Hybrid Framework Parameterization Reduction Combination in Soft Set

2019 ◽  
pp. 233-243
Author(s):  
Mohammed Adam Taheir Mohammed ◽  
Wan Maseri Wan Mohd ◽  
Ruzaini Abdullah Arshah ◽  
M. Mungad ◽  
Edi Sutoyo ◽  
...  
Keyword(s):  
Soft Set ◽  
Hybrid Framework

scholarly journals Hybrid structures applied to ideals in near-rings

2021 ◽  
Author(s):  
B. Elavarasan ◽  
G. Muhiuddin ◽  
K. Porselvi ◽  
Y. B. Jun
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Rough Set Theory ◽  
Wide Spectrum ◽  
Hybrid Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Classical Mathematics ◽  
Classical Means

AbstractHuman endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.

On soft set-valued maps and integral inclusions

2021 ◽  
pp. 1-15
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fixed Point Theorems ◽  
Soft Set ◽  
Mathematical Tool ◽  
Multivalued Maps ◽  
Soft Sets ◽  
Special Cases ◽  
New Development

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.

scholarly journals A Hybrid Framework for Mitigating Heading Drift for a Wearable Pedestrian Navigation System through Adaptive Fusion of Inertial and Magnetic Measurements

2021 ◽  
Vol 11 (4) ◽  
pp. 1902
Author(s):  
Liqiang Zhang ◽  
Yu Liu ◽  
Jinglin Sun
Keyword(s):  
Magnetic Measurements ◽  
Inertial Sensor ◽  
Angular Rate ◽  
Human Motion ◽  
Navigation Systems ◽  
Pedestrian Navigation ◽  
Hybrid Framework ◽  
Outdoor Environments ◽  
Adaptive Fusion ◽  
Indoor And Outdoor Environments

Pedestrian navigation systems could serve as a good supplement for other navigation methods or for extending navigation into areas where other navigation systems are invalid. Due to the accumulation of inertial sensing errors, foot-mounted inertial-sensor-based pedestrian navigation systems (PNSs) suffer from drift, especially heading drift. To mitigate heading drift, considering the complexity of human motion and the environment, we introduce a novel hybrid framework that integrates a foot-state classifier that triggers the zero-velocity update (ZUPT) algorithm, zero-angular-rate update (ZARU) algorithm, and a state lock, a magnetic disturbance detector, a human-motion-classifier-aided adaptive fusion module (AFM) that outputs an adaptive heading error measurement by fusing heuristic and magnetic algorithms rather than simply switching them, and an error-state Kalman filter (ESKF) that estimates the optimal systematic error. The validation datasets include a Vicon loop dataset that spans 324.3 m in a single room for approximately 300 s and challenging walking datasets that cover large indoor and outdoor environments with a total distance of 12.98 km. A total of five different frameworks with different heading drift correction methods, including the proposed framework, were validated on these datasets, which demonstrated that our proposed ZUPT–ZARU–AFM–ESKF-aided PNS outperforms other frameworks and clearly mitigates heading drift.

A new hybrid framework based on integration of optimization algorithms and numerical method for estimating monthly groundwater level

2021 ◽  
Vol 14 (11) ◽  
Author(s):  
Maryam Rezaei ◽  
Sayed-Farhad Mousavi ◽  
Ali Moridi ◽  
Majid Eshaghi Gordji ◽  
Hojat Karami
Keyword(s):  
Numerical Method ◽  
Groundwater Level ◽  
Optimization Algorithms ◽  
Hybrid Framework
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