Type-1 OWA operators

Type-1 OWA operators

Type-1 OWA operators are a set of aggregation operators that generalise the Yager's OWA (ordered weighted averaging) operators in the interest of aggregating fuzzy sets rather than crisp values in soft decision making and data mining. These operators provide a mathematical technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, where these uncertain objects are modelled by fuzzy sets. The two definitions for type-1 OWA operators are based on Zadeh's Extension Principle and α {\displaystyle \alpha } -cuts of fuzzy sets. The two definitions lead to equivalent results. == Definitions == === Definition 1 === Let F ( X ) {\displaystyle F(X)} be the set of fuzzy sets with domain of discourse X {\displaystyle X} , a type-1 OWA operator is defined as follows: Given n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,1]} , a type-1 OWA operator is a mapping, Φ {\displaystyle \Phi } , Φ : F ( X ) × ⋯ × F ( X ) ⟶ F ( X ) {\displaystyle \Phi \colon F(X)\times \cdots \times F(X)\longrightarrow F(X)} ( A 1 , ⋯ , A n ) ↦ Y {\displaystyle (A^{1},\cdots ,A^{n})\mapsto Y} such that μ Y ( y ) = sup ∑ k = 1 n w ¯ i a σ ( i ) = y ( μ W 1 ( w 1 ) ∧ ⋯ ∧ μ W n ( w n ) ∧ μ A 1 ( a 1 ) ∧ ⋯ ∧ μ A n ( a n ) ) {\displaystyle \mu _{Y}(y)=\displaystyle \sup _{\displaystyle \sum _{k=1}^{n}{\bar {w}}_{i}a_{\sigma (i)}=y}\left({\begin{array}{{1}l}\mu _{W^{1}}(w_{1})\wedge \cdots \wedge \mu _{W^{n}}(w_{n})\wedge \mu _{A^{1}}(a_{1})\wedge \cdots \wedge \mu _{A^{n}}(a_{n})\end{array}}\right)} where w ¯ i = w i ∑ i = 1 n w i {\displaystyle {\bar {w}}_{i}={\frac {w_{i}}{\sum _{i=1}^{n}{w_{i}}}}} , and σ : { 1 , ⋯ , n } ⟶ { 1 , ⋯ , n } {\displaystyle \sigma \colon \{1,\cdots ,n\}\longrightarrow \{1,\cdots ,n\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , ⋯ , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\ \forall i=1,\cdots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th highest element in the set { a 1 , ⋯ , a n } {\displaystyle \left\{{a_{1},\cdots ,a_{n}}\right\}} . === Definition 2 === Using the alpha-cuts of fuzzy sets: Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , then for each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,\;1]} , an α {\displaystyle \alpha } -level type-1 OWA operator with α {\displaystyle \alpha } -level sets { W α i } i = 1 n {\displaystyle \left\{{W_{\alpha }^{i}}\right\}_{i=1}^{n}} to aggregate the α {\displaystyle \alpha } -cuts of fuzzy sets { A i } i = 1 n {\displaystyle \left\{{A^{i}}\right\}_{i=1}^{n}} is: Φ α ( A α 1 , … , A α n ) = { ∑ i = 1 n w i a σ ( i ) ∑ i = 1 n w i | w i ∈ W α i , a i ∈ A α i , i = 1 , … , n } {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\ldots ,A_{\alpha }^{n}}\right)=\left\{{{\frac {\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}}}{\sum \limits _{i=1}^{n}{w_{i}}}}\left|{w_{i}\in W_{\alpha }^{i},\;a_{i}}\right.\in A_{\alpha }^{i},\;i=1,\ldots ,n}\right\}} where W α i = { w | μ W i ( w ) ≥ α } , A α i = { x | μ A i ( x ) ≥ α } {\displaystyle W_{\alpha }^{i}=\{w|\mu _{W_{i}}(w)\geq \alpha \},A_{\alpha }^{i}=\{x|\mu _{A_{i}}(x)\geq \alpha \}} , and σ : { 1 , ⋯ , n } → { 1 , ⋯ , n } {\displaystyle \sigma :\{\;1,\cdots ,n\;\}\to \{\;1,\cdots ,n\;\}} is a permutation function such that a σ ( i ) ≥ a σ ( i + 1 ) , ∀ i = 1 , ⋯ , n − 1 {\displaystyle a_{\sigma (i)}\geq a_{\sigma (i+1)},\;\forall \;i=1,\cdots ,n-1} , i.e., a σ ( i ) {\displaystyle a_{\sigma (i)}} is the i {\displaystyle i} th largest element in the set { a 1 , ⋯ , a n } {\displaystyle \left\{{a_{1},\cdots ,a_{n}}\right\}} . == Representation theorem of Type-1 OWA operators == Given the n linguistic weights { W i } i = 1 n {\displaystyle \left\{{W^{i}}\right\}_{i=1}^{n}} in the form of fuzzy sets defined on the domain of discourse U = [ 0 , 1 ] {\displaystyle U=[0,\;\;1]} , and the fuzzy sets A 1 , ⋯ , A n {\displaystyle A^{1},\cdots ,A^{n}} , then we have that Y = G {\displaystyle Y=G} where Y {\displaystyle Y} is the aggregation result obtained by Definition 1, and G {\displaystyle G} is the result obtained by in Definition 2. == Programming problems for Type-1 OWA operators == According to the Representation Theorem of Type-1 