Soft sets and their variants
Michael Voskoglou; Said Broumi
Abstract
Much of a person’s cognitive activity depends on the ability to reason analogically. Analogical Reasoning (AR) compares the similarities between new and past knowledge and uses them to obtain an understanding of the new knowledge. The mechanisms, however, under which the human mind works are not ...
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Much of a person’s cognitive activity depends on the ability to reason analogically. Analogical Reasoning (AR) compares the similarities between new and past knowledge and uses them to obtain an understanding of the new knowledge. The mechanisms, however, under which the human mind works are not fully investigated and as a result AR is characterized by a degree of fuzziness and uncertainty. Probability theory has been proved sufficient for dealing with the cases of uncertainty due to randomness. During the last 50-60 years, however, various mathematical theories have been introduced for tackling effectively the other forms of uncertainty, including fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, rough sets, etc. The combination of two or more of those theories gives frequently better results for the solution of the corresponding problems. A hybrid assessment method of AR skills under fuzzy conditions is developed in this work using Grey Numbers (GN) and soft sets as tools, which is illustrated by an application on evaluating student analogical problem solving skills.
