The fuzzy rough sets and generalized fuzzy rough sets have been extended by three pairs of fuzzy logical operators to deal with real-valued data for a variety of models. Three pairs of fuzzy logical operators are triangular norm or t-norm and its dual (t-conorm), residual implicator or R-implicator and its dual, fuzzy implicator and t-norm, which are frequently discussed in generalization model...

Graph theory has an important role in the area of applications of networks and clustering‎. ‎In the case of dealing with uncertain data‎, ‎we must utilize ambiguous data such as fuzzy value‎, ‎fuzzy interval value or values of fuzzy number‎. ‎In this study‎, ‎values of fuzzy number were used‎. ‎Initially‎, ‎we utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value f...

Fuzzy Description Logics (Fuzzy DLs) are logics that allow to deal with structured knowledge affected by fuzziness. Fuzzy DLs are at the heart of Fuzzy OWL 2, a fuzzy version of the standard ontology language OWL 2. Although a relatively important amount of work has been carried out in the last years, fuzzy DLs are open to be extended with several features worked out in other fields. In particu...

In this paper, we firstly propose some generalized prioritized aggregation operators to aggregate the intuitionistic fuzzy values (IFVs), such as the generalized intuitionistic fuzzy prioritized weighted geometric (GIFPWG) operator and the generalized intuitionistic fuzzy prioritized weighted average (GIFPWA) operator. It is shown that some existing intuitionistic fuzzy aggregation operators ar...

In digital-based information boom, the fuzzy covering rough set model is an important mathematical tool for artificial intelligence, and how to build the bridge between the fuzzy covering rough set theory and Pawlak’s model is becoming a hot research topic. In this paper, we first present the γ−fuzzy covering based probabilistic and grade approximation operators and double-quantitative approxim...

In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations ...

Potato image segmentation is an important part of image-based potato defect detection. This paper presents a robust potato color image segmentation through a combination of a fuzzy rule based system, an image thresholding based on Genetic Algorithm (GA) optimization and morphological operators. The proposed potato color image segmentation is robust against variation of background, distance and ...

In this paper we generate fuzzy relations and fuzzy operators using different kind of generators and we study the relationship between them. Firstly, we introduce a new fuzzy preorder induced by a fuzzy operator. We generalize this preorder to a fuzzy relation generated by two fuzzy operators and we analyze its properties. Secondly, we introduce and explore two ways of inducing a fuzzy operator...