Aggregation Operators with Undefined Inputs or Outputs

AbstractThe join and group-by aggregation are two memory intensive operators that are affecting the performance of relational databases. Hashing is a common approach used to implement both operators. Recent paradigm shifts in multi-core processor architectures have reinvigorated research into how the join and group-by aggregation operators can leverage these advances. However, the poor spatial locality of the hashing approach has hindered performance on multi-core processor architectures which rely on using large cache hierarchies for latency mitigation. Multithreaded architectures can better cope with poor spatial locality by masking memory latency with many outstanding requests. Nevertheless, the number of parallel threads, even in the most advanced multithreaded processors, such as UltraSPARC, is not enough to fully cover the main memory access latency. In this paper, we explore the hardware re-configurability of FPGAs to enable deeper execution pipelines that maintain hundreds (instead of tens) of outstanding memory requests across four FPGAs-drastically increasing concurrency and throughput. We present two end-to-end in-memory accelerators for the join and group-by aggregation operators using FPGAs. Both accelerators use massive multithreading to mask long memory delays of traversing linked-list data structures, while concurrently managing hundreds of thread states across four FPGAs locally. We explore how content addressable memories can be intermixed within our multithreaded designs to act as a synchronizing cache, which enforces locks and merges jobs together before they are written to memory. Throughput results for our hash-join operator accelerator show a speedup between 2$$\times $$ × and 3.4$$\times $$ × over the best multi-core approaches with comparable memory bandwidths on uniform and skewed datasets. The accelerator for the hash-based group-by aggregation operator demonstrates that leveraging CAMs achieves average speedup of 3.3$$\times $$ × with a best case of 9.4$$\times $$ × in terms of throughput over CPU implementations across five types of data distributions.

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Algorithm for T-spherical fuzzy MADM based on associated immediate probability interactive geometric aggregation operators

Artificial Intelligence Review ◽

10.1007/s10462-021-09959-1 ◽

2021 ◽

Author(s):

Muhammad Munir ◽

Tahir Mahmood ◽

Azmat Hussain

Keyword(s):

Aggregation Operators ◽

Fuzzy Madm

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A novel picture fuzzy linguistic Muirhead Mean aggregation operators and their application to multiple attribute decision making

Soft Computing ◽

10.1007/s00500-021-06121-5 ◽

2021 ◽

Author(s):

Sidong Xian ◽

Yue Cheng ◽

Zhou Liu

Keyword(s):

Decision Making ◽

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Multiple Attribute ◽

Fuzzy Linguistic

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Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽

10.3390/axioms10030145 ◽

2021 ◽

Vol 10 (3) ◽

pp. 145

Author(s):

Yun Jin ◽

Zareena Kousar ◽

Kifayat Ullah ◽

Tahir Mahmood ◽

Nimet Yapici Pehlivan ◽

...

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Evaluation Process ◽

Aggregation Operators ◽

Weighted Averaging ◽

Membership Degree ◽

Operational Laws ◽

Multi Attribute Decision Making ◽

Interval Valued ◽

Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

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