Intuitionistic Fuzzy Information Systems Research Articles

Attribute reduction based on intuitionistic fuzzy dominance mutual information in intuitionistic fuzzy information systems

Intuitionistic fuzzy information system (IFIS) is an extension of fuzzy information system that can represent more uncertain information and more accurately describe the essence of fuzziness. Attribute reduction is an important problem in processing and analyzing IFISs. The article tries to propose an attribute reduction method in view of intuitionistic fuzzy dominance mutual information in IFISs, whose information values are intuitionistic fuzzy numbers. First, an intuitionistic fuzzy dominance relation is established in IFISs according to intuitionistic fuzzy dominance degrees, and the intuitionistic fuzzy information structure generated by the intuitionistic fuzzy dominance relation is constructed. Then, the intuitionistic fuzzy dominance entropy and its variations are researched, and some of their properties are discussed. Subsequently, an attribute reduction method and its algorithm based on intuitionistic fuzzy dominance mutual information are given. Furthermore, numerical studies and statistical tests are presented to evaluate the performance of the proposed method. Theoretical research and experiments show that the raised attribute reduction method is applicable to IFISs.

Exploring static rebalancing strategies for dockless bicycle sharing systems based on multi-granularity behavioral decision-making

In the continuously evolving context of urbanization, more people flock to cities for job opportunities and an improved quality of life, resulting in undeniable pressure on transportation networks. This leads to severe daily commuting challenges for residents. To mitigate this urban traffic pressure, most cities have adopted urban dockless bicycle sharing systems (UDBSS) as an effective measure. However, making accurate decisions regarding UDBSS demand in different city locations is crucial, as incorrect choices can worsen transportation problems, causing difficulties in finding bicycles or excessive deployments leading to disorderly accumulation. To address this decision-making challenge, it is essential to consider uncertain factors like daily weather, temperature, and workdays. To tackle this effectively, we construct an adjustable multi-granularity (MG) complex intuitionistic fuzzy (CIF) information system using complex intuitionistic fuzzy sets (CIFSs). This system objectively determines classification thresholds using an evaluation-based three-way decision (TWD) method, creating adjustable MG CIF probability rough sets (PRSs). Additionally, to recognize the irrationality of decision-makers (DMs), we propose a method that combines prospect theory (PT) with regret theory (RT), providing a more comprehensive understanding of the influence of DMs' psychological factors on decision outcomes. Building upon these foundations, we present static rebalancing strategies for UDBSS based on MG PRSs and prospect-regret theory (P-RT) within the CIF information system. Finally, using UDBSS data collected from various sensors, we conduct experimental analysis to verify its feasibility and stability. In summary, this approach considers residents’ daily usage preferences, including bicycles utilization and return, with the aim of minimizing unmet resident demands and predicting usage patterns for the next day. It effectively addresses the issue of UDBSS distribution inefficiencies and holds a significant advantage in prediction, making it suitable for broader applications in transportation systems and contributing to the establishment of more advanced modern intelligent transportation systems (MITSs) in the future.

Incremental updating fuzzy tolerance rough set approach in intuitionistic fuzzy information systems with fuzzy decision

As information technology develops rapidly and data is constantly updated, efficient mining knowledge from dynamic intuitionistic fuzzy information systems with fuzzy decision (IFFD) is a significant topic. In the dynamic data environment, the corresponding IFFD is always changing with time when object sets of datasets may evolve in time. Fuzzy tolerance rough set (FTRS), as one of extended rough set models, has a strong capacity for the expression of information and better representation of uncertainty. Therefore, it is very effective and necessary to use FTRS to acquire valuable knowledge from dynamic IFFD. In this paper, we investigate the dynamic fuzzy tolerance rough set approach for IFFD. Firstly, a new fuzzy tolerance similarity is defined to describe fuzzy tolerance relation between objects in the IFFD. Second, we construct a fuzzy tolerance rough set model in the IFFD, discuss some properties, and propose the corresponding static algorithm. Subsequently, incremental approaches which update fuzzy tolerance rough approximations with the insertion and deletion of objects in the IFFD are investigated and the corresponding dynamic algorithms are also designed. Finally, the feasibility of the FTRS model and the effectiveness and efficiency of the dynamic algorithm in dynamic environments are validated through a series of comparative experiments on nine datasets.

