Three-way decisions in fuzzy incomplete information systems

Yang, Xiaoping; Li, Tong-Jun; Tan, Anhui

doi:10.1007/s13042-019-01025-1

Cited by 39 publications

(9 citation statements)

References 49 publications

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“…The decision classes for the incomplete IS given in U nct(ς)/SIM L(ϑ) = {{ω 3 }, {ω 5 , ω 7 }, {ω 5 , ω 7 }, {ω 8 }} Therefore, by (17) we get…”

Section: Preliminariesmentioning

confidence: 99%

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Uncertainty Optimization-Based Rough Set for Incomplete Information Systems

Sinha¹,

Shende²

2022

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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.

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“…The decision classes for the incomplete IS given in U nct(ς)/SIM L(ϑ) = {{ω 3 }, {ω 5 , ω 7 }, {ω 5 , ω 7 }, {ω 8 }} Therefore, by (17) we get…”

Section: Preliminariesmentioning

confidence: 99%

“…We often have to deal with information systems containing incomplete attribute values. Many studies are proposed to deal with incomplete information system [16,17,18,19,20]. The attribute values incompetent of describing a particular happening with a certainty is called as boundary region or the uncertainty region of the rough set [4].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Optimization-Based Rough Set for Incomplete Information Systems

Sinha¹,

Shende²

2022

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“…1.1 A brief review on (fuzzy) rough sets Rough set theory proposed by Pawlak is an important mathematical tool, which can be used to deal with fuzzy and uncertain information [26]. Nowadays, the (generalized) rough set theory has been applied in many fields, such as clinical medical diagnosis, machine learning and data mining, pattern recognition and classification, prediction and control [12,41,47,52].…”

Section: Introductionmentioning

confidence: 99%

L-fuzzy generalized neighborhood systems-based pessimistic L-fuzzy rough sets and its applications

Gao

Bing-xue

2022

Preprint

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In this paper, a notion of L-fuzzy generalized neighborhood system is introduced and then a novel L-fuzzy rough sets based on it are defined and discussed. It is verified that model is an extension of Pang’s generalized neighborhood system-based pessimistic rough sets, and so called L-fuzzy generalized neighborhood system-based pessimistic L-fuzzy rough sets. Firstly, the basic properties of the pessimistic L-fuzzy rough sets is studied. Later, to regain some Pawlak’s prop- erties those are lost in pessimistic L-fuzzy rough sets, the serial, reflexive, transitive and symmetric conditions for L-fuzzy general neighborhood systems are defined. Secondly, the axiomatic researches of the pessimistic L- fuzzy rough sets (include the serial, reflexive and sym- metric cases) are given. Thirdly, a reduction theory based on preserving L-fuzzy approximation operators is established. Finally, one applied in information system, i.e., a three-way decision model based on pessimistic L- fuzzy rough sets, is builded. A simple practical example to show the effectiveness of our model is also presented.

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“…To date, the research on three-way decisions can be categorized into the following two aspects, namely, modelling and application. In terms of model construction, the traditional method is to study three-way decisions by constructing different DTRS models (such as studying the conditional probability and loss functions in DTRS) [20][21][22][23][24][25][26][27][28][29][30][31][32]. For example, to solve the problem that the traditional DTRS model cannot deal with the multi-valued set loss function, Zhao et al [21] generalized DTRS models and investigated three-way decisions.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, experimental data in real life are not always clear and definite, and the three-way decision model should have the ability to handle uncertain and fuzzy information. Under the guidance of such ideas, the fuzzy three-way decision model [20], intuitionistic fuzzy three-way decision model [22,25], and three-way decision model of incomplete information systems [26,27] have successively been presented. Furthermore, interdisciplinary research has offered a possible way to separate the three-way decisions from the DTRS framework and form a set of independent ideological and theoretical systems.…”

Section: Introductionmentioning

confidence: 99%

Intuitionistic Fuzzy Three-Way Decision Model Based on the Three-Way Granular Computing Method

2020

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Three-way decisions, as a general model for uncertain information processing and decisions, mainly utilize the threshold generated by the decision cost matrix to determine the decision category of the object. However, the determination of the threshold is usually accompanied by varying degrees of subjectivity. In addition, the potential symmetrical relationship between the advantages and disadvantages of the decision cost is also a problem worthy of attention. In this study, we propose a novel intuitionistic fuzzy three-way decision (IFTWD) model based on a three-way granular computing method. First, we present the calculation methods for the possibility of membership state and non-membership state, as well as prove the related properties. Furthermore, we investigate the object information granules, i.e., the fine-grained, medium-grained, and coarse-grained objects, by combining the state probability distribution and probability distribution. Then, for decision and evaluation issues, we define the superiority-compatibility relation and inferiority-compatibility relation for IFTWD model construction. In addition, we use the superiority degree and inferiority degree instead of the original thresholds and design a new method for evaluating decision cost. Finally, we focus on the algorithm research of the proposed model and present an empirical study of agricultural ecological investment in Hubei Province to demonstrate the effectiveness of our model.

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Three-way decisions in fuzzy incomplete information systems

Cited by 39 publications

References 49 publications

Uncertainty Optimization-Based Rough Set for Incomplete Information Systems

Uncertainty Optimization-Based Rough Set for Incomplete Information Systems

L-fuzzy generalized neighborhood systems-based pessimistic L-fuzzy rough sets and its applications

Intuitionistic Fuzzy Three-Way Decision Model Based on the Three-Way Granular Computing Method

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