Fuzzy implications defined on the set of discrete fuzzy numbers

Riera, Juan Vicente; Torrens, Joan

doi:10.2991/eusflat.2011.97

Cited by 4 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using similar methods, Casasnovas and Riera [8,9] researched the problem of the maximum and minimum values of discrete fuzzy numbers and studied the triangular norms and triangular conorms to discrete fuzzy numbers in 2011. In the same year, Riera and Torrens [10] defined fuzzy implication functions on sets of discrete fuzzy numbers. Using the above operations, Riera and Torrens [11] defined an integration operator for discrete fuzzy numbers in 2012.…”

Section: Introductionmentioning

confidence: 99%

Special Discrete Fuzzy Numbers on Countable Sets and Their Applications

Qin,

Gong

2024

Symmetry

View full text Add to dashboard Cite

There are some drawbacks to arithmetic and logic operations of general discrete fuzzy numbers, which limit their application. For example, the result of the addition operation of general discrete fuzzy numbers defined by the Zadeh’s extension principle may not satisfy the condition of becoming a discrete fuzzy number. In order to solve these problems, special discrete fuzzy numbers on countable sets are investigated in this paper. Since the representation theorem of fuzzy numbers is the basic tool of fuzzy analysis, two kinds of representation theorems of special discrete fuzzy numbers on countable sets are studied first. Then, the metrics of special discrete fuzzy numbers on countable sets are defined, and the relationship between these metrics and the uniform Hausdorff metric (i.e., supremum metric) of general fuzzy numbers is discussed. In addition, the triangular norm and triangular conorm operations (t-norm and t-conorm for short) of special discrete fuzzy numbers on countable sets are presented, and the properties of these two operators are proven. We also prove that these two operators satisfy the basic conditions for closure of operation and present some examples. Finally, the applications of special discrete fuzzy numbers on countable sets in image fusion and aggregation of subjective evaluation are proposed.

show abstract