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.

Ranking Method of Intuitionistic Fuzzy Numbers and Multiple Attribute Decision Making Based on the Probabilistic Dominance Relationship

The uncertainty of intuitionistic fuzzy numbers (IFNs) is further enhanced by the existence of the degree of hesitation (DH). The shortcomings of existing researches are mainly reflected in the following situations: when comparing IFNs, the comparison rules of IFNs are difficult to apply to the comparison of any two IFNs, or the relevant methods do not fully consider the uncertainty expressed by DH. Thus, the rationality of the decision results needs to be improved. On the other hand, multi-attribute decision making (DADM) based on IFNs is often not objective due to the need to determine the attribute weight. Moreover, the strict condition of attribute aggregation of classical dominance relation makes it a method that fails considering the practical application. Aiming at the comparison problem of IFNs, this paper takes probability conversion as the starting point and proposes an IFN comparison method based on the area method, which can better deal with the comparison problem of “either superior or inferior” IFNs. In addition, aiming at the MADM problem of an intuitionistic fuzzy information system, we propose an intuitionistic fuzzy probabilistic dominance relation model and construct the MADM method under the probabilistic dominance relation. The series properties of IFNs and probabilistic dominance relation were summarized and proved, which theoretically ensured the scientificity and rigor of the method. The results show that the comparison and ranking method of IFNs proposed in this paper can be applied to the comparison of any two IFNs, and the dominance degree of IFNs is presented in the form of probability, which is more flexible and practical than the classical method. The probabilistic dominance relation method based on IFNs avoids the problem of determining attribute weights subjectively or objectively, and the decision maker can reflect decision preference by adjusting decision parameters to better match the actual problem. The application of this model to a campus express site evaluation further verifies the feasibility of the proposed method and the rationality of the results. In addition, various extension problems of the model and method proposed in this paper are discussed, which pave the way for future related research. This paper constructs a complete decision-making framework through theoretical analysis and application from practical problems, which provides a reference for enriching and improving uncertain decision-making theory and the MADM method.

Incomplete intuitionistic fuzzy behavioral group decision-making based on multigranulation probabilistic rough sets and MULTIMOORA for water quality inspection

Water quality inspection (WQI) is one of the primary ways to ensure the safe utilization of water resources, and complicated data modeling, fusion and analysis play a significant role in seeking the resource with the best water quality. Nevertheless, the challenges of missing data, relatively large differences in decision results and bounded rationality owned by decision-makers (DMs) in terms of WQI still exist nowadays. Thus, from the aspect of stable and behavioral decision-making in multi-granularity incomplete intuitionistic fuzzy information systems (MG-IIFISs), the paper investigates a comprehensive multi-attribute group decision-making (MAGDM) approach for the application of WQI. First, the concept of MG-IIFISs is built by modeling MAGDM problems with intuitionistic fuzzy numbers (IFNs), then a new transformation scheme is constructed for transforming MG-IIFISs into multi-granularity intuitionistic fuzzy information systems (MG-IFISs) based on the similarity principle. Second, three types of multigranulation intuitionistic fuzzy probabilistic rough sets (MG IF PRSs) are developed by referring to the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. Afterwards, attribute weights are objectively calculated based on the best-worst method (BWM), and a new stable and behavioral MAGDM approach is constructed by means of the TODIM (an acronym in Portuguese for interactive multi-criteria decision-making) method. At last, a case study in the setting of WQI is conducted with the support of a UCI data set, and sensitivity analysis, comparative analysis and experimental analysis are investigated to display the validity of the proposed approach. In general, the proposed approach improves the stability of decision results via MULTIMOORA and BWM, and also fully considers the bounded rationality of DMs’ psychological behaviors from the aspect of the TODIM method, which has certain advantages in the community of MAGDM studies.

Multigranulation-Based Granularity Selection for Intuitionistic Fuzzy Weighted Neighborhood IoT Data

Granular computing is to represent, construct, and process information granules formalized in many different approaches, and different formal approaches emphasize the same fundamental facet in different ways. In this paper, we present the multigranulation rough set models in the intuitionistic fuzzy neighborhood information system generated by Internet of Things (IoT) data with weighted features and develop the basic properties of the proposed models. Moreover, the multigranulation-based optimal granularity selection approach is established by introducing the concept of granularity significance. The experimental results on eight IoT datasets demonstrate that the proposed methods exhibit better efficiency by comparing three classical methods under the intuitionistic fuzzy weighted neighborhood information system.