OWA Operators, a general type-1 OWA operator can be decomposed into a series of α {\displaystyle \alpha } -level type-1 OWA operators. In practice, this series of α {\displaystyle \alpha } -level type-1 OWA operators is used to construct the resulting aggregation fuzzy set. So we only need to compute the left end-points and right end-points of the intervals Φ α ( A α 1 , ⋯ , A α n ) {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)} . Then, the resulting aggregation fuzzy set is constructed with the membership function as follows: μ G ( x ) = ⋁ α : x ∈ Φ α ( A α 1 , ⋯ , A α n ) α ⁡ α {\displaystyle \mu _{G}(x)=\operatorname {\bigvee } \limits _{\alpha :x\in \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{\alpha }}\alpha } For the left end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) − = min W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ⁡ ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{-}=\operatorname {\min } \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} while for the right end-points, we need to solve the following programming problem: Φ α ( A α 1 , ⋯ , A α n ) + = max W α − i ≤ w i ≤ W α + i A α − i ≤ a i ≤ A α + i ⁡ ∑ i = 1 n w i a σ ( i ) / ∑ i = 1 n w i {\displaystyle \Phi _{\alpha }\left({A_{\alpha }^{1},\cdots ,A_{\alpha }^{n}}\right)_{+}=\operatorname {\max } \limits _{\begin{array}{l}W_{\alpha -}^{i}\leq w_{i}\leq W_{\alpha +}^{i}A_{\alpha -}^{i}\leq a_{i}\leq A_{\alpha +}^{i}\end{array}}\sum \limits _{i=1}^{n}{w_{i}a_{\sigma (i)}/\sum \limits _{i=1}^{n}{w_{i}}}} A fast method has been presented to solve two programming problem so that the type-1 OWA aggregation operation can be performed efficiently, for details, please see the paper. == Alpha-level approach to Type-1 OWA operation == Three-step process: Step 1—To set up the α {\displaystyle \alpha } - level resolution in [0, 1]. Step 2—For each α ∈ [ 0 , 1 ] {\displaystyle \alpha \in [0,1]} , Step 2.1—To calculate ρ α + i 0 ∗ {\displaystyle \rho _{\alpha +}^{i_{0}^{\ast }}} Let i 0 = 1 {\displaystyle i_{0}=1} ; If ρ α + i 0 ≥ A α + σ ( i 0 ) {\displaystyle \rho _{\alpha +}^{i_{0}}\geq A_{\alpha +}^{\sigma (i_{0})}} , stop, ρ α + i 0 {\displaystyle \rho _{\alpha +}^{i_{0}}} is the solution; otherwise go to Step 2.1-3. i 0 ← i 0 + 1 {\displaystyle i_{0}\leftarrow i_{0}+1} , go to Step 2.1-2. Step 2.2 To calculate ρ α − i 0 ∗ {\displaystyle \rho _{\alpha -}^{i_{0}^{\ast }}} Let i 0 = 1 {\displaystyle i_{0}=1} ; If ρ α − i 0 ≥ A α − σ ( i 0 ) {\displaystyle \rho _{\alpha -}^{i_{0}}\geq A_{\alpha -}^{\sigma (i_{0})}} , stop, ρ α − i 0 {\displaystyle \rho _{\alpha -}^{i_{0}}} is the solution; otherwise go to Step 2.2-3. i 0 ← i 0 + 1 {\displaystyle i_{0}\leftarrow i_{0}+1} , go to step Step 2.2-2. Step 3—To construct the aggregation resulting fuzzy set G {\displaystyle G} based on all the available intervals [ ρ α − i 0 ∗ , ρ α + i 0 ∗ ] {\displaystyle \left[{\rho _{\alpha -}^{i_{0}^{\ast }},\;\rho _{\alpha +}^{i_{0}^{\ast }}}\right]} : μ G ( x ) = ⋁ α : x ∈ [ ρ α − i 0 ∗ , ρ α + i 0 ∗ ] ⁡ α {\displaystyle \mu _{G}(x)=\operatorname {\bigvee } \limits _{\alpha :x\in \left[{\rho _{\alpha -}^{i_{0}^{\ast }},\;\rho _{\alpha +}^{i_{0}^{\ast }}}\right]}\alpha } == Some Examples == The type-1 OWA operator with the weights shown in the top figure is used to aggregate the fuzzy sets (solide lines) in the bottom figure, and the dashed line is the aggregation result. == Special cases == Any OWA operators, like maximum, minimum, mean operators; Join operators of (type-1) fuzzy sets, i.e., fuzzy maximum operators; Meet operators of (type-1) fuzzy sets, i.e., fuzzy minimum operators; Join-like operators of (type-1) fuzzy sets; Meet-like operators of (type-1) fuzzy sets. == Generalizations == Type-2 OWA operators have been suggested to aggregate the type-2 fuzzy sets for soft decision making. == Applications == Type-1 OWA operators have been applied to different domains for soft decision making. Improved efficiency of computing approach ; Type reduction of type-2 fuzzy sets ; Group decision making ; Credit risk evaluation ; Information fusion ; Linguistic expressions and symbolic translation ; Sentiment analysis ; Ro

