In order to be recognized quickly, generally we have chosen the names of the functions with some conventions. The names contain three parts which are prefix, suffix, and middle names that are separated by a point. The following is a description of

each part.

- prefix: There are some different prefixes for names of functions expressing a kind of task to be performed. The function names with prefix BC refer to basic concepts which means that the functions are created for implementing the basic concepts of RST and FRST. For instance, the function BC.IND.relation.RST is used to calculate the indiscernibility relation which is one of the basic concepts of RST. Generally, functions having the prefix BC are called by many other functions. While prefix D refers to discretization, FS, IS, RI, and C refer to feature selection, instance selection, rule induction and classifier domains. Furthermore, SF and X mean that functions are used as supporting functions which are not related directly with RST and FRST and auxiliary functions which are called as a parameter.
- suffix: It is located at the end of names. There are two types available which are RST and FRST. RST represents rough set theory while FRST shows that the function is applied to fuzzy rough set theory. Additionally, some functions that do not have RST or FRST suffix are used for both theories.
- middle: All other words in the middle of the names are used to express the name of a particular method/algorithm or functionality. In this case, it could consist of more than one word separated by points.

Other functions that have names not based on the above rules are S3 functions e.g. summary and predict which are used to summarize objects and predict new data, respectively. The RoughSets package contains two main groups which are implementations of algorithms based on rough set and fuzzy rough set theories. For each part, we have considered many algorithms/methods to be implemented. The complete description about the algorithms and their associated functions is

illustrated briefly as follows.

**1. The implementations of RST:** This part outlines some considered algorihtms/methods based on RST. The approaches can be classified based on their tasks as follows:

- The basic concepts of RST: The following is a list showing tasks and their implementation as functions.
- Indiscernibility relation: It is a relation determining whether two objects are indiscernible by some attributes. It has been implemented in BC.IND.relation.RST.
- Lower and upper approximations: These approximations show whether objects can classified with certainty or not. It has been implemented in BC.LU.approximation.RST.
- Positive region: It is used to determine objects that are included in positive region and the corresponding degree of dependency. It has been implemented in BC.positive.reg.RST.
- Discernibility matrix: It is used to create discernibility matrix showing attributes that discern each pair of objects. It has been implemented in BC.discernibility.mat.RST.

- Discretization: There are several methods that have been considered in the package. The methods are implemented in the following functions.
- D.max.discernibility.matrix.RST: It implements the maximal discernibility algorithm to choose the cut values which discern the largest number of pairs of objects in the decision-relative discernibility matrix.
- D.local.discernibility.matrix.RST: It implements the local strategy which implements decision tree to calculate the quality of a cut (i.e. number of objects discerned by cut).
- D.global.discernibility.heuristic.RST: It implements the global discernibility algorithm which is computing globally semi-optimal cuts using the maximum discernibility heuristic.
- D.discretize.quantiles.RST: It is a function used for computing cuts of the "quantilebased" discretization into n intervals.
- D.discretize.equal.intervals.RST: It is a function used for computing cuts of the "equal interval size" discretization into n intervals. The output of these methods is a list of cut values which are the values for converting real to nominal values. So, we provide the function SF.applyDecTable that is used to generate a new decision table according to the cut values we got by discretization methods. Additionally, we have implemented D.discretization.RST as a wrapper function collecting all methods considered to perform discretization tasks.

- Feature selection: The output of this task can be classified into the following three groups as follows:
- Feature subset: It refers to a superreduct which is not necessarily minimal. In other words, the methods in this group might generate just a subset of attributes.

- QuickReduct algorithm: It has been implemented in FS.quickreduct.RST.
- Superreduct generation based on some criteria: It is based on different criteria which are entropy, gini index, discernibility measure, size of positive region. It has been implemented in FS.greedy.heuristic.superreduct.RST. Furthermore, we provide a wrapper function FS.feature.subset.computation in order to give a user interface for many methods of RST and FRST.
- Reduct: The following are methods that produce a single decision reduct.

- Reduct generation based on some criteria: It is based on different criteria which are entropy, gini index, discernibility measure, size of positive region. It has been implemented in FS.greedy.heuristic.reduct.RST.
- Permutation reduct: It is based on a permutation schema over all attributes. It has been implemented in FS.permutation.heuristic.reduct.RST. Furthermore, we provide a wrapper function FS.reduct.computation in order to give a user interface toward many methods of RST and FRST.
- All reducts: In order to get all decision reducts, first we execute the BC.discernibility.mat.RST function for constructing a decision-relative discernibility matrix. After obtaining the matrix, FS.all.reducts.computation is called to get all reducts. The output of the above methods is a class containing a decision reduct/feature subset and other descriptions. For generating a new decision table according to the decision reduct, we provide the function SF.applyDecTable.

- Feature subset: It refers to a superreduct which is not necessarily minimal. In other words, the methods in this group might generate just a subset of attributes.
- Rule induction: We have provided the function RI.indiscernibilityBasedRules.RST to generate rules. This function requires the output of feature selection functions for getting a superreduct/reduct. After obtaining the rules, in the predicting process, we execute predict.RuleSetRST considering our rules and given newdata/testing data.

2. The implementations of FRST: As in the RST part, this group contains several algorithms that can be classified into several groups based on their purpose. The following is a description of all methods that have been implemented in functions.

