Incomplete Information Systems Research Articles

Three-way multi-attribute decision making under incomplete mixed environments using probabilistic similarity

In recent years, many scholars have explored a variety of methods integrating three-way decision (3WD) and multi-attribute decision making (MADM), which enables the classification and priority ranking of alternatives possible and fully reflects the effectiveness and advantages of 3WD in solving MADM problems. However, few of these methods can effectively deal with the MADM problems with incomplete mixed information that are frequently encountered in real-world situations. This study proposes a three-way MADM method for an incomplete mixed information system (IMIS), where the objective determination of conditional probabilities and utility functions in IMIS without decision label is the pivotal issue. To overcome this issue, we define a probabilistic similarity measure for incomplete mixed information. The probabilistic similarity measure is used to replace the distance measure of classical TOPSIS for estimating the conditional probabilities objectively. The probabilistic similarity class is introduced with arithmetic average method to design a conversion mechanism and obtain the objective relative utility functions of incomplete evaluation values. We then construct a novel 3WD model in IMIS and combine it with two customized ranking principles, to solve the incomplete mixed MADM problems from the perspective of classification and ranking in a more thoughtful and interpretable manner. Our study provides a new perspective for the research on MADM in incomplete mixed information environment. Several examples and experimental comparisons verify the effectiveness and stability of the proposed method. The experiments demonstrate that our method can meet more decision-making requirements and is more accurate and rational in some decision-making scenarios than several prior similar methods.

A regret-theory-based three-way decision method with a priori probability tolerance dominance relation in fuzzy incomplete information systems

In real world, decision-makers’ regret psychology often affects decision outcomes due to uncertain risks. Moreover, decision information may be missing in the process of data acquisitions or data storages. Three-way decision has been widely explored in the risky decision-making area by providing effective strategies to divide objects into three mutually disjoint regions. Existing three-way decision methods in fuzzy incomplete information systems rarely consider the influence of decision-makers’ psychological states on decision outcomes. In the current paper, we primarily study a new decision-making method that combines regret theory with three-way decision in fuzzy incomplete information systems. First, a prior probability tolerance dominance relation in a fuzzy incomplete information system is defined to handle a binary relation among evaluation values, and a method to calculate objective weights is designed as well. When an incomplete information system does not contain a fuzzy decision attribute value, we put forward a new method to calculate the decision attribute value of each object in the incomplete information system. Then, integrated utility perception values are obtained by combining with regret theory. Further, a regret theory-based three-way decision method with a priori probability tolerance dominance relation is proposed for fuzzy incomplete information systems. At last, the stability and validity of the presented method are verified via corresponding experimental and comparative analysis of realistic cases.

Regret-based three-way decision making with possibility dominance and SPA theory in incomplete information system

In the field of decision making, three-way decision making has been proven more fruitful for providing scopes to make delayed decision along with acceptance and rejection simultaneously. As a result, the decision risk and loss, which could occur due to take rapid decisions in traditional two-way decision making, are effectively reduced. Accordingly, this paper offers a novel three-way multi-attribute decision making model by combining three-way decision making and multi-attribute decision making under an incomplete information system. The incertitude in the information system is illustrated by introducing interval-valued Fermatean connection number based on interval-valued Fermatean fuzzy number and set pair analysis theory. Thereafter, the achievement of this study is five-fold. First, a possibility dominance relation is developed under incomplete information system in the basis of possibility degree measure of interval-valued Fermatean connection number. Second, we put forward a novel procedure to set up the fuzzy state set. Third, the conditional probability is estimated in light of the fuzzy state set and probability dominance relation. Fourth, the relative utility functions are determined in the virtue of regret theory. Lastly, a three-way multi-attribute decision making model is implemented in incomplete information system and exploited to deal with incomplete multi-attribute decision making problems. Eventually, the propriety, stability and superiority of the proposed model is established via conducting the comparative and experimental analysis.