AI-assisted software development

AI-assisted software development is the use of artificial intelligence (AI) to augment software development. It uses large language models (LLMs), AI agents and other AI technologies to assist software developers. It helps in a range of tasks of the software development life cycle, from code generation to debugging, editing, testing, UI design, understanding the code, and documentation. Agentic coding denotes the use of AI agents for software development. == Technologies == === Source code generation === Large language models trained or fine-tuned on source-code corpora can generate source code from natural-language descriptions, comments, or docstrings. Research on code-generation systems often evaluates generated programs by functional correctness, such as whether the output passes automated test cases, rather than by syntax alone. Such tools can be features or extensions of integrated development environments (IDEs). === Intelligent code completion === AI agents using pre-trained and fine-tuned LLMs can predict and suggest code completions based on context. According to Husein, Aburajouh & Catal in a 2025 literature review in Computer Standards & Interfaces, "LLMs significantly enhance code completion performance across several programming languages and contexts, and their capability to predict relevant code snippets based on context and partial input boosts developer productivity substantially." === Testing, debugging, code review and analysis === AI is used to automatically generate test cases, identify potential bugs and security vulnerabilities, and suggest fixes. AI can also be used to perform static code analysis and suggest potential performance improvements. == Limitations == Both ownership of and responsibility for AI-generated code is disputed. According to a report from the German Federal Office for Information Security, the use of AI coding assistants without careful oversight from experienced developers can introduce both minor and major security vulnerabilities, and any potential gain in productivity should be weighed against the cost of additional quality control and security measures. According to Deloitte, outputs from AI-assisted software development must be validated through a combination of automated testing, static analysis tools and human review, creating a governance layer to improve quality and accountability. == Vibe coding ==

