Abstract
In this contribution results connected with using new types of aggregation functions in medical diagnosis support are presented. These aggregation functions belong to the recently introduced families of possible and necessary aggregation functions as well as aggregation functions with respect to admissible linear orders. Examples of the mentioned families of aggregation functions proved to be comparably effective (if it comes to statistical measures and lower cost of prediction) to the previously used aggregation functions in medical diagnosis support systems. The considered classes of aggregation functions differ from the ones previously applied by the comparability relations between intervals involved in the monotonicity conditions.
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Alcázar, J.L., Mercé, L.T., et al.: A new scoring system to differentiate benign from malignant adnexal masses. Obstet. Gynecol. Surv. 58(7), 462–463 (2003)
Bentkowska, U., Król, A.: Preservation of fuzzy relation properties based on fuzzy conjunctions and disjunctions during aggregation process. Fuzzy Sets Syst. 291, 98–113 (2016)
Bentkowska, U.: Aggregation of diverse types of fuzzy orders for decision making problems. Inf. Sci. 424, 317–336 (2018)
Bentkowska, U.: New types of aggregation functions for interval-valued fuzzy setting and preservation of pos-B and nec-B-transitivity in decision making problems. Inform. Sci. 424, 385–399 (2018)
Bustince, H., Fernandez, J., Kolesárová, A., Mesiar, R.: Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst. 220, 69–77 (2013)
Bustince, H., Galar, M., Bedregal, B., Kolesárová, A., Mesiar, R.: A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy sets applications. IEEE Trans. Fuzzy Syst. 21(6), 1150–1162 (2013)
Calvo, T., Kolesárová, A., Komorníková, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Calvo, T., et al. (eds.) Aggregation Operators, pp. 3–104. Physica-Verlag, Heidelberg (2002)
De Miguel, L., Bustince, H., Pȩkala, B., Bentkowska, U., Da Silva, I., Bedregal, B., Mesiar, R., Ochoa, G.: Interval-valued atanassov intuitionistic owa aggregations using admissible linear orders and their application to decision making. IEEE Trans. Fuzzy Syst. 24(6), 1586–1597 (2016)
Deschrijver, G.: Arithmetic operators in interval-valued fuzzy set theory. Inform. Sci. 177, 2906–2924 (2007)
Deschrijver, G.: Quasi-arithmetic means and OWA functions in interval-valued and Atanassov intuitionistic fuzzy set theory. In: Galichet, S., et al. (eds.) Proceedings of EUSFLAT-LFA 2011, 18–22 July 2011, Aix-les-Bains, France, pp. 506–513 (2011)
Dubois, D., Prade, H.: Possibility Theory. Plenum Press, New York (1988)
Dubois, D., Prade, H.: Gradualness, uncertainty and bipolarity: making sense of fuzzy sets. Fuzzy Sets Syst. 192, 3–24 (2012)
Dudziak, U.: Weak and graded properties of fuzzy relations in the context of aggregation process. Fuzzy Sets Syst. 161, 216–233 (2010)
Dudziak, U., Pȩkala, B.: Intuitionistic fuzzy preference relations. In: Galichet, S., et al. (eds.) Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) and LFA-2011, pp. 529–536. Atlantis Press (2011)
Dyczkowski, K., Wójtowicz, A., Żywica, P., Stachowiak, A., Moszyński, R., Szubert, S.: An intelligent system for computer-aided ovarian tumor diagnosis. In: Filev, D., et al. (eds.) Intelligent Systems’2014. AISC, vol. 323, pp. 335–343. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-11310-4_29
Dyczkowski, K.: Intelligent Medical Decision Support System Based on Imperfect Information. SCI, vol. 735. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-67005-8
Jacobs, I., Oram, D., et al.: A risk of malignancy index incorporating CA 125, ultrasound and menopausal status for the accurate preoperative diagnosis ofovarian cancer. BJOG 97(10), 922–929 (1990)
Komorníková, M., Mesiar, R.: Aggregation functions on bounded partially ordered sets and their classification. Fuzzy Sets Syst. 175, 48–56 (2011)
Moszyński, R., Żywica, P., Wójtowicz, A., Szubert, S., Sajdak, S., Stachowiak, A., Dyczkowski, K., Wygralak, M., Szpurek, D.: Menopausal status strongly influences the utility of predictive models in differential diagnosis of ovarian tumors: an external validation of selected diagnostic tools. Ginekol. Pol. 85(12), 892–899 (2014)
