Decision-theoretic Rough Set Approach Research Articles

A Novel Interval-Valued Decision Theoretic Rough Set Model with Intuitionistic Fuzzy Numbers Based on Power Aggregation Operators and Their Application in Medical Diagnosis

Intuitionistic fuzzy information is a potent tool for medical diagnosis applications as it can represent imprecise and uncertain data. However, making decisions based on this information can be challenging due to its inherent ambiguity. To overcome this, power aggregation operators can effectively combine various sources of information, including expert opinions and patient data, to arrive at a more accurate diagnosis. The timely and accurate diagnosis of medical conditions is crucial for determining the appropriate treatment plans and improving patient outcomes. In this paper, we developed a novel approach for the three-way decision model by utilizing decision-theoretic rough sets and power aggregation operators. The decision-theoretic rough set approach is essential in medical diagnosis as it can manage vague and uncertain data. The redesign of the model using interval-valued classes for intuitionistic fuzzy information further improved the accuracy of the diagnoses. The intuitionistic fuzzy power weighted average (IFPWA) and intuitionistic fuzzy power weighted geometric (IFPWG) aggregation operators are used to aggregate the attribute values of the information system. The established operators are used to combine information within the intuitionistic fuzzy information system. The outcomes of various alternatives are then transformed into interval-valued classes through discretization. Bayesian decision rules, incorporating expected loss factors, are subsequently generated based on this foundation. This approach helps in effectively combining various sources of information to arrive at more accurate diagnoses. The proposed approach is validated through a medical case study where the participants are classified into three different regions based on their symptoms. In conclusion, the decision-theoretic rough set approach, along with power aggregation operators, can effectively manage vague and uncertain information in medical diagnosis applications. The proposed approach can lead to timely and accurate diagnoses, thereby improving patient outcomes.

A Fuzzy Decision-Theoretic Rough Set Approach for Type-2 Fuzzy Conditional Information Systems and Its Application in Decision-Making

A Fuzzy Decision-Theoretic Rough Set Approach for Type-2 Fuzzy Conditional Information Systems and Its Application in Decision-Making

Multi-granulation interval-valued fuzzy probabilistic rough sets and their corresponding three-way decisions based on interval-valued fuzzy preference relations

In this paper, we study interval-valued fuzzy probabilistic rough sets (IVF-PRSs) based on multiple interval-valued fuzzy preference relations (IVFPRs) and consistency matrices, i.e., the multi-granulation interval-valued fuzzy preference relation probabilistic rough sets (MG-IVFPR-PRSs). First, in the proposed study, we convert IVFPRs into fuzzy preference relations (FPRs), and then construct the consistency matrix, the collective consistency matrix, the weighted collective preference relations, and the group collective preference relation (GCPR). Using this GCPR, four types of MG-IVFPR-PRSs are founded in terms of different constraints on parameter. Finally, to find a suitable way of explaining and determining these parameters in each model, three-way decisions are studied based on Bayesian minimum-risk procedure, i.e., the multi-granulation interval-valued fuzzy preference relation decision-theoretic rough set approach. An example is included to show the feasibility and potential of the theoretic results obtained.

Decision-theoretic rough set approach for fuzzy decisions based on fuzzy probability measure and decision making

Most existing studies on decision-theoretic rough set approach focus on crisp decisions. However, in many cases, we need to handle fuzzy concepts. This paper investigates decision-theoretic rough set approach for fuzzy decisions. By introducing fuzzy operators, we extend the traditional decision-theoretic rough set approach with crisp decisions to fuzzy concepts. Decision-theoretic rough set approach with fuzzy concepts is investigated based on fuzzy probabilistic approxi- mation space. Bayesian decision procedure based on fuzzy probabilistic approximation space with fuzzy concepts and fuzzy probabilistic decision systems with fuzzy or continuous decision attributes are studied. The application of the proposed approach in decision making is also illustrated by an example. This study may expand the applications of decision-theoretic rough set model.