Cobocards

CoboCards is a web application for creation, study and sharing of flashcards. They also provide mobile application for Android and iOS mobile devices, to help study of flashcards on the move. Based on the freemium model, CoboCards provides users a free account with two card sets compared to paid subscription with premium features such as unlimited card sets, Leitner system based trainer and collaborative learning. == History == CoboCards is a project of Jamil Soufan and Tamim Swaid. Tamim Swaid has developed the concept and interface of a collaboratively usable e-learning platform in his diploma thesis at the University of Applied Sciences in February 2007. In January 2010 they founded the CoboCards GmbH (limited company) together with Ali Yildirim. CoboCards is supported by its strategic partners Prof. Schroeder (RWTH Aachen University), Prof. Oliver Wrede (University for Applied Sciences Aachen) and Prof. Klaus Gasteier (University of Arts Berlin). With the idea of creating and studying flashcards online and offering an active control of learning progress they won the start2grow business idea competition in September 2009 (€25.000 ). Additionally CoboCards was funded by German Authorities with approximately €100.000 .

Distributed manufacturing

Distributed manufacturing, also known as distributed production, cloud producing, distributed digital manufacturing, and local manufacturing, is a form of decentralized manufacturing practiced by enterprises using a network of geographically dispersed manufacturing facilities that are coordinated using information technology. It can also refer to local manufacture via the historic cottage industry model, or manufacturing that takes place in the homes of consumers. == Enterprise == In enterprise environments, the primary attribute of distributed manufacturing is the ability to create value at geographically dispersed locations. For example, shipping costs could be minimized when products are built geographically close to their intended markets. Also, products manufactured in a number of small facilities distributed over a wide area can be customized with details adapted to individual or regional tastes. Manufacturing components in different physical locations and then managing the supply chain to bring them together for final assembly of a product is also considered a form of distributed manufacturing. Digital networks combined with additive manufacturing allow companies a decentralized and geographically independent distributed production (cloud manufacturing). == Consumer == Within the maker movement and DIY culture, small scale production by consumers often using peer-to-peer resources is being referred to as distributed manufacturing. Consumers download digital designs from an open design repository website like Youmagine or Thingiverse and produce a product for low costs through a distributed network of 3D printing services such as 3D Hubs, Geomiq. In the most distributed form of distributed manufacturing the consumer becomes a prosumer and manufacturers products at home with an open-source 3-D printer such as the RepRap. In 2013 a desktop 3-D printer could be economically justified as a personal product fabricator and the number of free and open hardware designs were growing exponentially. Today there are millions of open hardware product designs at hundreds of repositories and there is some evidence consumers are 3-D printing to save money. For example, 2017 case studies probed the quality of: (1) six common complex toys; (2) Lego blocks; and (3) the customizability of open source board games and found that all filaments analyzed saved the prosumer over 75% of the cost of commercially available true alternative toys and over 90% for recyclebot filament. Overall, these results indicate a single 3D printing repository, MyMiniFactory, is saving consumers well over $60 million/year in offset purchases of only toys. These 3-D printers can now be used to make sophisticated high-value products like scientific instruments. Similarly, a study in 2022 found that 81% of open source designs provided economic savings and the total savings for the 3D printing community is more than $35 million from downloading only the top 100 products at YouMagine. In general, the savings are largest when compared to conventional products when prosumers use recycled materials in 'distributed recycling and additive manufacturing' (DRAM). == Emergency Distributed Manufacturing During COVID-19 Pandemic == Distributed manufacturing became far more visible during the COVID-19 pandemic because it offered a practical response to the breakdown of centralized global supply chains. As lock downs, border restrictions, and factory shutdowns disrupted conventional production, decentralized networks using local facilities such as Open Source Medical Supplies stepped in and manufactured over 48 million products. Additive manufacturing /3D printing were used to produce urgently needed items such as face shields, ventilators and their components, nasopharyngeal