A three-way decision approach with a probability dominance relation based on prospect theory for incomplete information systems

The processing scheme of typical incomplete information systems has been widely explored nowadays, however most of these approaches may change the original data information and can not guarantee the integrity of original information systems. Meanwhile, psychological behaviors of decision makers usually have an influence on the decision-making results. In light of these facts, the paper explores a new three-way decision approach by using prospect theory for an incomplete information system, which handles the default information of an incomplete information system by virtue of a probability dominance relation. First, a probability dominance relation of an incomplete information system is defined to process a binary relation between evaluation values, and the way for calculating the relative value function in the behavior decision-making process is also given. Moreover, the conditional probability with a decision attribute in an incomplete decision information system is put forward, and an objective weight function via prospect theory is further obtained. On this basis, a prospect-theory-based three-way decision approach with a probability dominance relation for an incomplete information system is proposed. Finally, the stability, effectiveness and superiority of the presented approach are validated via corresponding experimental studies and comparative analysis with two realistic cases.

Analyzing the Effectiveness of Finance in Supply Chain in Solving the Financing Difficulties of SMEs Based on Grey Theory Model.

Small and medium-sized enterprises (SMEs) play an indispensable role in China's national economic system, and they can play a critical role in promoting economic growth and full employment. The main reason for the disruption and impediment to the development of SME clusters is that the enterprises in the clusters are experiencing a “capital shortage,” as a result of the double contradiction between the clusters' financial benefits and the difficulties in financing. Grey theory is a relatively new concept in the field of information processing. It proposes theories and methods for processing and analyzing incomplete information systems using mathematical methods. This study uses finance in supply chain as a new research perspective to investigate the effectiveness of finance in supply chain in resolving SMEs' financing problems using the Grey theory model, with the goal of resolving SMEs' financing problems. When comparing the results of the Grey theory model and the regression analysis model, the relative error of the Grey theory model is on average 12.2% lower than that of the regression analysis model, indicating that the Grey theory model greatly improves accuracy. As a result, using the Grey theory model to solve supply chain financing and SMEs' difficulties can share risks, share credit, reduce transaction costs, weaken information asymmetry, and achieve mutual benefits and a win-win situation. It is expected to promote the development of the finance in supply chain model, mobilise enterprise enthusiasm for using finance in supply chain, improve finance in supply chain operational efficiency, and promote finance in supply chain development.

A ranking method with a preference relation based on the PROMETHEE method in incomplete multi-scale information systems

Multi-scale information systems (MSISs) contain more comprehensive evaluations with different scales than general single-scale counterparts, thus multi-criteria decision-making (MCDM) problems from MSISs are in line with practical scenarios. However, the loss problem of information encountered in decision-making processes brings certain troubles to MCDM. Due to this limitation, a ranking method based on a preference relation in incomplete multi-scale information systems (IMSISs) is proposed in this article. The core idea of the preference ranking organization method for enrichment evaluation II (PROMETHEE II method) is first introduced into IMSISs and a process on dealing with incomplete information in an IMSIS is developed. Then, a corresponding MCDM method is constructed into IMSISs. Finally, a numerical example with different parameters is employed to verify the usefulness of the constructed method, and a comparative study of the constructed method with other MCDM methods is explored to demonstrate the effectiveness of the newly presented method.

Uncertainty Optimization-Based Rough Set for Incomplete Information Systems

Often the information in the surrounding world is incomplete, and such incomplete information gives rise to uncertainties. Pawlak's rough set model is an approach to approximation under uncertainty. It uses a tolerance relation to obtain single granulation of the incomplete information system for approximation. In this work, we extend the single granulation rough set for the incomplete information system to an uncertainty optimization-based rough set (UOBRS). The proposed approach is used to minimize the uncertainty using multiple tolerance relations. We list properties of the UOBRS for incomplete information systems. We compare UOBRS with the classical single granulation rough set (SGRS) and multi-granular rough set (MGRS). We list the basic properties of the UOBMGRS. We introduce the application of the UOBRS for attribute subset selection in case of incomplete information system. We use the measure of approximation quality to assess the uncertainties of the attributes. We compare the approximation quality of the attributes using UOBRS with the approximation quality using SGRS and MGRS. We get higher approximation quality with the less number of attributes using UOBRS as compared to SGRS and MGRS. The proposed method is a novel approach to dealing with incomplete information systems for more effective dataset analysis.