Attribute reduction in intuitionistic fuzzy formal concepts

Knowledge acquisition in intuitionistic fuzzy information systems is of importance because those fuzzy information systems are often encountered in many real-life problems. Formal concept analysis is a simple and effective tool for knowledge acquisition. However, there is still little work on introducing knowledge acquisition methods based on formal concept analysis into intuitionistic fuzzy information systems. This paper mainly extends the formal concept theory into intuitionistic fuzzy information systems. Firstly, two pairs of adjoint mappings are defined in intuitionistic fuzzy formal contexts. It is verified that both pairs of adjoint mappings form Galois connections. Secondly, two types of intuitionistic fuzzy concept lattices are constructed. After that, we also present the main theorems and propositions of the intuitionistic fuzzy concept lattices. Thirdly, we deeply discuss the attribute characteristics for type-1 generalized one-sided intuitionistic fuzzy concept lattice. Furthermore, a discernibility matrix-based algorithm is proposed for attribute reduction and the effectiveness of this algorithm is demonstrated by a practical example. The construction of intuitionistic fuzzy conceptS is meaningful for the complex and fuzzy information in real life.

Analysis and Applications of Bonferroni Mean Operators and TOPSIS Method in Complete Cubic Intuitionistic Complex Fuzzy Information Systems

This article manages vagueness, asymmetric data, and risk demonstrated in awkward information. The ambiguity is handled with the help of possibility and strategic decision-making theory. A MADM (multi-attribute decision-making) tool, the sub-part of the strategic decision theory, plays an important role in the circumstances of fuzzy data. The major influence of this analysis is to initiate the mathematical ideology of cubic intuitionistic complex fuzzy (CICF) information and its well-known properties such as algebraic laws, score values, and accuracy values. It is also to determine various inequalities for finding the relation between any two CICF numbers (CICFNs). Further, we know that the Bonferroni mean (BM) operator is more generalized than the simple averaging/geometric aggregation operators due to parameters involved in the mathematical form of BM operators. Keeping the supremacy and consistency of BM operators, the idea of CICF Bonferroni mean (CICFBM) and CICF weighted BM (CICFWBM) operators are diagnosed. We try to describe their well-known results and properties such as idempotency, monotonicity, commutativity, and boundedness with various specific cases. Further, we investigate three different sorts of decision-making procedures such as MADM tool, TOPSIS (Technique for order of preference by similarity to ideal solution) method using similarity measures, and TOPSIS method using aggregation operators to enhance the quality of the decision-making process. This analysis expressed how to make decisions when there is asymmetric data about companies. Finally, we compute the comparative analysis of the diagnostic approaches with various existing theories to demonstrate the feasibility and flexibility of the exposed work to try to illustrate with the help of geometrical expressions.

Uncertainty Measure for Multisource Intuitionistic Fuzzy Information System

Multisource information systems and multigranulation intuitionistic fuzzy rough sets are important extended types of Pawlak’s classical rough set model. Multigranulation intuitionistic fuzzy rough sets have been investigated in depth in recent years. However, few studies have considered this combination of multisource information systems and intuitionistic fuzzy rough sets. In this paper, we give the uncertainty measure for multisource intuitionistic fuzzy information system. Against the background of multisource intuitionistic fuzzy information system, each information source is regarded as a granularity level. Considering the different importance of information sources, we assign different weights to them. Firstly, the paper proposes an optimal source selection method. Secondly, we study the weighted generalized, weighted optimistic, and weighted pessimistic multigranularity intuitionistic fuzzy rough set models and uncertainty measurement methods in the multisource intuitionistic fuzzy information system, and we further study the relationship between the three models and related properties. Finally, an example is given to verify the validity of the models and methods.

