In this work, we introduce the concept of fuzzy parameterized intervalvalued fuzzy soft set theory (fpivfss) and study their operations. We then define fpivfss-aggregation operator to form fpivfss-decision making method that allows constructing more efficient decision processes. Finally, some numerical examples are employed to substantiate the conceptual arguments.

In our earlier work we have developed the axiomatic theory of the scalar cardinality of interval-valued fuzzy sets following Wygralak’s axiomatic theory of scalar cardinalities of fuzzy sets. The cardinality has been defined as a mapping from the set of interval-valued fuzzy sets with finite support to the set of closed subintervals of [0,+∞). We have shown that each scalar cardinality of inter...

–Rough set theory is a powerful tool to extract classification rules from a database that usually is given in the form of information system in which information is expressed by attributes and their values. In this paper, we first evaluate every example data (tuple) using, not a singleton but, a fuzzy number (or, suppose the original information system is along with such fuzzy numbers), due to ...

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

Decision-theoretic rough set theory (DTRS) is becoming one of the important research directions for studying set approximations using Bayesian decision procedure and probability theory in rough set community. In this paper, a novel model, fuzzy multigranulation decision-theoretic rough set model (FM-DTRS), is proposed in terms of inclusion measure of fuzzy rough sets in the viewpoint of fuzzy m...

in this paper, for a complete lattice l, we introduce interval-valued l-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. some characterization and properties are discussed.

Since the early 1990s, many authors have studied fuzzy rough set models and their application in machine learning and data reduction. In this work, we adjust the β-precision and the ordered weighted average based fuzzy rough set models in such a way that the number of theoretical properties increases. Furthermore, we evaluate the robustness of the new models a-β-PREC and a-OWA to noisy data and...

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

This paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used. In constructive approach, a pair of lower and upper generalized fuzzy rough (and rough fuzzy, respectively) approximation operators is first defined. The representations of both fuzzy rough approximation operators and rough...

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 ...