- Basic concepts of FRST: The following is a list showing tasks and their implementation as functions.
- Indiscernibility relations: the are fuzzy relations determining to which degree two objects are similar. This package provides several types of relations which are implemented in a single function called BC.IND.relation.FRST. In this package, we consider several types of relations e.g. fuzzy equivalence, tolerance, and T-similarity relations. These relations can be chosen by assigning type.relation. Additionally, In this function, we provide several options to calculate aggregation e.g. triangular norm operator (e.g. "lukasiewicz", "min", etc) and user-defined operator.
- Lower and upper approximations: These approximations show to what extent objects can be classified with certainty or not. This task has been implemented in BC.LU.approximation.FRST. There are many approaches available in this package that can be selected by assigning the parameter type.LU. The considered methods are implication/t-norm, -precision fuzzy rough sets (-PFRS), vaquely quantified rough sets (VQRS), fuzzy variable precision rough sets (FVPRS), ordered weighted average (OWA), soft fuzzy rough sets (SFRS), and robust fuzzy rough sets (RFRS). Furthermore, we provide a facility which is "custom" where users can create their own approximations by defining functions to calculate lower and upper approximations. Many options to calculate implicator and triangular norm are also available.
- Positive region: It is used to determine the membership degree of each object to the positive region and the corresponding degree of dependency. It has been implemented in BC.positive.reg.FRST.
- Discernibility matrix: It is used to construct the decision-relative discernibility matrix. There are some approaches to construct the matrix, e.g. based on standard approach, gaussian reduction, alpha reduction, and minimal element in discernibility matrix. They have been implemented in BC.discernibility.mat.FRST.

- Feature selection: Generally, for dealing with this problem we have considered two different kinds of approaches which are methods employing heuristics to produce a nearoptimal reduction such as the fuzzy QuickReduct algorithm and approaches based on the decision-relative discernibility matrix (see BC.discernibility.mat.FRST). In the context of their outputs, one of the differences between them is on the type of produced reduct which are a single superreduct or a subset of features, a reduct and all reducts. The following is a description of all above types.
- Feature subset: It refers to methods which produce a superreduct which is not necessarily a reduct. In other words methods in this group might generate just a subset of attributes. The following is a complete list of methods considered in this package.
- positive region based algorithms: It refers to positive regions, as a way to evaluate attributes to be selected. Furthermore, we provide several different measures based on the positive region in this function. All methods included in this part employ the QuickReduct algorithm to obtain selected features. In order to choose a particular algorithm, we assign parameter type.method in FS.quickreduct.FRST.
- boundary region based algorithm: This algorithm is based on the membership degree to the fuzzy boundary region which is determined by subtracting the values of fuzzy upper and lower approximations. This algorithm has been implemented in FS.quickreduct.FRST by setting the parameter as type.method = "fuzzy.boundary.reg". Furthermore, we provide a wrapper function FS.feature.subset.computation in

order to give a user interface for many methods of RST and FRST.

- Reduct: The following methods produce a single decision reduct.

- The near-optimal reduction based algorithm: It is an algorihtm proposed by Zhao et al, which results a near-optimal reduction by modifying the discernibility matrix. Additionally, this algorithm uses fuzzy variable precision rough sets (FVPRS) for calculating the lower approximation. It has been implemented in FS.nearOpt.fvprs.FRST. Furthermore, we provide a wrapper function FS.reduct.computation in order to

provide a user interface toward many methods of RST and FRST.

- The near-optimal reduction based algorithm: It is an algorihtm proposed by Zhao et al, which results a near-optimal reduction by modifying the discernibility matrix. Additionally, this algorithm uses fuzzy variable precision rough sets (FVPRS) for calculating the lower approximation. It has been implemented in FS.nearOpt.fvprs.FRST. Furthermore, we provide a wrapper function FS.reduct.computation in order to
- All reducts: In order to get all decision reducts, first we execute the BC.discernibility.mat.FRST function for constructing a decision-relative discernibility matrix. After obtaining the matrix, FS.all.reducts.computation is called to get all reducts. The output of the above methods is a class containing a decision reduct/feature subset and other descriptions. For generating a new decision table according to the decision reduct, we provide the function SF.applyDecTable.

- Feature subset: It refers to methods which produce a superreduct which is not necessarily a reduct. In other words methods in this group might generate just a subset of attributes. The following is a complete list of methods considered in this package.
- Rule induction: As we mentioned before, rule induction is a task used to generate rules representing knowledge of a decision table. Commonly, this process is called learning phase in machine learning. The following methods are considered to generate rules:

- RI.hybridFS.FRST: It combines fuzzy-rough rule induction and feature selection. See RI.hybridFS.FRST.
- RI.GFRS.FRST: It refers to rule induction based on generalized fuzzy rough sets (GFRS). See RI.GFRS.FRST.

After generating rules, we can use them to predict decision values of new data by executing a predicting function which is predict.RuleSetFRST.

- Instance selection: The following functions select instances to improve accuracy by removing noisy, superflous or inconsistent ones from training datasets.

- IS.FRIS.FRST: It was proposed by Jensen and Cornelis. It evaluates the degree of membership to the positive region of each instance. If an instance’s membership degree is less than the threshold, then the instance can be removed. See IS.FRIS.FRST.
- IS.FRPS.FRST: The fuzzy-rough prototype selection (FRPS) based on Verbiest, et al’s method. See IS.FRPS.FRST. We provide the function SF.applyDecTable that is used to generate a new decision table

according to the output of instance selection functions.

- Fuzzy-rough nearest neighbor-based approaches: This part provides nearest neighbour based methods for predicting decision values/classes of new datasets. In other words, by supplying a decision table as training data we can predict decision values of new data at the same time. We have considered the following methods:

- C.FRNN.FRST: The fuzzy-rough nearest neighbors based on Jensen and Cornelis’ technique. See C.FRNN.FRST.
- C.FRNN.O.FRST: The fuzzy-rough ownership nearest neighbour algorithm based on Sarkar’s method. See C.FRNN.O.FRST.
- C.POSNN.FRST: The positive region based fuzzy-rough nearest neighbour algorithm based on Verbiest et al’s technique. See C.POSNN.FRST.