# What is rough set & fuzzy set approach?

## What is rough set & fuzzy set approach?

In its abstract form, it is a new area of uncertainty mathematics closely related to fuzzy theory. We can use rough set approach to discover structural relationship within imprecise and noisy data. Rough sets and fuzzy sets are complementary generalizations of classical sets.

**What are rough set properties?**

A rough set definition for a given class, C, is approximated by two sets—a lower approximation of C and an upper approximation of C. The lower approximation of C consists of all the data tuples that, based on the knowledge of the attributes, are certain to belong to C without ambiguity.

**What is rough set approach?**

Rough Set Approach The Rough Set Theory is based on the establishment of equivalence classes within the given training data. The tuples that forms the equivalence class are indiscernible. It means the samples are identical with respect to the attributes describing the data.

### What is Indiscernibility relation?

Indiscernibility Relation is a central concept in Rough Set Theory, and is considered as a relation between two objects or more, where all the values are identical in relation to a subset of considered attributes.

**What is the main goal of rough sets?**

The main goal of the rough set analysis is induction of (learning) approximations of concepts. Rough sets constitutes a sound basis for KDD. It offers mathematical tools to discover patterns hidden in data.

**What is soft set theory?**

Soft set theory is a generalization of fuzzy set theory, that was proposed by Molodtsov in 1999 to deal with uncertainty in a parametric manner. A soft set is a parameterised family of sets – intuitively, this is “soft” because the boundary of the set depends on the parameters.

#### What is reduct and core in rough set theory explain with an example?

Reduct and core are the two most important concept of rough set theory. Reduct is a reduced subset of original set which retains the accuracy of original set. Reduct is often used in the attribute selection process to reduce unnecessary attributes towards decision making applications[1].

**How do you define the optimum reduct?**

If the classification measurements are better and the number of elements in the reduct is small, we can deem it a optimum reduct. Meanwhile, the so-called optimum reduct is also depended on the task you want to perform.

**How do you find the core and reduct?**

Using the discernibility matrix, the reduct of a decision table can be found[1]. The core can be found as the set of all singleton entries in the discernibility matrix. The reduct is the minimal element in the discernibility matrix, which intersects all the element of the discernibility matrix.

## What are fuzzy soft sets?

A fuzzy soft relation is defined as soft set over the fuzzy power set of the cartesian product of two crisp sets. Let and be two crisp sets and is the set of parameters, then a function R : E → I X × Y is called a fuzzy soft relation.

**Why do we use soft set?**

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty and vagueness, and many researchers have created some models to solve problems in decision making and medical diagnosis.

**What do you mean by fuzzy set?**

A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one.