| 1. |
- Rakus-Andersson, Elisabeth
(author)
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Rough set theory in the classification of diagnoses
- 2009
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In: Computers in Medical Activity. Series. - Berlin : Springer. - 9783642044618 ; , s. 41-52
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Conference paper (peer-reviewed)abstract
- Rough sets, surrounded by two approximation sets filled with sure and possible members constitute perfect mathematical tools of the classification of some objects. In this work we adopt the rough technique to verify diagnostic decisions concerning a sample of patients whose symptoms are typical of a considered diagnosis. The objective is to extract the patients who surely Suffer from the diagnosis, to indicate the patients who are free from it, and even to make decisions in undefined diagnostic cases. By applying selected logical decision rules, we also discuss a possibility of reducing of symptom sets to their minimal collections preserving the previous results in order to minimize a number of numerical calculations.
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| 2. |
- Rakus-Andersson, Elisabeth
(author)
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Rough Sets Based on Reducts of Conditional Attributes in Medical Classification of the Diagnosis Status
- 2024
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Conference paper (peer-reviewed)abstract
- Rough sets constitute helpful mathematical tools of the classification of objects belonging to a certain universe when dividing the universe in two collections filled with sure and possible members. In this work we adopt the rough technique to verify diagnostic decisions concerning a sample of patients whose symptoms are typical of a considered diagnosis. The objective is to extract the patients who surely suffer from the diagnosis, to indicate the patients who are free from it, and even to make decisions in undefined diagnostic cases. We also consider a decisive power of reducts being minimal collections of symptoms, which preserve the previous classification results. We use them in order to minimize a number of numerical calculations in the classification process. Finally, by testing influence of symptom intensity levels on the diagnosis indisputable appearance we select these standards, whose either presence or absence in the patients allows us to add complementary remarks making the classification effects even more readable.
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| 3. |
- Rakus-Andersson, Elisabeth
(author)
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The Composition of the Book in Fuzzy Logic Adapted to Stationary and Distance Courses for Advanced Students
- 2007
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Other publication (other academic/artistic)abstract
- The project titled: “The Composition of the Book in Fuzzy Logic Adapted to Stationary and Distance Courses for Advanced Students” has been granted by the Swedish Royal Academy of Sciences in 2007 The following contents of the book “Basic Concepts and Applications of Fuzzy Set Theory” is primarily designed as: Contents 1. Introduction 2. Fuzzy sets 3. Fuzzy and linguistic variables 4. Operations on fuzzy sets 5. T and S Norms 6. Fuzzy measures and measures of fuzziness 7. Extension principles 8. Fuzzy numbers and their arithmetic 9. The L-R, interval and alpha-cut representations of fuzzy numbers 10. Fuzzy relations, The compositional rule of inference 11. The eigen sets of a fuzzy relation 12. Fuzzy analysis 13. Possibility theory, Probability of fuzzy events 14. Fuzzy logic and approximate reasoning 15. Fuzzy decision making, 16. Fuzzy control, 17. Imprecise optimization 18. Choquet and Sugeno integrals 19. Rough set theory 20. Discussion of other imprecise theories
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| 4. |
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| 5. |
- Rakus-Andersson, Elisabeth
(author)
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Continuous Fuzzy Sets as Probabilities of Continuous Fuzzy Events
- 2010
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Conference paper (peer-reviewed)abstract
- In the first part of this study we explore continuous fuzzy numbers in the interval- and the alpha-cut forms to detect their similar nature. The conversion from one form to the other is a question of using the appropriate apparatus, which we also provide. Since the fuzzy numbers can reproduce fuzzy events we then will make a trial of extending the concept of fuzzy probability, defined by R. Yager for discrete fuzzy events, on continuous fuzzy events. In order to fulfill the task we utilize conclusions made about fuzzy numbers to propose an initial conception of approximating the Gauss curve by a particularly designed function originated from the pi-class functions. Due to the procedure of the approximation, characterized by an irrelevant cumulative error, we expand fuzzy probabilities of continuous fuzzy events in the form of continuous fuzzy sets. Furthermore, we assume that this sort of probability holds some conditions formulated for probabilities of discrete fuzzy events.
