An effective similarity measurement under epistemic uncertainty

The epistemic uncertainty stems from the lack of knowledge and it can be reduced when the knowledge increases. Such inter-pretation works well with data represented as a set of possible states and therefore, multivalued similarity measures. Unfortunately, set-valued extensions of similarity measures are not computationally feasible even when the data is finite. Measures with properties that allow efficient calculation of their extensions, need to be found. Analysis of various similarity measures indicated logic-based (additive) measures as an excellent candidate. Their unique properties are discussed and efficient algorithms for computing set-valued extensions are given. The work presents results related to various classes of fuzzy set families: general ones, intervals of fuzzy sets, and their finite sums. The first case is related to the concept of the Fuzzy Membership Function Family, the second corresponds to the Interval-Valued Fuzzy Sets, while the third class is equivalent to the concept of Typical Interval-Valued Hesitant Fuzzy Sets

Similarity Measures of Interval-Valued Fuzzy Sets in Classification of Uncertain Data. Applications in Ovarian Tumor Diagnosis.

Wydział Matematyki i InformatykiRozprawa dotyczy problemu mierzenia podobieństwa w sytuacji, gdy wiedza na temat reprezentowanych przez przedziałowe zbiory rozmyte obiektów jest tylko częściowa i niepewna. Dokonano przeglądu literatury oraz porównania obecnych podejść do mierzenia podobieństwa klasycznych i przedziałowych zbiorów rozmytych. Okazuje się, że aby możliwe było pełne uwzględnienie niekompletności danych konieczne jest wyrażenie podobieństwa przy pomocy przedziału. Zbudowano teorię niezbędną do poprawnego modelowania przedziałowego podobieństwa. Sformułowane zostały podstawowe własności, jakie w takiej sytuacji powinna spełniać miara podobieństwa, a następnie zaproponowano metodę konstrukcji nieskończenie wielu takich miar. Metoda ta pozwala na skonstruowanie nowej miary na podstawie miary podobieństwa zbiorów rozmytych, o ile ta spełnia pewne warunki. Zbadano problem efektywnego obliczania nowych miar uzyskanych tą metodą. Szczególną uwagę poświęcono uogólnionej wersji indeksu Jaccarda. Korzystając z przedziałowych miar podobieństwa zaproponowano dwie metody klasyfikacji umożliwiające pełne wsparcie dla danych niepewnych zarówno na etapie budowy klasyfikatora, jak i jego stosowania. Dokonano obszernej ewaluacji jakości klasyfikacji z wykorzystaniem rzeczywistych danych medycznych. Jedna z zaproponowanych metod została wykorzystana w inteligentnym systemie wspomagania diagnostyki guzów jajnika - OvaExpert.The dissertation deals with the problem of measuring the similarity when knowledge about objects represented by the Interval-Valued Fuzzy Sets is incomplete and uncertain. Various current approaches to measuring similarity of classical and interval-valued fuzzy sets were investigated and compared. It appears that to be able to take full account of the data incompleteness, it is necessary to express the similarity as an interval. Theory necessary to properly model interval similarity was built. Basic properties, which in this case should be fulfilled by similarity measure were formulated, and a method of construction of infinitely many such measures was proposed. This method allows to construct a new interval measure from a similarity measure of fuzzy sets, as long as it meets certain conditions. Problem of effective calculation of the new measures obtained by this method was examined. Special attention was given to the generalized version of the Jaccard index. Using the interval similarity measures, two classification methods that allow full support for data uncertainty, both at the stage of building a classifier and its usage, were proposed. Comprehensive evaluation of the classification quality using real medical data was performed. One of the proposed methods was applied in the intelligent diagnosis support system for ovarian tumor - OvaExpert

Framework of machine criticality assessment with criteria interactions

Criticality is considered as a fundamental category of production planning, maintenance process planning and management. The criticality assessment of machines and devices can be a structured set of activities allowing to identify failures which have the greatest potential impact on the company’s business goals. It can be also used to define maintenance strategies, investment strategies and development plans, assisting the company in prioritizing their allocations of financial resources to those machines and devices that are critical in accordance with the predefined business criteria. In a criticality assessment process many different and interacting criteria have to be taken into consideration, despite the fact that there is a high level of uncertainty related to various parameters. In addition, not all assessment criteria are equally important. Therefore, it is necessary to determine the weight of each criterion taking into account different requirements of machine criticality process stakeholders. That is why a novel model of a machine criticality assessment is proposed in this paper. The model extends the existing methods of assessing machines criticality, taking into account not only the importance of machine criticality assessment criteria, but also possible interactions between them

Performance of Selected Models for Predicting Malignancy in Ovarian Tumors in Relation to the Degree of Diagnostic Uncertainty by Subjective Assessment With Ultrasound

Preprint artykułuObjectives The study's main aim was to evaluate the relationship between the performance of predictive models for differential diagnoses of ovarian tumors and levels of diagnostic confidence in subjective assessment (SA) with ultrasound. The second aim was to identify the parameters that differentiate between malignant and benign tumors among tumors initially diagnosed as uncertain by SA. Methods The study included 250 (55%) benign ovarian masses and 201 (45%) malignant tumors. According to ultrasound findings, the tumors were divided into 6 groups: certainly benign, probably benign, uncertain but benign, uncertain but malignant, probably malignant, and certainly malignant. The performance of the risk of malignancy index, International Ovarian Tumor Analysis assessment of different neoplasias in the adnexa model, and International Ovarian Tumor Analysis logistic regression model 2 was analyzed in subgroups as follows: SA-certain tumors (including certainly benign and certainly malignant) versus SA-probable tumors (probably benign and probably malignant) versus SA-uncertain tumors (uncertain but benign and uncertain but malignant). Results We found a progressive decrease in the performance of all models in association with the increased uncertainty in SA. The areas under the receiver operating characteristic curve for the risk of malignancy index, logistic regression model 2, and assessment of different neoplasias in the adnexa model decreased between the SA-certain and SA-uncertain groups by 20%, 28%, and 20%, respectively. The presence of solid parts and a high color score were the discriminatory features between uncertain but benign and uncertain but malignant tumors. Conclusions Studies are needed that focus on the subgroup of ovarian tumors that are difficult to classify by SA. In cases of uncertain tumors by SA, the presence of solid components or a high color score should prompt a gynecologic oncology clinic referral