Abstract
The paper examines fuzzy quantifiers, which serve to formalize human reasoning. In this paper, quantifiers are considered in relation to the problems of decision-making on a set of alternatives based on a combination of criteria. Using fuzzy quantifiers and OWA aggregation operators, in which quantifiers are used to calculate weights, it is possible to implement basic decision-making strategies. In this paper, we study various quantifiers that are most often used when choosing the best alternative, such as “Most”, “The more, the better”, “At least k%”. As a result of the study of these quantifiers, the boundaries of the values of the parameters of the membership functions were found, at which the OWA operator will have compensatory properties. The paper also points out the disadvantages of the most commonly used quantifiers when they are used in the OWA operator. The presence of “insensitivity zones” of the quantifier with piecewise linear functions of belonging to the change in the values of the components of the criteria vector is established. It is shown that this problem is solved when passing to a continuous membership function in the form of an s-shaped (logistic) curve. A modification of the OWA operator is proposed in the form of a superposition of partial estimates and a membership function of the fuzzy concept of “Good correspondence”. This modification ensures that when comparing alternatives, not only the number of private assessments that meet the criteria is taken into account, but also the quality of compliance.
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Matveev, M., Alejnikova, N., Safonov, V., Korobova, L. (2022). The Study of Fuzzy Quantifiers in Multi-criteria Decision-Making. In: Taratukhin, V., Matveev, M., Becker, J., Kupriyanov, Y. (eds) Information Systems and Design. ICID 2021. Communications in Computer and Information Science, vol 1539. Springer, Cham. https://doi.org/10.1007/978-3-030-95494-9_14
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