This paper introduces the intuitionistic rough set and intuitionistic rough relational and rough object oriented database models. Rough set, fuzzy set, and intuitionistic set uncertainty management are discussed and compared, and the model based on intuitionistic and rough sets developed here is applied to databases. The intuitionistic rough set database models draw benefits from both the rough...

In this paper the concept of intuitionistic fuzzy slightly precontinuous functions are introduced and studied. Intuitionistic fuzzy slightly precontinuity generalize intuitionistic fuzzy precontinuity. Besides giving characterizations and basic properties of this function, preservation theorems of intuitionistic fuzzy slightly precontinuous are also obtained. We also study relationships between...

The aim of this paper is to study the generalization of the intuitionistic fuzzy normed spaces such as intuitionistic fuzzy 2-normed space. In this structure, we have discussed the intuitionistic fuzzy 2continuity and intuitionistic fuzzy 2-boundedness. Also, we have introduced the intuitionistic fuzzy ψ-2-normed space which is a generalization of intuitionistic fuzzy 2-normed space. We have di...

In this paper, the intuitionistic fuzzy Lie sub-superalgebras and ideals of Lie superalgebras are studied further. We define the intuitionistic fuzzy quotient Lie superalgebra by an intuitionistic fuzzy Lie ideal and prove that it is a Lie superalgebra. The intuitionistic fuzzy set of quotient Lie superalgebra is also considered. Finally, solvable intuitionistic fuzzy Lie ideals and nilpotent i...

The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

In some multi-attribute decision making (MADM) problems, various relationships among the decision attributes should be considered. This paper investigates the prioritization relationship of attributes in MADM with trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFNs are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. Fir...

In this paper, we characterize the intuitionistic fuzzy δ-continuous, intuitionistic fuzzy weakly δ-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly θ-continuous functions in terms of intuitionistic fuzzy δ-closure and interior or θ-closure and interior.

The notion of intuitionistic fuzzy metric space was introduced by Park (2004) and the concept of intuitionistic fuzzy normed space by Saadati and Park (2006). Recently Mursaleen and Lohani introduced the concept of intuitionistic fuzzy 2-metric space (2009) and intuitionistic fuzzy 2-norm space. This paper studies precompactness and metrizability in this new setup of intuitionistic fuzzy 2-metr...

The object of this paper is to introduce the notion of intuitionistic fuzzy continuous mappings and intuitionistic fuzzy bounded linear operators from one intuitionistic fuzzy n-normed linear space to another. Relation between intuitionistic fuzzy continuity and intuitionistic fuzzy bounded linear operators are studied and some interesting results are obtained.

In this paper, we generalize Ying’s model of linguistic quantifiers [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence, 170 (2006) 581-606] to intuitionistic linguistic quantifiers. An intuitionistic linguistic quantifier is represented by a family of intuitionistic fuzzy-valued fuzzy measures and the intuitionistic truth value (the degrees of satisfaction a...