$T$-superiority and $\rm{t}$-norm-based images of fuzzy sets

Rok, strany: 2016, 25 - 37

Comparisons of finite fuzzy sets based on the results of conjunctive and disjunctive aggregations of their membership grades are studied. For a given t-norm $T$, the notion of $T$-superiority of fuzzy sets is introduced. When a fuzzy set $g$ is $T$-superior to a fuzzy set $f$, the description of a vague concept by $g$ is much more desirable than the description by $f$. For a comparison of a fuzzy set $f$ with the ``standard'' fuzzy set $g$ (describing the desirable or historically the most common characterization of the vague concept in question) t-norm-based transformations of $f$ with respect to $g$, called the $T$-images of $f$, are suggested. A special type of the $T$-image of $f$ with respect to $g$ may be considered as a soft evaluation of $T$-uperiority of $g$ to $f$.

ISO 690:

Bodjanova, S., Kalina, M. 2016. $T$-superiority and $\rm{t}$-norm-based images of fuzzy sets. In Tatra Mountains Mathematical Publications, vol. 66, no.2, pp. 25-37. 1210-3195.

APA:

Bodjanova, S., Kalina, M. (2016). $T$-superiority and $\rm{t}$-norm-based images of fuzzy sets. Tatra Mountains Mathematical Publications, 66(2), 25-37. 1210-3195.