swabs, and other personal protective equipment. This demonstrated that distributed manufacturing could reduce lead times, improve responsiveness, and lessen dependence on distant suppliers during crisis conditions for a wide range of products. Peer-reviewed studies on pandemic-era manufacturing note that additive manufacturing was especially valuable because digital design files could be shared rapidly and produced close to the point of need, enabling hospitals, universities, small firms, and maker communities to supplement strained medical supply chains. The pandemic also helped shift distributed manufacturing from being seen as a niche or experimental model to a credible strategy for resilience, flexibility, and emergency response. At the same time, scholars caution that its wider adoption depends on solving issues related to quality assurance, regulation, material consistency, and coordination across distributed production sites. Overall, COVID-19 popularized distributed manufacturing by showing that localized, digitally enabled production could complement traditional manufacturing systems when speed, adaptability, and supply-chain resilience were critical. == Social change == Some call attention to the conjunction of commons-based peer production with distributed manufacturing techniques. The self-reinforced fantasy of a system of eternal growth can be overcome with the development of economies of scope, and here, the civil society can play an important role contributing to the raising of the whole productive structure to a higher plateau of more sustainable and customised productivity. Further, it is true that many issues, problems and threats rise due to the large democratization of the means of production, and especially regarding the physical ones. For instance, the recyclability of advanced nanomaterials is still questioned; weapons manufacturing could become easier; not to mention the implications on counterfeiting and on "intellectual property". It might be maintained that in contrast to the industrial paradigm whose competitive dynamics were about economies of scale, commons-based peer production and distributed manufacturing could develop economies of scope. While the advantages of scale rest on cheap global transportation, the economies of scope share infrastructure costs (intangible and tangible productive resources), taking advantage of the capabilities of the fabrication tools. And following Neil Gershenfeld in that "some of the least developed parts of the world need some of the most advanced technologies", commons-based peer production and distributed manufacturing may offer the necessary tools for thinking globally but act locally in response to certain problems and needs. As well as supporting individual personal manufacturing social and economic benefits are expected to result from the development of local production economies. In particular, the humanitarian and development sector are becoming increasingly interested in how distributed manufacturing can overcome the supply chain challenges of last mile distribution. Further, distributed manufacturing has been proposed as a key element in the Cosmopolitan localism or cosmolocalism framework to reconfigure production by prioritizing socio-ecological well-being over corporate profits, over-production and excess consumption. == Technology == By localizing manufacturing, distributed manufacturing may enable a balance between two opposite extreme qualities in technology development: Low technology and High tech. This balance is understood as an inclusive middle, a "mid-tech", that may go beyond the two polarities, incorporating them into a higher synthesis. Thus, in such an approach, low-tech and high-tech stop being mutually exclusive. They instead become a dialectic totality. Mid-tech may be abbreviated to "both…and…" instead of "neither…nor…". Mid-tech combines the efficiency and versatility of digital/automated technology with low-tech's potential for autonomy and resilience. == Contracting in Distributed Manufacturing == Research into contracting and order processing models tailored for distributed manufacturing has highlighted the need for flexible, role-based frameworks and advanced digital tools. These tools and frameworks are essential for addressing issues related to quality assurance, payment structures, legal compliance, and coordination among multiple actors. By addressing these challenges, contracting models for distributed manufacturing can unlock its potential for more localized, efficient, and sustainable production systems. A system prototype has been developed to simplify contracting for distributed manufacturing. This tool allows buyers to manage orders across multiple manufacturers using a single interface, automating workflows to ensure clarity and accountability for everyone involved. This research was led by the Internet of Production, as part of the mAkE project (African European Maker Innovation Ecosystem), funded by the European Horizon 2020 research and innovation programme.