Pȩkala, B.: Operations on interval matrices. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 613–621. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73451-2_64
Pȩkala, B.: Properties of interval-valued fuzzy relations, atanassov’s operators and decomposable operations. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. CCIS, vol. 80, pp. 647–655. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14055-6_68
Pȩkala, B., Bentkowska, U., De Baets, B.: On comparability relations in the class of interval-valued fuzzy relations. Tatra Mountains Math. Publ. 66, 91–101 (2016)
Pȩkala B., De Baets B.: Structures of the class of interval-valued fuzzy relations created by different comparability relations. Inf. Sci. (submitted)
Sambuc, R.: Fonctions \(\phi \)-floues: Application á l’aide au diagnostic en pathologie thyroidienne. Ph.D. Thesis, Universit\(\acute{e}\) de Marseille, France (1975) (in French)
Sanz, J., Fernandez, A., Bustince, H., Herrera, F.: A genetic tuning to improve the performance of fuzzy rule-based classification systems with intervalvalued fuzzy sets: degree of ignorance and lateral position. Int. J. Approx. Reason. 52(6), 751–766 (2011)
Stachowiak, A., Dyczkowski, K., Wójtowicz, A., Żywica, P., Wygralak, M.: A bipolar view on medical diagnosis in OvaExpert system. Flexible Query Answering Systems 2015. AISC, vol. 400, pp. 483–492. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-26154-6_37
Szpurek, D., Moszyński, R., et al.: An ultrasonographic morphological index forprediction of ovarian tumor malignancy. Eur. J. Gynaecol. Oncol. 26(1), 51–54 (2005)
Szubert, S., Wójtowicz, A., Moszyński, R., Żywica, P., Dyczkowski, K., Stachowiak, A., Sajdak, S., Szpurek, D., Alcázar, J.L.: External validation of the IOTA ADNEX model performed by two independent gynecologic centers. Gynecol. Oncol. 142(3), 490–495 (2016)
Timmerman, D., Bourne, T.H., et al.: comparison of methods for preoperative discrimination between malignant and benign adnexal masses: the development of a new logistic regression model. Am. J. Obstet. Gynecol. 181(1), 57–65 (1999)
Timmerman, D., Testa, A.C., et al.: Logistic regression model to distinguish between the benign and malignant adnexal mass before surgery: amulticenter study by the international Ovarian tumor analysis group. J. Clin. Oncol. 23(34), 8794–8801 (2005)
Wójtowicz, A., Żywica, P., Szarzyński, K., Moszyński, R., Szubert, S., Dyczkowski, K., Stachowiak, A., Szpurek, D., Wygralak, M.: Dealing with uncertinity in ovarian tumor diagnosis. In: Modern Approaches in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, Volume II: Applications, pp. 151–158. IBS PAN-SRI PAS (2014)
Wójtowicz, A., Żywica, P., Stachowiak, A., Dyczkowski, K.: Solving the problem of incomplete data in medical diagnosis via interval modeling. Appl. Soft Comput. 47, 424–437 (2016)
Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 8, 199–249 (1975)
Zapata, H., Bustince, H., Montes, S., Bedregal, B., Dimuro, G.P., Takáč, Z., Baczyński, M., Fernandez, J.: Interval-valued implications and interval-valued strong equality index with admissible orders. Internat. J. Approx. Reason. 88, 91–109 (2017)
Żywica, P., Wójtowicz, A., Stachowiak, A., Dyczkowski, K.: Improving medical decisions under incomplete data using intervalvalued fuzzy aggregation. In: Proceedings of IFSA-EUSFLAT 2015, pp. 577–584. Atlantis Press (2015)
Żywica, P., Dyczkowski, K., Wójtowicz, A., Stachowiak, A., Szubert, S., Moszyński, R.: Development of a fuzzy-driven system for ovarian tumor diagnosis. Biocybern. Biomed. Eng. 36(4), 632–643 (2016)
Acknowledgements
The authors would like to express gratitude to the OvaExpert authors for their valuable comments concerning the presented material.
This contribution was supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge of University of Rzeszów, Poland, the project RPPK.01.03.00-18-001/10.
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Bentkowska, U., Pȩkala, B. (2018). Diverse Classes of Interval-Valued Aggregation Functions in Medical Diagnosis Support. In: Medina, J., Ojeda-Aciego, M., Verdegay, J., Perfilieva, I., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. IPMU 2018. Communications in Computer and Information Science, vol 855. Springer, Cham. https://doi.org/10.1007/978-3-319-91479-4_33
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