Rough Approximation Operators on a Complete Orthomodular Lattice

Dai, Songsong

doi:10.3390/axioms10030164

Cited by 4 publications

(8 citation statements)

References 48 publications

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“…Step 2: Calculating the gray scale fitness value of each particle according to the Equation (20). If it is better than the individual extreme value of the current position of the particle, set pbest to the position of the particle, record the position of the particle and update the global extreme value.…”

Section: Image Segmentation Algorithm Based On Psomentioning

confidence: 99%

“…Rough set was first proposed by Polish professor Z. Pawlak in 1982. It is another mathematical method for processing uncertain information after probability theory and fuzzy set theory [20,21]. As a mathematical tool for describing uncertainty, it can effectually analyze and process incomplete information such as inconsistency, inaccuracy and incompleteness, it can find hidden knowledge and reveal potential laws [22,23].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Fractional Image Enhancement Algorithm Based on Rough Set and Particle Swarm Optimization

et al. 2022

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This paper proposes a new image enhancement algorithm. At first, the paper uses the combination of rough set and particle swarm optimization (PSO) algorithm to distinguish the smooth area, edge and texture area of the image. Then, according to the results of image segmentation, an adaptive fractional differential filter is used to enhance the image. Finally, the experimental results show that the image enhanced by this algorithm has clear edge, rich texture details, and retains the information of the smooth area of the image.

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Section: Image Segmentation Algorithm Based On Psomentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive Fractional Image Enhancement Algorithm Based on Rough Set and Particle Swarm Optimization

et al. 2022

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“…Pawlak formed rough sets by assigning objects related to the confirmation of ideas that fell within the boundary line region, which is defined as the difference set between the upper and lower approximation sets [10][11][12]. Because rough sets can be described by explicit mathematical formulas, the number of fuzzy set elements can be calculated (i.e., the fuzziness between 0 and 1 can be determined through calculation) [10][11][12]. This feature offers an effective means of dealing with the routine nature of unclear problems and managing uncertainty with incomplete information or knowledge.…”

Section: Rough Set Theorymentioning

confidence: 99%

“…In addition, the study also used rough set theory to discover the weighting of the attributes affecting students' final scores. Rough set theory, proposed by Pawlak, has advantage of being able to obtain the same knowledge as the original decision-making system without losing any information, and without obeying any assumptions [10][11][12]. The main purpose of rough set theory is to extract rules from an information system composed of an object and its corresponding attribute factors that are sufficient to describe under which attribute conditions an object should be classified [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Establishing Effective Remedial Instruction Grouping Using the Rough Set Theory and Grey Structural Modeling

Wang¹

2021

Axioms

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In the field of education, the assessment of a student’s learning performance is based on his final course scores. Few people care about what is behind the numbers. Most of the time, the final scores represent the end of the course because students have already passed the subject. Low-level students especially, still have a lot of misconceptions, but they do not know how to make up for their poor grasp of the subject in preparation for future study. Instead of just giving students their scores, teachers are encouraged to provide remedial instruction to students for their future learning. This study aims to establish an effective method using rough set theory and grey structural modeling to determine which attributes affect students’ final scores and to cluster students accordingly. A rough set algorithm generates a set of attributes for an assessment list. Grey structural modeling (GSM) is then used to cluster students who have the same weaknesses in English. GSM changes from one dimension to two dimensions, and calculates the relative distance, so that cluster analysis can be performed. Targeted remedial instruction can then be given to each similar ability student grouping. The results revealed that through integrating the two theories, teachers could more effectively sort students into groups. Students benefit by coming to understand their weaknesses in English instead of just receiving a single score at the end of the semester, and they can learn with their peers as well. Teachers can adjust their teaching strategies and syllabus design based on the analytical results to target the students’ needs.

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“…In 2017, Hassan [25] showed that rough set model with quantum logic can be used for recognition and classification systems. In our previous work [26,27], we proposed a rough set model based on quantum logic. We defined rough approximation operators via join and meet on a complete orthomodular lattice (COL).…”

Section: Introductionmentioning

confidence: 99%

Generalized Rough Sets via Quantum Implications on Quantum Logic

Dai

2021

Axioms

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This paper introduces some new concepts of rough approximations via five quantum implications satisfying Birkhoff–von Neumann condition. We first establish rough approximations via Sasaki implication and show the equivalence between distributivity of multiplication over join and some properties of rough approximations. We further establish rough approximations via other four quantum implication and examine their properties.

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Rough Approximation Operators on a Complete Orthomodular Lattice

Cited by 4 publications

References 48 publications

Adaptive Fractional Image Enhancement Algorithm Based on Rough Set and Particle Swarm Optimization

Adaptive Fractional Image Enhancement Algorithm Based on Rough Set and Particle Swarm Optimization

Establishing Effective Remedial Instruction Grouping Using the Rough Set Theory and Grey Structural Modeling

Generalized Rough Sets via Quantum Implications on Quantum Logic

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