Generalized Interval-Valued Fuzzy Rough Sets Based on Interval-Valued Fuzzy Logical Operators
نویسندگان
چکیده
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 models of rough sets. There are recent researches into generalized interval-valued fuzzy rough sets for interval-valued fuzzy datasets. However, only fuzzy implicator and t-norm are used in generalized interval-valued fuzzy rough sets and another two pairs of fuzzy logical operators, t-norm and t-conorm, R-implicator and its dual, have not been considered in generalized interval-valued fuzzy rough sets. In this paper, these models are generalized to a new approach that not only considers interval-valued fuzzy sets but also two pairs of fuzzy logical operators. First, we study the interval representations of interval-valued fuzzy t-norm, interval-valued fuzzy negator, interval-valued fuzzy R-implicator and their duals, which provide a theoretical basis for interval-valued fuzzy rough sets based on interval-valued fuzzy logical operators. Second, we propose generalized interval-valued fuzzy rough sets based on two pairs of fuzzy logical operators: interval-valued fuzzy t-norms and t-conorm, and interval-valued fuzzy R-implicators and its dual. Finally, we confirm that some existing models, including rough sets, interval-valued fuzzy rough sets and generalized fuzzy rough sets based on fuzzy logical operators are special cases of the proposed models.
منابع مشابه
Generalized interval-valued fuzzy variable precision rough sets determined by fuzzy logical operators
For interval-valued fuzzy datasets, people have started to do research on interval-valued fuzzy rough sets and relevant models. However, these models could not be effectively applied to handle the real-valued datasets such as interval-valued fuzzy datasets as variable precision problems were not considered in interval-valued fuzzy rough sets. In this paper, fuzzy variable precision rough sets a...
متن کاملGroup Generalized Interval-valued Intuitionistic Fuzzy Soft Sets and Their Applications in\ Decision Making
Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...
متن کاملGeneralized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral operators for multicriteria decision making
The interval-valued intuitionistic fuzzy set (IVIFS) which is an extension of the Atanassov’s intuitionistic fuzzy set is a powerful tool for modeling real life decision making problems. In this paper, we propose the emph{generalized interval-valued intuitionistic fuzzy Hamacher generalized Shapley Choquet integral} (GIVIFHGSCI) and the emph{interval-valued intuitionistic fuzzy Hamacher general...
متن کاملA Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators
Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are s...
متن کاملRough approximation operators based on quantale-valued fuzzy generalized neighborhood systems
Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...
متن کامل