MeeMix

MeeMix Ltd is a company specializing in personalizing media-related content recommendations, discovery and advertising for the telecommunication industry, founded in 2006. On January 1, 2008, MeeMix launched meemix.com, a public personalized internet radio serving as an online testbed for the development of music taste-prediction technologies. Subsequently, MeeMix released in 2009 a line of Business-to-business commercial services intended to personalize media recommendations, discovery and advertising. MeeMix hybrid taste-prediction technology relies on integrating machine learning algorithms, digital signal processing, behavior analysis, metadata analysis and collaborative filtering, and is provided via API web service. In August 2009, MeeMix was announced as Innovator Nominee in the GSM Association’s Mobile Innovation Grand Prix worldwide contest. As of 2013, MeeMix no longer features internet radios on meemix.com. On Sep 28, 2014, meemix.com went offline.

DaVinci (software)

DaVinci was a development tool produced by Incross, which aimed at creating HTML5 mobile applications and media content. It included a jQuery framework and a JavaScript library that enabled developers and designers to craft web applications designed for mobile devices with a user experience similar to native applications. Business applications, games, rich media content, such as HTML5 multi-media magazines, advertisements, and animation, may be produced with the tool. DaVinci was based on standard web technology – including HTML5, CSS3, and JavaScript. == Features == DaVinci comprised DaVinci Studio and DaVinci Animator, which handled application programming and UI design. The tool had a WYSIWYG authoring environment. Open-source libraries, such as KnockOut, JsRender/JsViews, Impress.js, and turn.js, were included in the tool. Other open-source frameworks could also be integrated. The Model View Controller (MVC) and Data Binding in JavaScript could be handled through DaVinci's Data-Set Editor. In this mode, view components and model data could be visually bound, which allowed users to create web applications with server-integrated UI components without coding. Additionally, DaVinci included an N-Screen editor, which automatically adjusted designs and functionalities to fit the screen sizes of various devices, including smartphones, tablet PCs, and TVs. == DaVinci and jQuery == In collaboration with the jQuery Foundation, DaVinci played a significant role in hosting the first jQuery conference in an Asian district, which took place on November 12, 2012, in Seoul, South Korea. The conference showcased how DaVinci could be utilized in application development demonstrations.

Business Controls Corporation

Business Controls Corporation is a privately held computer company that developed an application-program-generator and also a series of accounting software packages. These packages were widely enough used for various business magazines to have back-of-the-book ads for companies seeking accountants with experience in one or more of them. Computer magazines ran coverage for their SB-5 application-program-generator as from time to time new versions were released, each with new or improved features. == Early days == The company's initial offerings were packages for the DEC PDP-8, although Business Controls Corporation also wrote custom-written programs for customers. Large customers with mainframes who also used smaller systems for departmental use and distributed processing also used BCC's services. == SB-5 == The addition of an application-program-generator named SB-5 that, from specifications, could generate COBOL code was a major step forward. Although this began with supporting the DEC PDP-11, they subsequently began to support COBOL on DEC's DECsystem-10 & DECSYSTEM-20. VAX support came later. The specifications also permitted COBOL inserts and overrides: SB-5 could build an application that was all COBOL, yet only code the portions that varied from BCC's "vanilla" accounting packages. === Similar offerings === A similar idea was done for the IBM mainframe world in the form of a series of application-program-generators from Dylakor Corporation. They were named DYL-250, DYL-260, DYL-270 & DYL-280. Dylakor was acquired by Computer Associates. The specific syntax was different, but it had wider use, and - a mark of success and recognition in the industry - syntax-compatible implementations were released by a competitor. Still another alternative was Peat Marwick Mitchell's PMM2170 application-program-generator package. Like the others, it supported COBOL inserts and overrides. === Extended integration === Business Controls Corporation subsequently extended SB-5's feature set to provide support for System 1022, a product for the DECsystem-10 & DECSYSTEM-20; 1022's vendor also had a VAX/VMS (later OpenVMS) product, System 1032.