A method for solving linear difference equation in Gaussian fuzzy environments

Rahaman, Mostafijur; Mondal, Sankar Prasad; Algehyne, Ebrahem A.; Biswas, Amiya; Alam, Shariful

doi:10.1007/s41066-020-00251-1

Cited by 16 publications

(3 citation statements)

References 42 publications

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“…To better recover the 3D model of furniture based on the pictures and improve the generalization ability of the model, a side branch structure is added with reference to some advanced methods. First, Difference of Gaussians (DOG) [28] is used to process the original input image to obtain the Gaussian difference map. This process can remove the high frequency noise components in the image, and can capture more corner point information features, so as to better learn the detail information and topology of the target object.…”

Section: Side Branchmentioning

confidence: 99%

Home Environment Augmented Reality System Based on 3D Reconstruction of a Single Furniture Picture

Wei

Tang

Wang

et al. 2022

Sensors

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With the popularization of the concept of “metaverse”, Augmented Reality (AR) technology is slowly being applied to people’s daily life as its underlying technology support. In recent years, rapid 3D reconstruction of interior furniture to meet AR shopping needs has become a new method. In this paper, a virtual home environment system is designed and the related core technologies in the system are studied. Background removal and instance segmentation are performed for furniture images containing complex backgrounds, and a Bayesian Classifier and GrabCut (BCGC) algorithm is proposed to improve on the traditional foreground background separation technique. The reconstruction part takes the classical occupancy network reconstruction algorithm as the network basis and proposes a precise occupancy network (PONet) algorithm, which can reconstruct the structural details of furniture images, and the model accuracy is improved. Because the traditional 3D registration model is prone to the problems of model position shift and inaccurate matching with the scene, the AKAZE-based tracking registration algorithm is improved, and a Multiple Filtering-AKAZE (MF-AKAZE) based on AKAZE is proposed to remove the matching points. The matching accuracy is increased by improving the RANSAC filtering mis-matching algorithm based on further screening of the matching results. Finally, the system is verified to realize the function of the AR visualization furniture model, which can better complete the reconstruction as well as registration effect.

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Section: Side Branchmentioning

confidence: 99%

Home Environment Augmented Reality System Based on 3D Reconstruction of a Single Furniture Picture

Wei

Tang

Wang

et al. 2022

Sensors

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“…Mondal and Roy [54] solved the linear FDE by Lagrange multiplier method using Hukuhara derivative. Recently, Rahaman et al [55] has added a new literature exploring a new method of solving difference equation under Gaussian fuzzy environment.…”

Section: Fuzzy Differential Equation In Inventory Management Problemmentioning

confidence: 99%

Solution of an Economic Production Quantity model using the generalized Hukuhara derivative approach

Rahaman

Maity²,

et al. 2021

Scientia Iranica

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In this study, an economic production quantity (EPQ) model with deterioration is developed where the production rate is stock dependent and the demand rate is unit selling price and stock dependent. The low unit selling price and more stocks correspond high demandbut more stock corresponds to slow production because of the avoidance of unnecessary stocks. First of all, we develop the production model by solving some ordinary differential equations having deterministic profit function under some specific assumptions. Later, we develop the fuzzymodel by solving the fuzzy differential equations using Generalized Hukuhara derivative. In fact, the differential equation of the model has been split into two parts namely gH(L-R) and gH(R-L) on the basis of left(L) and right(R)𝛼 − cuts of fuzzy numbers for which the problem itself is transformed into multi-objective EPQ problem. A new formula of aggregation of several objective values obtained at different aspiration levelshas been discussed to defuzzify the fuzzy multi-objective problems.We solve the crisp and fuzzy models using LINGO software. Numerical and graphical illustrations confirm thatthe model under Generalized Hukuhara derivative of (R-L) type contributes more profit which is one of the basic novelties of the proposed approach.

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“…Tudu et al [18] also proposed a new representation of type-2 fuzzy numbers, namely, generalized type-2 fuzzy numbers, and developed theorems for solving generalized type-2 fuzzy boundary value problems. Rahaman et al [19] applied a Gaussian method to solve the linear difference equation in a fuzzy environment. In addition, Ghorui et al [20] applied FAHP and FTOPSIS for shopping mall site selection, and Ghosh et al [21] applied FAHP and FTOPSIS for selecting the best e-rickshaw available.…”

mentioning

confidence: 99%