Three-Way Group Decisions with Incomplete Spherical Fuzzy Information for Treating Parkinson’s Disease Using IoMT Devices

As Internet of Things (IoT) is extensively employed in diverse realistic areas, it is vital to effectively and timely analyze the data collected by IoT devices. To cope with this problem, by integrating adjustable MG SF probabilistic rough sets (PRSs) with the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method, this paper explores a three-way multi-attribute group decision-making (MAGDM) approach in the context of multigranulation (MG) spherical fuzzy (SF) incomplete information systems (IISs) and further applies the presented method to the analysis of leg muscle data obtained from Internet of Medical Things (IoMT) devices for Parkinson’s patients. First, the concept of MG SF IISs is established, and the completion method is provided. Then, adjustable MG SF PRSs are proposed for information fusion. Afterwards, considering the bounded rationality of decision-makers (DMs), a new three-way MAGDM method is designed by fusing adjustable MG SF PRSs with the TODIM method. Finally, in the context of IoMT-based detecting abnormal knee joints in Parkinson’s patients, the applicability and validity of the presented method are eventually verified.

Dynamic information fusion in multi-source incomplete interval-valued information system with variation of information sources and attributes

Interval-valued data describe the random phenomenon that abounds in the real world, a pivotal research orientation in uncertainty processing. With the rapid development of big data, we may gather information from multiple information sources. To effectively acquire knowledge from multiple information sources, information fusion is commonly used to get a unified representation. However, sometimes data gathered from multiple sources may be lost; it is meaningful and necessary to study the fusion of multi-source incomplete interval-valued data. We propose a novel information fusion method based on information entropy for multi-source incomplete interval-valued data and four incremental fusion mechanisms characterized by the change in information sources and attributes. The corresponding static and dynamic fusion algorithms are designed, and their time complexities are analyzed. Experimental results show that the proposed method outperforms the mean, max, and min fusion methods. Furthermore, the four incremental fusion mechanisms reduced the runtime compared with the static fusion mechanism.

Information entropy based attribute reduction for incomplete heterogeneous data

Attribute reduction in an information system (IS) is an important research topic in rough set theory (RST). This paper investigates attribute reduction for incomplete heterogeneous data based on information entropy. Information entropy in an incomplete IS with heterogeneous data (IISH) is first defined. Then, some derived notions of information entropy, such as joint information entropy, conditional information entropy, mutual information entropy, gain and gain ratio in an incomplete decision IS with heterogeneous data (IDISH), are presented. Next, information entropy is applied to perform attribute reduction in an IDISH. Two attribute reduction algorithms, based on gain and gain ratio, respectively, are proposed. Finally, in order to illustrate the feasibility and efficiency of the proposed algorithms, experimental analysis is carried out and comparisons are done. It is worth mentioning that the incomplete rate is used to deal with incomplete heterogeneous data.

Incomplete three-way multi-attribute group decision making based on adjustable multigranulation Pythagorean fuzzy probabilistic rough sets

Different from the traditional two-way decision paradigm, three-way decisions (3WD) have been extensively explored in addressing realistic multi-attribute decision making (MADM) by virtue of its powerful performances in minimizing decision risks with the added non-commitment option. Since existing 3WD models can not efficiently handle MADM issues in the group setting with incomplete high-order fuzzy information systems (ISs), the current paper focuses on exploring viable three-way multi-attribute group decision making (MAGDM) methods in light of the multi-granularity 3WD paradigm under incomplete Pythagorean fuzzy (PF) environments. First, the notion of Multigranulation (MG) incomplete PF ISs is constructed. Then, optimistic, pessimistic and adjustable MG PF probabilistic rough sets (PRSs) are proposed after patching lost values. Afterwards, the decision-making-driven 3WD method is extended via adjustable MG PF PRSs, and an improved technique for order preference by similarity to ideal solution (TOPSIS) method with entropy weights is utilized for optimal granularity selections. According to adjustable MG PF PRSs and the improved TOPSIS method, a new three-way MAGDM method is eventually established. At last, two case studies are investigated in the background of mine ventilator fault diagnosis (MVFD) and air quality evaluations (AQE), and several comparative experiments and sensitivity analysis are performed for presenting the effectiveness of the constructed theoretical methodology.

