Pythagorean fuzzy set, generalized by Yager, is a new tool to deal with vagueness considering the membership grade $$\mu $$
 and non-membership $$\nu $$
 satisfying the condition $$\mu ^2+\nu ^2\le 1$$
 . It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Pythagorean fuzzy set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as decision making, aggregation operators, and information measures. Because of such a growth, we present an overview on Pythagorean fuzzy set with aim of offering a clear perspective on the different concepts, tools and trends related to their extension. In particular, we provide two novel algorithms in decision making problems under Pythagorean fuzzy environment. It may be served as a foundation for developing more algorithms in decision making.

Pythagorean fuzzy set: state of the art and future directions

Theory and applications of granular labelled partitions in multi-scale decision tables

The original Pawlaks rough set approach based on indiscernibility relation (single granularity) has been extended to multigranulation rough set structure in the recent years. Multigranulation rough set approach has become a flouring research direction in rough set theory. This paper considers rough approximation of a fuzzy concept under the framework of multigranulation over two different universes of discourse, i.e., multigranulation fuzzy rough set models over two universes. We present three types of multigranulation fuzzy rough set over two universes by the constructive approach, respectively. Some interesting properties of the proposed models are discussed and also the interrelationships between the proposed models and the existing rough set models are given. We then propose a new approach to a kind of multiple criteria group decision making problem based on multigranulation fuzzy rough set model over two universes. The decision rules and algorithm of the proposed method are given and an example of handling multiple criteria group decision making problem of clothes ranking illustrates this approach. The main contribution of this paper is twofold. One is to establish the multigranulation fuzzy rough set theory over two universes. Another is to try presenting a new approach to multiple criteria group decision making based on multigranulation fuzzy rough set over two universes. The proposed models not only enrich the theory of multigranulation rough set but also make a tentative to provide a new perspective for multiple criteria group decision making with uncertainty.

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Multigranulation fuzzy rough set over two universes and its application to decision making

A basic notion shared by rough set analysis and formal concept analysis is the definability of a set of objects based on a set of properties. The two theories can be compared, combined and applied to each other based on definability. In this paper, the notion of rough set approximations is introduced into formal concept analysis. Rough set approximations are defined by using a system of definable sets. The similar idea can be used in formal concept analysis. The families of the sets of objects and the sets of properties established in formal concept analysis are viewed as two systems of definable sets. The approximation operators are then formulated with respect to the systems. Two types of approximation operators, with respect to lattice-theoretic and set-theoretic interpretations, are studied. The results provide a better understanding of data analysis using rough set analysis and formal concept analysis.

Rough set approximations in formal concept analysis

Topology vs generalized rough sets

This paper focuses on rough set models on two universes and reveals some new properties. A revised rough set model is proposed which provides a new selection of interval structures for uncertain reasoning using rough set theory and methods.

Zong-Ben Xu †

Papers

Rough Set Models on Two universes