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| 6. |
- Rakus-Andersson, Elisabeth
(author)
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Factor Analysis with Qualitative Factors and Yager’s Probability in the Lattice of Verbal Fuzzy Numbers
- 2005
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In: Issues in Soft Computing Theory and Applications. - Warsaw : EXIT - the Publishing House of Polish Academy of Sciences. - 8387674982 ; , s. 241-260
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Book chapter (other academic/artistic)abstract
- The classical crisp version of Factor Analysis seldom is used in the case of qualitative factors, which often are presented by codes. It is rather difficult to divide codes in level groups without possessing appropriate criteria. To omit this obstacle, we thus propose a fuzzy application of Factor Analysis, which gives a possibility to investigate the strength of an influence of qualitative factors on a tested qualitative variable. When making a new approach to the analysis of factors, we introduce a space of verbal fuzzy numbers that first are expressed as descriptions coming from a natural language and then designed in L-R form. Since the definition of newly created verbal fuzzy numbers deviates from the general conception of fuzzy numbers, we also will check effects of other operations performed on verbal numbers, which are different from the arithmetic based on the extension principle. The verbal fuzzy numbers represent both the qualitative variable and the qualitative factors in all computations that follow the Factor Analysis algorithm. For the first time we also formulate the Yager probability of an event expanded as the verbal fuzzy number.
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| 7. |
- Rakus-Andersson, Elisabeth, et al.
(author)
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The Choquet and Sugeno Integrals as Measures of Total Effectiveness of Medicines
- 2007
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Conference paper (peer-reviewed)abstract
- The concepts of the Choquet and Sugeno integrals, based on a fuzzy measure, can be adopted as useful tools in estimation of the total effectiveness of a drug when appreciating its positive influence on a collection of symptoms typical of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting the words at first to fuzzy sets and then numbers we can regard the effectiveness structures as measures in the Choquet and Sugeno problem formu-lations. After comparing the quantities of total effectiveness among medicines, expressed as the values of the Choquet or Sugeno integrals, we accomplish the selection of the most efficacious drug.
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| 8. |
- Rakus-Andersson, Elisabeth
(author)
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The fuzzy development and adaptation of statistical and numerical methods to applications to technical and medical models with imprecise data
- 2002
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Other publication (other academic/artistic)abstract
- All the solutions to the problems sketched below will be created on the basis of Fuzzy Set Theory. Fuzzy Set Theory is applied instead of the classical set theory when data involved in the problem to solve is imprecise, verbally described or cannot be measured exactly. The models, which are the contents of the project should contain some proposed solutions to such problems as: 1) the approximation of the mean value and the standard deviation for some imprecise data, 2) a probability distribution filled with fuzzy probability sets (Yager’s probabilities) that replace the probability values from the normal distribution, 3) the application of the last distribution to statistical tests with imprecise data, 4) the development of Factor Analysis for qualitative variables and factors provided that the data is collected by means of a questionnaire, 5) the interpolation of a set of points with imprecise coordinates by a fuzzy function.
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| 9. |
- Rakus-Andersson, Elisabeth
(author)
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The verbal space of fuzzy numbers in the fuzzy development and adaptation of statistical and numerical methods
- 2003
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Other publication (other academic/artistic)abstract
- This project is a continuation of the last one from 2002 with the supplement, which introduces the space of verbally defined fuzzy numbers in the L-R form. The space has its total order, and the numbers in it have borders from the interval [0, 1]. This gives a possibility of testing the fuzzy norms as the operations on fuzzy numbers from the space. The models discussed earlier can now be solved again by using this new technique.
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| 10. |
- Rakus-Andersson, Elisabeth, et al.
(author)
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Finite Fuzzy Sets in the Medication Decision Concerning the Retreat of Symptoms in Radiation Cystitis
- 2015
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In: The Proceedings of the International Conference eHEALTH 2015. - : IADIS PRESS. - 9789898533425 ; , s. 55-62
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Conference paper (peer-reviewed)abstract
- Radiation cystitis is a rare disease, appearing as the result of radiation of pelvic tumors. We support mathematically the recognition of the most efficacious treatments, which reduce the impact of symptoms typical of the illness. To permute the therapies in the ordering, commencing with the optimal therapy, we apply the fuzzy decision making model furnished with finite fuzzy sets. These act as measures of the treatment effectiveness-utility. In the solution, we adopt the older operations on fuzzy sets of type 1, which make the model simple to be easily converted into a computer program.
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