Multi‐granularity decision rough set attribute reduction algorithm under quantum particle swarm optimization

The existing attribute reductions are carried out using equivalence relations under a complete information system, and there is less research on attribute reductions of incomplete information systems with new theoretical models such as multi-granularity decision rough sets. To address the above shortcomings, this paper first makes up a pessimistic-optimistic multi-granularity decision rough set model based on tolerance relations in incomplete information systems. The concepts of attribute importance and approximate distribution quality are introduced into the model to form an attribute reduction algorithm under incomplete information systems. Secondly, due to the NP-hard problem of attribute reduction, in order to further ensure the accuracy of the reduction result, this paper proposes a pessimistic-optimistic multi-granularity reduction algorithm under quantum particle swarm optimization. Experimental results on multiple-attribute data proved that the algorithm proposed in this paper can effectively attribute reduction in the decision table with missing data. At the same time, the algorithm of this paper has the role of iterative optimization search, ensuring the accuracy of the reduction results and increasing the applicability of multi-granularity decision rough sets.

Generalized neighborhood systems-based pessimistic rough sets and their applications in incomplete information systems

In this paper, we point out that Lin’s general neighborhood systems-based rough set model is an extension of Qian’s optimistic rough set model, and thus called optimistic general neighborhood systmes-based rough set model. Then we present a new rough set model based on general neighborhood systems, and prove that it is an extension of Qian’s pessimistic rough set model. Later, we study the basic properties of the proposed pessimistic rough sets, and define the serial, reflexive, symmetric, transitive and Euclidean conditions for general neighborhood systems, and explore the further properties of related rough sets. Furthermore, we apply the pessimistic general neighborhood systems-based rough set model in the research of incomplete information system, and build a three-way decision model based on it. A simple practical example to show the effectiveness of our model is also presented.

Multiple attribute group decision making based on multigranulation probabilistic models, MULTIMOORA and TPOP in incomplete q-rung orthopair fuzzy information systems

The concept of q-rung orthopair fuzzy sets (q-ROFSs) severs as an extended form of orthopair fuzzy sets, which excels in flexibly depicting imprecise information existed in multiple attribute group decision making (MAGDM) via allowing a greater space in terms of membership degrees (MD) and non-membership degrees (ND). Moreover, incomplete information systems play a significant role in depicting incomplete information existed in MAGDM. In this paper, for the sake of exploring MAGDM with imprecise and incomplete information, a new MAGDM method based on multigranulation probabilistic models, MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) and the technique of precise order preference (TPOP) method in incomplete q-rung orthopair fuzzy (q-ROF) information systems is systematically investigated. First, the concept of multigranulation (MG) incomplete q-ROF information systems is established. Then, a completion technique is put forward to obtain MG q-ROF information systems via patching lost values. Moreover, three versions of MG q-ROF probabilistic rough sets (PRSs) are put forward in light of MG q-ROF information systems. Afterwards, a new MAGDM method is constructed by means of MG q-ROF PRSs, MULTIMOORA and the TPOP method. At last, two experimental studies from open datasets are performed to present the applicability of the constructed MAGDM method, and corresponding sensitivity analysis and comparative analysis are further conducted to demonstrate the validity of the presented methodology.