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

A three-way decision approach with probabilistic dominance relations under intuitionistic fuzzy information

As a complicated cognitive process, multi-attribute decision-making usually focuses on the decision-making issue of seeking the optimal alternative or ranking alternatives under the framework of multiple attributes. The three-way decision approach with the delayed decision can more effectively reduce decision risks than traditional two-way counterparts for multi-attribute decision-making. In this article, we aim to put forward a novel three-way multi-attribute decision-making model in light of a probabilistic dominance relation with intuitionistic fuzzy sets. First, we investigate the three-way multi-attribute decision-making in light of a probabilistic dominance relation in an intuitionistic fuzzy information system. Second, we derive the conditional probability of the intuitionistic fuzzy set. Third, we evaluate the part supplier selection via the constructed model. At last, for the sake of showing the validity and applicability of the constructed three-way intuitionistic fuzzy multi-attribute decision-making model, we further perform extensive comparative analysis along with experimental analysis from diverse perspectives.

Classification Rule Mining Algorithm Combining Intuitionistic Fuzzy Rough Sets and Genetic Algorithm

This paper has proposed a classification rule base mining algorithm combining the genetic algorithm and intuitionistic fuzzy-rough set for large-scale intuitionistic fuzzy information system. The algorithm has proposed innovatively the definitions and measurement metrics of completeness, interaction and compatibility describing the whole rule base, and constructed a multi-objective optimization model to optimize the population size of data sample, and used the intuitionistic fuzzy-rough set to reduce the attribute set of fuzzy information system, and used intuitionistic fuzzy similar class to extract large-scale intuitionistic fuzzy information system rules, and obtained an optimal rule base with the minimal size, configuration, generation time and storage space. A threshold control mechanism is used to evaluate the completeness, interaction and correlation of rule population and improves the robustness and flexibility of sample population optimization and rule base generation. The algorithm is verified by the real aircraft health data sets. The algorithm is validated by similar mature and effective algorithms in accuracy, time complexity using real data and has good robustness and adaptability to different size large-scale fuzzy information system.

Generalized dynamic attribute reduction based on similarity relation of intuitionistic fuzzy rough set

In view of the characteristics with big data, high feature dimension, and dynamic for a large-scale intuitionistic fuzzy information systems, this paper integrates intuitionistic fuzzy rough sets and generalized dynamic sampling theory, proposes a generalized attribute reduction algorithm based on similarity relation of intuitionistic fuzzy rough sets and dynamic reduction. It uses dynamic reduction sampling theory to divide a big data set into small data sets and relative positive domain cardinality instead of dependency degree as decision-making condition, and obtains reduction attributes of big intuitionistic fuzzy decision information systems, and achieves the goal of extracting key features and fault diagnosis. The innovation of this paper is that it integrates generalized dynamic reduction and intuitionistic fuzzy rough set, and solves the problem of big data set which cannot be solved by intuitionistic fuzzy rough set. Taking an actual data as an example, the scientificity, rationality and effectiveness of the algorithm are verified from the aspects of stability, diagnostic accuracy, optimization ability and time complexity. Compared with similar algorithms, the advantages of the proposed algorithm for big data processing are confirmed.

Approximate Reasoning Based on IFRS and DS Theory With its Application in Threat Assessment

Threat assessment for aerial attack targets is an important aspect of air defense weapon systems in responding to multiple attacks. We establish a model based on intuitionistic fuzzy rough sets (IFRS) and D-S evidence theory for threat assessment from the required data with uncertainty in stages. Using the overall degree of dependency and attribute importance of the intuitionistic fuzzy information system as a heuristic function, we study algorithms to extract threat elements and rules based on IFRS, to generate an intuitionistic fuzzy rule base for threat assessment with degrees of belief and disbelief. Based on the threat assessment rule base, we study the BPA determination algorithm in multi-stage threat assessment. The intuitionistic fuzzy semantics of degree of belief in the rule conclusion are used to determine the focal elements corresponding to each aggregate rule, and to obtain the degree of support of the data in a stage for each threat level. A case study shows that, compared to a threat assessment method based solely on D-S evidence theory or intuitionistic fuzzy reasoning, the advantage of IFRS knowledge acquisition makes the selection of threat assessment elements and determination of BPA more objective and less dependent on domain experts, so as to yield strong, objective results.

