод, а также прикладные разделы, связанные с применением нечеткой математики в анализе данных (нечеткая регрессия, нечеткая кластеризация, нечеткая классификация) и принятии решений (нечеткая оптимизация, многокритериальные методы принятия решений с нечеткими данными, ранжирование нечетких данных, нечеткое моделирование). Каждая глава заканчивается разделом задач для самостоятельного решения. Поэтому данное пособие можно использовать не только как учебник, но и как задачник на семинарских занятиях или для самостоятельной подготовки. Учебное пособие адресовано студентам, обучающимся по образовательным программам, связанным с анализом данных и принятием решений («Прикладная математика и информатика», «Экономика», «Экономика и статистика», «Бизнес-информатика» и др.).Книга также будет полезна аспирантам и преподавателям образовательных программ, как непосредственно связанных с анализом данных, так и использующих анализ данных и принятие решений в своих исследованиях, — бизнес-информатикам, экономистам, финансовым аналитикам, политологам и т.д.

Regression with Evidential Coefficients

2025 · CHAPTER · en

This article considers a regression model with coefficients that are specified by bodies of evidence defined on the numerical axis. Optimization problems of finding such evidential coefficients have been set. The relationship between the evidential formulation of the problem and some formulations of fuzzy regression problems is sho wn. The advantages of evidential regression compared to possibilistic fuzzy regression (better robustness, lower degree of fuzziness of coefficients) are demonstrated using a numerical example.

Evidential Estimation of Dependences Based on Data

2025 · ARTICLE · en

The classical problem of parametric estimation (recovery, fitting, regression) of dependencies from data is considered. But the so-called simple bodies of evidence are coefficients in the proposed formulation. These bodies of evidence model both the inaccuracy of the assignment of coefficients and the possible unreliability of information sources. Some formulations of optimization problems for recovering dependencies with such coefficients are discussed. A comparison of the formulations and results with the fuzzy regression problem was carried out. The robustness of the model is investigated.

Three types of internal conflict and its measurement in Dempster-Shafer theory

2025 · ARTICLE · en

In this paper, we extend the ideas of measuring conflict among belief functions based on solving Kantorovich problems to the case of measuring conflict within a belief function. We consider three possible interpretations of conflict-free information and propose the functionals for measuring conflict, which can be considered as counterparts of known functionals like the auto-conflict measure, the measure of dissonance, and the measure of logical inconsistency.

Combining Dependent Sources of Information Within the Framework of Evidence Theory

2025 · CHAPTER · en

The paper introduces and discusses a family of conjunctive information aggregation operators within the framework of evidence theory based on the use of copulas and t-norms. Such operators allow modeling the dependence of information sources and aggregating many sources. It is shown that the introduced operators will satisfy to a certain extent the general requirements (desirable properties) imposed on the rules of combination in the theory of evidence. A new type of conjunctive aggregation for jointly consonant bodies of evidence is explored in more detail. The choice of one or another t-norm or copula in such a conjunctive rule can be based on solving a multi-criteria choice problem with respect to several aggregation quality functionals.

Aggregation and Ranking on an Ordinal Scale Using Threshold Evidential Combination Rules

2024 · ARTICLE · en

A new method of aggregation and ranking on an ordinal scale is proposed based on the method of evidential ranking previously developed by the author, but using the tools of threshold aggregation of bodies of evidence. This method has better robustness and stability compared to the threshold-free method. The method allows you to take into account focal elements that are significant and insignificant for aggregation with different weights, which improves its sensitivity. The application of the developed method to aggregating information from reviewers and ranking reports/articles in a conference management system such as EasyChair is considered. This method can be used to rank alternatives presented as a set of bodies of evidence obtained from different sources of information.

Threshold Aggregation of Fuzzy Data Using Fuzzy Cardinalities of a Set of Fuzzy Estimates

2024 · CHAPTER · en

Threshold Functions and Operations in the Theory of Evidence

2024 · CHAPTER · en

The article introduces and discusses threshold belief and plausibility functions. When forming such functions, only focal elements that are “significant” for a given set are taken into account. The significance of focal elements is determined using a similarity measure and a threshold. Threshold functionals of uncertainty, external and internal conflicts, threshold rules of combination are introduced and considered on the basis of threshold functions of the theory of evidence. A number of examples are given to illustrate the use of threshold tools.

Пороговое агрегирование вероятностных ранжировок

2024 · CHAPTER · ru

Рассматривается задача обобщения известного порогового правила агрегирования трехградационных ранжировок, на случай, когда критериальные значения заданы вероятностными распределениями. Если в классической постановке пороговое правило агрегирования сводится к лексикографическому правилу сравнения векторов мощностей оценок разной градации, то в случае вероятностных оценок их мощность будет представлять собой случайную величину. Рассматриваются свойства этой величины. Приведен численный пример применения порогового агрегирования вероятностных ранжировок.