Matrix approach to decision-theoretic rough sets for evolving data

Decision-theoretic rough sets is a generalized probabilistic model for the expression of uncertainties and the representation of knowledge from data. It provides a semantic explanation and systematically computation of probabilistic thresholds to define probabilistic rough set approximations, which offers a ternary classification framework based on Bayesian decision theory. In practice, data for decision making process resides in a dynamic database whose data is typically evolving through the periodical or occasional updating, e.g., new data are appended and obsolete data are removed. It is impractical to have a maturity decision model, stalled until the preparation of all helpful training data. To address this issue, incremental learning appeared to be a feasible solution for continuous knowledge modeling from evolving data with the incorporation of unlearned knowledge embedded in the updating data. In this paper, we exploit matrix approaches to study incremental decision-theoretic rough set approach for evolving data. Starting from the representation of object subset and indiscernibility relation in matrix form, we obtain a matrix characterization of probabilistic rough set approximations in decision-theoretic rough sets by using matrix properties associated with the multiplication operator. We also develop incremental algorithms for updating probabilistic rough set approximations with respect to the addition/deletion of objects, which enables decision theoretic rough sets to deal gracefully with evolving data. A detailed experimental study is conducted to examine the performance of the proposed incremental algorithms on UCI data sets.

A Decision-Theoretic Rough Set Approach for Dynamic Data Mining

Uncertainty and fuzziness generally exist in real-life data. Approximations are employed to describe the uncertain information approximately in rough set theory. Certain and uncertain rules are induced directly from different regions partitioned by approximations. Approximation can further be applied to data-mining-related task, $\hbox{e.g.}$ , attribute reduction. Nowadays, different types of data collected from different applications evolve with time, especially new attributes may appear while new objects are added. This paper presents an approach for dynamic maintenance of approximations $\hbox{w.r.t.}$ objects and attributes added simultaneously under the framework of decision-theoretic rough set (DTRS). Equivalence feature vector and matrix are defined first to update approximations of DTRS in different levels of granularity. Then, the information system is decomposed into subspaces, and the equivalence feature matrix is updated in different subspaces incrementally. Finally, the approximations of DTRS are renewed during the process of updating the equivalence feature matrix. Extensive experimental results verify the effectiveness of the proposed methods.

Fuzzy probabilistic rough sets and their corresponding three-way decisions

The concept of probabilistic rough sets, as a main subject of this paper, is intimately connected with the concept of decision-theoretic rough sets. This paper investigates fuzzy and interval-valued fuzzy probabilistic rough sets within frameworks of fuzzy and interval-valued fuzzy probabilistic approximation spaces, respectively. Four types of fuzzy probabilistic rough sets as well as interval-valued fuzzy probabilistic rough sets are established in terms of different constraints on parameters. To find a suitable way of explaining and determining these parameters in each model, three-way decisions are studied based on Bayesian minimum risk decision procedure, i.e., the decision-theoretic rough set approach. The proposed models in this paper broaden applications of probabilistic rough sets due to their abilities of directly dealing with real-valued and interval-valued data.

Multigranulation Decision-theoretic Rough Set in Ordered Information System

The decision-theoretic rough set model based on Bayesian decision theory is a main development tendency in the research of rough sets. To extend the theory of decision-theoretic rough set, the article devotes this study to presenting multigranulation decision-theoretic rough set model in ordered information systems. This new multigranulation decision-theoretic rough set approach is characterized by introducing the basic set assignment function in an ordered information system. It is addressed about how to construct probabilistic rough set and multigranulation decision-theoretic rough set models in an ordered information system. Moreover, three kinds of multigranulation decision-theoretic rough set model are analyzed carefully in an ordered information system. In order to explain probabilistic rough set model and multigranulation decision-theoretic rough set models in an ordered information system, an illustrative example is considered, which is helpful for applying these theories to deal with practical issues.

Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on fuzzy probability measure

This paper investigates decision-theoretic rough set (DTRS) approach in the frameworks of fuzzy and interval-valued fuzzy (IVF) probabilistic approximation spaces, respectively. It takes fuzzy probability and IVF probability into consideration. Bayesian decision procedure is a basis of DTRS approach. By integrating fuzzy probability measure and IVF probability measure into Bayesian decision procedure, there come fuzzy decision-theoretic rough set (FDTRS) approach and interval-valued fuzzy decision-theoretic rough set (IVF-DTRS) approach. The new approaches have the ability to directly deal with real-valued and interval-valued data. This makes FDTRS and IVF-DTRS more applicable than DTRS. Two methods are presented to compare intervals while constructing the IVF-DTRS approach: one is compatible with DTRS and FDTRS approaches; the other is a total order based on which the decision procedure is much easier to operate. Cases of two different universes of discourse for FDTRS and IVF-DTRS are also taken into account.