The Approach to Probabilistic Decision-Theoretic Rough Set in Intuitionistic Fuzzy Information Systems

For the moment, the representative and hot research is decision-theoretic rough set (DTRS) which provides a new viewpoint to deal with decision-making problems under risk and uncertainty, and has been applied in many fields. Based on rough set theory, Yao proposed the three-way decision theory which is a prolongation of the classical two-way decision approach. This paper investigates the probabilistic DTRS in the framework of intuitionistic fuzzy information system (IFIS). Firstly, based on IFIS, this paper constructs fuzzy approximate spaces and intuitionistic fuzzy (IF) approximate spaces by defining fuzzy equivalence relation and IF equivalence relation, respectively. And the fuzzy probabilistic spaces and IF probabilistic spaces are based on fuzzy approximate spaces and IF approximate spaces, respectively. Thus, the fuzzy probabilistic approximate spaces and the IF probabilistic approximate spaces are constructed, respectively. Then, based on the three-way decision theory, this paper structures DTRS approach model on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. So, the fuzzy decision-theoretic rough set (FDTRS) model and the intuitionistic fuzzy decision-theoretic rough set (IFDTRS) model are constructed on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. Finally, based on the above DTRS model, some illustrative examples about the risk investment of projects are introduced to make decision analysis. Furthermore, the effectiveness of this method is verified.

Multi‐adjoint intuitionistic fuzzy rough sets

The combination of fuzzy information systems (ISs) and multi-adjoint theory has become a hot issue in the study and applications of artificial intelligence. An intuitionistic fuzzy set has more flexible and practical ability to represent information and is better in dealing with ambiguity and uncertainty when compared with the fuzzy set. Multi- adjoint intuitionistic fuzzy rough sets are constructed by using adjoint triples under intuitionistic fuzzy IS. For this purpose, the authors propose intuitionistic fuzzy indiscernibility relation and multi-adjoint approximation operators. The basic results in the multi-adjoint fuzzy rough set model are generalised to multi-adjoint intuitionistic fuzzy rough set model. The analogous results are also verified. After that, a novel approach of attribute reduction is proposed. First, a kind of approximate reduction to keep the dependence of the positive region to a degree α is formulated. Second, they propose a heuristic algorithm to compute the attribute reduction. At last, they employ an example to describe the processing of the algorithm.

Multi-adjoint based group decision-making under an intuitionistic fuzzy information system Using LATEX*

Multi-adjoint based group decision-making under an intuitionistic fuzzy information system Using LATEX*

Multi-adjoint based group decision-making under an intuitionistic fuzzy information system

The construction of belief intervals is crucial for decision-making in multi-attribute group information integration. Based on multi-adjoint and evidence theory, an approach to multi-criteria group decision-making(MCGDM) in intuitionistic fuzzy information system is proposed. First, the upper and lower approximations of alternatives are calculated by multi-adjoint operators under the correlation matrices which were given by different experts. After that the belief and plausibility functions are gained by intuitionistic fuzzy probability formulas. Second, the belief intervals of alternatives are acquired by combining all experts’ evidence. Then the alternatives are ranked by comparing the belief intervals. Finally, the effectiveness of the method is verified by an application of business transaction. Compared with the existing model, the method introduced in this paper is more effective and accurate.

Generalized dominance rough set models for the dominance intuitionistic fuzzy information systems

Dominance rough sets generalize classical rough sets by replacing the equivalence relation with a dominance relation. However, the existing dominance relations are still too restrictive to convenient for its practical applications because they are always considering a strict decreasing or increasing order for each attribute. In fact, in many real-world problems, we only need to employ the decreasing or increasing order in terms of partial attributes rather than all attributes or even just focus on overall evaluations of objects. Based on this phenomenon, in this paper we define two new dominance relations and obtain two generalized dominance rough set models according to define the overall evaluations and add particular requirements for some individual attributes. Meanwhile, the attribute reductions of dominance intuitionistic fuzzy decision information systems are also examined with these two models. Firstly, we define a generalized dominance relation and obtain a generalized dominance rough set model by using the intuitionistic fuzzy additive operator to aggregate individual attribute value of each object into a overall evaluation. The attribute reduction of intuitionistic fuzzy information systems with generalized dominance rough set are also explored. Secondly, we introduce another dominance relation named as generalized β-dominance relation and the generalized β-dominance rough set model by adding a parameter β ∈ [0, 1] in generalized dominance relation in order to control the number of attributes which satisfy dominance relations, from which we can induce all “at least” and “at most” decision rules. An algorithm is developed to compute the lower and upper β-dominance approximations in order to get all the lower and upper reducts of intuitionistic fuzzy decision systems. Some numerical examples are employed to substantiate the conceptual arguments.