Covering-based rough sets and modal logics. Part I

Ma, Minghui; Chakraborty, Mihir K.

doi:10.1016/j.ijar.2016.06.002

Cited by 20 publications

(5 citation statements)

References 35 publications

(42 reference statements)

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“…Furthermore, the possibility of new modal systems also arises. In 2016, Ma and Chakraborty [23] pointed out that the P4 logic is exactly the modal system S5. The modal systems for the remaining logic are so far unknown.…”

Section: Introductionmentioning

confidence: 99%

Graded Many-Valued Modal Logic and Its Graded Rough Truth

Gong

2022

Axioms

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Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses the graded modal logic and puts forward the graded many-valued modal logic G(S5). Secondly, by employing the graded operators that correspond to graded modal operations in G(S5), we introduce the concept of graded upper and lower rough truth degrees of a logical formula. Then, we propose the graded upper and lower conditional rough truth degrees. Several basic interesting properties are addressed. Finally, in order to make a distinction between any two rough formulas in graded many-valued modal logic, the graded upper and lower rough similarity degrees between two graded modal formulas are established in a very natural way.

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Section: Introductionmentioning

confidence: 99%

Graded Many-Valued Modal Logic and Its Graded Rough Truth

Gong

2022

Axioms

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“…Furthermore, combined with fuzzy sets, rough sets are also extended to fuzzy environments [15,23,24,27,38]. For instance, the (fuzzy) relation-based fuzzy rough sets [5,7,31,38], the fuzzy covering-based fuzzy rough sets [18,22] and the fuzzy neighborhood (systems)-based fuzzy rough sets [6,11,16,40,55].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the classical rough set model has been proved to be useful in discovering the decision rules of the complete information systems. It is well known that the requirements of equivalence relation are too strict, so the equivalence relation is extended to any binary relation [7,31], covering [22,50], neighborhood(systems) [4,14,16,39,[42][43][44].…”

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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“…The theory of rough sets [1,2] is an effective mathematical tool to handle uncertainty. Nowadays, many kinds of generalized rough sets have been developed [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], and some of them have been successfully applied in many areas including approximate classification, machine learning, conflict analysis, pattern recognition, data mining, and automated knowledge acquisition [2,8,13,14,[18][19][20][21][22]. The theoretical core of generalized rough sets is a pair of approximate operators.…”

Section: Introductionmentioning

confidence: 99%

“…There are usually two approaches to study these approximate operators: constructive approach and axiomatic approach. The constructive approach is to construct the approximation operators from binary relations, coverings, neighborhoods, and other structures [3][4][5][6][7]9,11,13,14]; the axiomatic approach is to find the axiom (set) for a given operator such that the operator is precisely an approximation operator defined through the constructive approach [10,[15][16][17].…”

Section: Introductionmentioning

confidence: 99%

L-Fuzzy Rough Approximation Operators Based on Co-Implication and Their (Single) Axiomatic Characterizations

Jin

2021

Axioms

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For L a complete co-residuated lattice and R an L-fuzzy relation, an L-fuzzy upper approximation operator based on co-implication adjoint with L is constructed and discussed. It is proved that, when L is regular, the new approximation operator is the dual operator of the Qiao–Hu L-fuzzy lower approximation operator defined in 2018. Then, the new approximation operator is characterized by using an axiom set (in particular, by single axiom). Furthermore, the L-fuzzy upper approximation operators generated by serial, symmetric, reflexive, mediate, transitive, and Euclidean L-fuzzy relations and their compositions are characterize through axiom set (single axiom), respectively.

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Covering-based rough sets and modal logics. Part I

Cited by 20 publications

References 35 publications

Graded Many-Valued Modal Logic and Its Graded Rough Truth

Graded Many-Valued Modal Logic and Its Graded Rough Truth

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

L-Fuzzy Rough Approximation Operators Based on Co-Implication and Their (Single) Axiomatic Characterizations

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