Incorporation of Excluding Features in Fuzzy Relational Compositions Based on Generalized Quantifiers
The concepts of incorporation of excluding features in fuzzy relational compositions and the compositions based on generalized quantifiers are useful tools for improving relevance and precision of the suspicion provided by the standard fuzzy relational compositions initial studied by Willis Bandler and Ladislav Kohout. They are independently extended from the standard compositions. However, it may become a very effective tool if they are used together. Taking this natural motivation leads us to introduce the concept of incorporation of excluding features in fuzzy relational compositions based on generalized quantifiers. Most of valid properties preserved for the two mentioned approaches will be proved for the new concept as well. Furthermore, an illustrative example will be presented for showing the usefulness of the approach.
KeywordsFuzzy relational compositions Fuzzy relational products Bandler-Kohout products Fuzzy measures Generalized (fuzzy) quantifiers Medical diagnosis Classification
This research was partially supported by the NPU II project LQ1602 “IT4Innovations excellence in science” provided by the MŠMT.
- 4.Burda, M.: Linguistic fuzzy logic in R. In: Proceedings of IEEE International Conference on Fuzzy Systems, Istanbul, Turkey (2015)Google Scholar
- 6.Cao, N., Štěpnička, M.: How to incorporate excluding features in fuzzy relational compositions and what for. In: Proceedings of 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Communications in Computer and Information Science, vol. 611, pp. 470–481. Springer, Heidelberg (2016)Google Scholar
- 7.Cao, N., Štěpnička, M.: Properties of ‘excluding symptoms’ in fuzzy relational compositions. In: Proceedings of 12th Conference on Uncertainty Modelling in Knowledge Engineering and Decision Making (FLINS), vol. 10, pp. 555–560. World Scientific (2016)Google Scholar
- 9.Cao, N., Štěpnička, M., Holčapek, M.: An extension of fuzzy relational compositions using generalized quantifiers. In: Proceedings of 16th World Congress of the International Fuzzy Systems Association (IFSA) and 9th Conference of the European Society for Fuzzy-Logic and Technology (EUSFLAT). Advances in Intelligent Systems Research, vol. 89, pp. 49–58. Atlantis press, Gijón (2015)Google Scholar
- 10.Cao, N., Štěpnička, M., Holčapek, M.: Non-preservation of chosen properties of fuzzy relational compositions based on fuzzy quantifiers. In: IEEE International Conference on Fuzzy Systems (2017, in press)Google Scholar
- 11.Cao, N., Štěpnička, M., Holčapek, M.: Extensions of fuzzy relational compositions based on generalized quantifer. Fuzzy Sets Syst. (submitted)Google Scholar
- 12.De Baets, B.: Analytical solution methods for fuzzy relational equations. In: Dubois, D., Prade, H. (eds.) The Handbook of Fuzzy Set Series, vol. 1, pp. 291–340. Academic Kluwer Publishers, Boston (2000)Google Scholar
- 24.Štěpnička, M., Holčapek, M.: Fuzzy relational compositions based on generalized quantifiers. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems, PT II, Communications in Computer and Information Science, IPMU 2014, vol. 443, pp. 224–233. Springer, Berlin (2014)Google Scholar