Attribute reduction in an incomplete categorical decision information system based on fuzzy rough sets

Attribute reduction in an incomplete categorical decision information system based on fuzzy rough sets

A Creative Approach on Bipolar Neutrosophic Nano Topology

In this article, Bipolar neutrosophic nano topology is introduced and some of its properties are studied. We found that, it is difficult to find a nano topology for every bipolar neutrosophic set. So we introduced a bipolar neutrosophic nano topology, which is a generalization of bipolar neutrosophic nano topology and its fundamental features are investigated with appropriate examples. This approach is used for real life multi criteria decision making situations. The practical problems may be solved by finding CORE values through the criterion reduction.One can apply the basis of the bipolar neutrosophic nano topology as the key factors of a particular decision making problem using topological reduction of attributes in complete or incomplete information system.

Information Entropy-Based Attribute Reduction for Incomplete Set-Valued Data

This paper investigates attribute reduction for incomplete set-valued data based on information entropy. The similarity degree between information values on a conditional attribute of an incomplete set-valued decision information system (ISVDIS) is first proposed. Then, the tolerance relation on the object set with respect to a conditional attribute subset in an ISVDIS is obtained. Next, <inline-formula> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula>-reduction in an ISVDIS is presented. What&#x2019;s more, connections between the proposed attribute reduction and uncertainty measurement are exhibited. Furthermore, an attribute reduction algorithm based on <inline-formula> <tex-math notation="LaTeX">$\lambda $ </tex-math></inline-formula>-information entropy in an ISVDIS is provided. Finally, experiments to evaluate the performance of the proposed algorithm are carried out, and Friedman test and Nemenyi test in statistics are conducted. The experimental results indicate that the proposed algorithm is more effective for an ISVDIS than some existing algorithms.

A novel intuitionistic fuzzy three-way decision model based on an intuitionistic fuzzy incomplete information system

A novel intuitionistic fuzzy three-way decision model based on an intuitionistic fuzzy incomplete information system

Attribute significance based on inclusion degree for incomplete information systems and their applications to MADM problems

Attribute significance is very important in multiple-attribute decision-making (MADM) problems. In a MADM problem, the significance of attributes is often different. In order to overcome the shortcoming that attribute significance is usually given artificially. The purpose of this paper is to give attribute significance computation formulas based on inclusion degree. We note that in the real-world application, there is a lot of incomplete information due to the error of data measurement, the limitation of data understanding and data acquisition, etc. Firstly, we give a general description and the definition of incomplete information systems. We then establish the tolerance relation for incomplete linguistic information system, with the tolerance classes and inclusion degree, significance of attribute is proposed and the corresponding computation formula is obtained. Subsequently, for incomplete fuzzy information system and incomplete interval-valued fuzzy information system, the dominance relation and interval dominance relation is established, respectively. And the dominance class and interval dominance class of an element are got as well. With the help of inclusion degree, the computation formulas of attribute significance for incomplete fuzzy information system and incomplete interval-valued fuzzy information system are also obtained. At the same time, results show that the reduction of attribute set can be obtained by computing the significance of attributes in these incomplete information systems. Finally, as the applications of attribute significance, the attribute significance is viewed as attribute weights to solve MADM problems and the corresponding TOPSIS methods for three incomplete information systems are proposed. The numerical examples are also employed to illustrate the feasibility and effectiveness of the proposed approaches.

Feature selection for incomplete set-valued data

Set-valued data is a significant kind of data, such as data obtained from different search engines, market data, patients’ symptoms and behaviours. An information system (IS) based on incomplete set-valued data is called an incomplete set-valued information system (ISVIS), which generalized model of a single-valued incomplete information system. This paper gives feature selection for an ISVIS by means of uncertainty measurement. Firstly, the similarity degree between two information values on a given feature of an ISVIS is proposed. Then, the tolerance relation on the object set with respect to a given feature subset in an ISVIS is obtained. Next, λ-reduction in an ISVIS is presented. What’s more, connections between the proposed feature selection and uncertainty measurement are exhibited. Lastly, feature selection algorithms based on λ-discernibility matrix, λ-information granulation, λ-information entropy and λ-significance in an ISVIS are provided. In order to better prove the practical significance of the provided algorithms, a numerical experiment is carried out, and experiment results show the number of features and average size of features by each feature selection algorithm.