Metric on the space of systems behavior functions represented by fuzzy measures
G. Klir proposed to describe the behavior of complex systems using behavior functions (BFs) - invariant constraints on the set of system states. BFs are one of the most productive tools for studying the functioning of systems. To study systems, it is necessary to have a metric for measuring of the d...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Belgrade
2024-01-01
|
| Series: | Yugoslav Journal of Operations Research |
| Subjects: | |
| Online Access: | https://doiserbia.nb.rs/img/doi/0354-0243/2024/0354-02432300012B.pdf |
| _version_ | 1797215423639322624 |
|---|---|
| author | Bocharnikov Victor Sveshnikov Sergey |
| author_facet | Bocharnikov Victor Sveshnikov Sergey |
| author_sort | Bocharnikov Victor |
| collection | DOAJ |
| description | G. Klir proposed to describe the behavior of complex systems using behavior functions (BFs) - invariant constraints on the set of system states. BFs are one of the most productive tools for studying the functioning of systems. To study systems, it is necessary to have a metric for measuring of the difference between two BFs. To describe BFs modern researchers do not use distributions other than probability or possibility. But these distributions can be considered as special cases of Sugeno fuzzy measures, the use of which greatly expands the possibilities in the study of systems. However, metrics to measure the difference between fuzzy measures have not been developed. Therefore, in this article, the authors proposed a new metric and an algorithm for its calculation for the case when BFs are described by Sugeno fuzzy measures. This metric is based on the Cartesian product of fuzzy measures and the use of our proposed concentration function. The metric makes it possible to compare the behavior of systems in the case of describing BFs by Sugeno fuzzy measures with different modalities, as well as to ensure the priority of taking into account the set of the most significant states of the system. |
| first_indexed | 2024-04-24T11:29:50Z |
| format | Article |
| id | doaj.art-61d19afe1a804cfd8251d2a5b44ab3f9 |
| institution | Directory Open Access Journal |
| issn | 0354-0243 1820-743X |
| language | English |
| last_indexed | 2024-04-24T11:29:50Z |
| publishDate | 2024-01-01 |
| publisher | University of Belgrade |
| record_format | Article |
| series | Yugoslav Journal of Operations Research |
| spelling | doaj.art-61d19afe1a804cfd8251d2a5b44ab3f92024-04-10T10:28:46ZengUniversity of BelgradeYugoslav Journal of Operations Research0354-02431820-743X2024-01-0134112110.2298/YJOR230315012B0354-02432300012BMetric on the space of systems behavior functions represented by fuzzy measuresBocharnikov Victor0Sveshnikov Sergey1Consulting group INEX-FT, Kyiv, UkraineConsulting group INEX-FT, Kyiv, UkraineG. Klir proposed to describe the behavior of complex systems using behavior functions (BFs) - invariant constraints on the set of system states. BFs are one of the most productive tools for studying the functioning of systems. To study systems, it is necessary to have a metric for measuring of the difference between two BFs. To describe BFs modern researchers do not use distributions other than probability or possibility. But these distributions can be considered as special cases of Sugeno fuzzy measures, the use of which greatly expands the possibilities in the study of systems. However, metrics to measure the difference between fuzzy measures have not been developed. Therefore, in this article, the authors proposed a new metric and an algorithm for its calculation for the case when BFs are described by Sugeno fuzzy measures. This metric is based on the Cartesian product of fuzzy measures and the use of our proposed concentration function. The metric makes it possible to compare the behavior of systems in the case of describing BFs by Sugeno fuzzy measures with different modalities, as well as to ensure the priority of taking into account the set of the most significant states of the system.https://doiserbia.nb.rs/img/doi/0354-0243/2024/0354-02432300012B.pdfsystembehavior functionmetricmetric spacefuzzy measurefuzzy integraldistance functionnorm |
| spellingShingle | Bocharnikov Victor Sveshnikov Sergey Metric on the space of systems behavior functions represented by fuzzy measures Yugoslav Journal of Operations Research system behavior function metric metric space fuzzy measure fuzzy integral distance function norm |
| title | Metric on the space of systems behavior functions represented by fuzzy measures |
| title_full | Metric on the space of systems behavior functions represented by fuzzy measures |
| title_fullStr | Metric on the space of systems behavior functions represented by fuzzy measures |
| title_full_unstemmed | Metric on the space of systems behavior functions represented by fuzzy measures |
| title_short | Metric on the space of systems behavior functions represented by fuzzy measures |
| title_sort | metric on the space of systems behavior functions represented by fuzzy measures |
| topic | system behavior function metric metric space fuzzy measure fuzzy integral distance function norm |
| url | https://doiserbia.nb.rs/img/doi/0354-0243/2024/0354-02432300012B.pdf |
| work_keys_str_mv | AT bocharnikovvictor metriconthespaceofsystemsbehaviorfunctionsrepresentedbyfuzzymeasures AT sveshnikovsergey metriconthespaceofsystemsbehaviorfunctionsrepresentedbyfuzzymeasures |