Rough interval-valued intuitionistic fuzzy sets

Annals of Data Science, 2022

It has been found that fuzzy sets, rough sets and soft sets are closely related concepts. Many complicated problems in economics, engineering, social sciences, medical science and many other fields involve uncertain data. These problems, which one comes in real life, cannot be solved using classical mathematical methods. There are several well-known theories to describe uncertainty, for instance, fuzzy set theory, rough set theory, and other mathematical tools. But all of these theories have their inherit difficulties as pointed out by D. Molodtsov. In 1999, D. Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainties. The concept of rough sets, proposed by Z. Pawlak as a framework for the construction of approximations of concepts. It is a formal tool for modeling and processing insufficient and incomplete information. Zhou and Wu first proposed the concept of intuitionistic fuzzy rough sets (IFrough sets). The aim of this paper is to introduce the concept of interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets). We also investigate some properties of IVIFS rough approximation operators. Some basic operations and properties are studied. Lastly applications have been shown in decision making problems.

New trends in mathematical sciences, 2015

Fuzzy set theory, rough set theory and soft set theory are all mathematical tools dealing with uncertainties. The concept of type-2 fuzzy sets was introduced by Zadeh in 1975 which was extended to interval valued intuitionistic fuzzy sets of type-2 by the authors.This paper is devoted to the discussions of the combinations of interval valued intuitionistic sets of type-2, soft sets and rough sets.Three different types of new hybrid models, namely-interval valued intuitionistic fuzzy soft sets of type-2, soft rough interval valued intuitionistic fuzzy sets of type-2 and soft interval valued intuitionistic fuzzy rough sets of type-2 are proposed and their properties are derived.

2015

Fuzzy set theory, rough set theory and soft set theory are all mathematical tools dealing with uncertainties. The concept of type-2 fuzzy sets was introduced by Zadeh in 1975 which was extended to interval valued intuitionistic fuzzy sets of type-2 by the authors.This paper is devoted to the discussions of the combinations of interval valued intuitionistic sets of type-2, soft sets and rough sets.Three different types of new hybrid models, namely-interval valued intuitionistic fuzzy soft sets of type-2, soft rough interval valued intuitionistic fuzzy sets of type-2 and soft interval valued intuitionistic fuzzy rough sets of type-2 are proposed and their properties are derived. Keywords: Soft set, rough set, soft rough set, soft rough fuzzy set, soft fuzzy rough set, interval valued intuitionistic fuzzy set of type-2,interval valued intuitionistic fuzzy soft set of type-2, soft roughinterval valued intuitionistic fuzzy set of type-2,soft interval valued intuitionistic fuzzy rough set...

Studies in Fuzziness and Soft Computing, 2015

Soft set theory, fuzzy set theory and rough set theory are all mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the discussions of the combinations of intervalvalued intuitionistic fuzzy set, rough set and soft set. A new model, namely soft interval-valued intuitionistic fuzzy rough set is proposed and it's properties are derived. Also a soft interval-valued intuitionistic fuzzy rough set based multi criteria group decision making scheme is presented. The proposed scheme is illustrated by an example regarding the car selection problem.

2006 3rd International IEEE Conference Intelligent Systems, 2006

The notion of intuitionistic fuzzy approximation space is introduced. Rough sets on such spaces are defined and some of their properties are studied.

Computers & Mathematics with Applications, 2010

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, the notion of the interval-valued intuitionistic fuzzy soft set theory is proposed. Our interval-valued intuitionistic fuzzy soft set theory is a combination of an interval-valued intuitionistic fuzzy set theory and a soft set theory. In other words, our interval-valued intuitionistic fuzzy soft set theory is an interval-valued fuzzy extension of the intuitionistic fuzzy soft set theory or an intuitionistic fuzzy extension of the interval-valued fuzzy soft set theory. The complement, ''and'', ''or'', union, intersection, necessity and possibility operations are defined on the interval-valued intuitionistic fuzzy soft sets. The basic properties of the interval-valued intuitionistic fuzzy soft sets are also presented and discussed.

In this paper we define rough intuitionistic fuzzy sets (analogous to the definition of rough fuzzy sets introduced by Dubois and Prade [8] ) and study their properties. Some propositions in this notion are proved.

Studies in Fuzziness and Soft Computing, 2015

In this paper the concept of interval valued intuitionistic fuzzy soft rough sets is introduced. Also interval valued intuitionistic fuzzy soft rough set based multi criteria group decision making scheme is presented, which refines the primary evaluation of the whole expert group and enables us to select the optimal object in a most reliable manner. The proposed scheme is illustrated by an example regarding the candidate selection problem.

2013

In this paper the concept of interval valued intuitionistic fuzzy soft set relations (IVIFSS-relations for short) is proposed. Our relations on interval valued intuitionistic fuzzy soft sets is an extension of the relations on intuitionistic fuzzy soft sets, introduced by Mukherjee and Chakraborty in 2009. The basic properties of the IVIFSS-relations are also presented and discussed. It is seen that the sub collection of the family of IVIFSS-relations form a relational topology. Also various types of IVIFSSrelations are presented. Then a solution to a decision making problem using IVIFSS-relation is presented. Finally the lower and upper soft interval valued intuitionistic fuzzy rough approximations of a IVIFSS-relation with respect to a soft interval valued intuitionistic fuzzy approximation space are presented. 2010 AMS Classification: 03E722, 54A40, 06D72.

The concept of fuzzy approximation space that depends on a fuzzy proximity relation is a generalization of the concept of the knowledge base. But intuitionistic fuzzy approximation space that depends on an intuitionistic fuzzy proximity relation is a better generalization of the concept of knowledge base than fuzzy approximation space. Therefore, rough sets defined on intuitionistic fuzzy approximation spaces extend the concept of rough sets on fuzzy approximation spaces. This paper presents how rough sets on intuitionistic fuzzy approximation spaces provides better result over rough sets on fuzzy approximation spaces on knowledge representation. Index Terms: Fuzzy relation, fuzzy proximity relation, fuzzy approximation space, intuitionistic fuzzy approximation space and rough set.