Data Transformation Services (DTS) is a Microsoft database tool with a set of objects and utilities to allow the automation of extract, transform and load operations to or from a database. The objects are DTS packages and their components, and the utilities are called DTS tools. DTS was included with earlier versions of Microsoft SQL Server, and was almost always used with SQL Server databases, although it could be used independently with other databases. DTS allows data to be transformed and loaded from heterogeneous sources using OLE DB, ODBC, or text-only files, into any supported database. DTS can also allow automation of data import or transformation on a scheduled basis, and can perform additional functions such as FTPing files and executing external programs. In addition, DTS provides an alternative method of version control and backup for packages when used in conjunction with a version control system, such as Microsoft Visual SourceSafe. DTS has been superseded by SQL Server Integration Services in later releases of Microsoft SQL Server though there was some backwards compatibility and ability to run DTS packages in the new SSIS for a time. == History == In SQL Server versions 6.5 and earlier, database administrators (DBAs) used SQL Server Transfer Manager and Bulk Copy Program, included with SQL Server, to transfer data. These tools had significant shortcomings, and many DBAs used third-party tools such as Pervasive Data Integrator to transfer data more flexibly and easily. With the release of SQL Server 7 in 1998, "Data Transformation Services" was packaged with it to replace all these tools. The concept, design, and implementation of the Data Transformation Services was led by Stewart P. MacLeod (SQL Server Development Group Program Manager), Vij Rajarajan (SQL Server Lead Developer), and Ted Hart (SQL Server Lead Developer). The goal was to make it easier to import, export, and transform heterogeneous data and simplify the creation of data warehouses from operational data sources. SQL Server 2000 expanded DTS functionality in several ways. It introduced new types of tasks, including the ability to FTP files, move databases or database components, and add messages into Microsoft Message Queue. DTS packages can be saved as a Visual Basic file in SQL Server 2000, and this can be expanded to save into any COM-compliant language. Microsoft also integrated packages into Windows 2000 security and made DTS tools more user-friendly; tasks can accept input and output parameters. DTS comes with all editions of SQL Server 7 and 2000, but was superseded by SQL Server Integration Services in the Microsoft SQL Server 2005 release in 2005. == DTS packages == The DTS package is the fundamental logical component of DTS; every DTS object is a child component of the package. Packages are used whenever one modifies data using DTS. All the metadata about the data transformation is contained within the package. Packages can be saved directly in a SQL Server, or can be saved in the Microsoft Repository or in COM files. SQL Server 2000 also allows a programmer to save packages in a Visual Basic or other language file (when stored to a VB file, the package is actually scripted—that is, a VB script is executed to dynamically create the package objects and its component objects). A package can contain any number of connection objects, but does not have to contain any. These allow the package to read data from any OLE DB-compliant data source, and can be expanded to handle other sorts of data. The functionality of a package is organized into tasks and steps. A DTS Task is a discrete set of functionalities executed as a single step in a DTS package. Each task defines a work item to be performed as part of the data movement and data transformation process or as a job to be executed. Data Transformation Services supplies a number of tasks that are part of the DTS object model and that can be accessed graphically through the DTS Designer or accessed programmatically. These tasks, which can be configured individually, cover a wide variety of data copying, data transformation and notification situations. For example, the following types of tasks represent some actions that you can perform by using DTS: executing a single SQL statement, sending an email, and transferring a file with FTP. A step within a DTS package describes the order in which tasks are run and the precedence constraints that describe what to do in the case damage or of failure. These steps can be executed sequentially or in parallel. Packages can also contain global variables which can be used throughout the package. SQL Server 2000 allows input and output parameters for tasks, greatly expanding the usefulness of global variables. DTS packages can be edited, password protected, scheduled for execution, and retrieved by version. == DTS tools == DTS tools packaged with SQL Server include the DTS wizards, DTS Designer, and DTS Programming Interfaces. === DTS wizards === The DTS wizards can be used to perform simple or common DTS tasks. These include the Import/Export Wizard and the Copy of Database Wizard. They provide the simplest method of copying data between OLE DB data sources. There is a great deal of functionality that is not available by merely using a wizard. However, a package created with a wizard can be saved and later altered with one of the other DTS tools. A Create Publishing Wizard is also available to schedule packages to run at certain times. This only works if SQL Server Agent is running; otherwise the package will be scheduled, but will not be executed. === DTS Designer === The DTS Designer is a graphical tool used to build complex DTS Packages with workflows and event-driven logic. DTS Designer can also be used to edit and customize DTS Packages created with the DTS wizard. Each connection and task in DTS Designer is shown with a specific icon. These icons are joined with precedence constraints, which specify the order and requirements for tasks to be run. One task may run, for instance, only if another task succeeds (or fails). Other tasks may run concurrently. The DTS Designer has been criticized for having unusual quirks and limitations, such as the inability to visually copy and paste multiple tasks at one time. Many of these shortcomings have been overcome in SQL Server Integration Services, DTS's successor. === DTS Query Designer === A graphical tool used to build queries in DTS. === DTS Run Utility === DTS Packages can be run from the command line using the DTSRUN Utility. The utility is invoked using the following syntax: dtsrun /S server_name[\instance_name] { {/[~]U user_name [/[~]P password]} | /E } ] { {/[~]N package_name } | {/[~]G package_guid_string} | {/[~]V package_version_guid_string} } [/[~]M package_password] [/[~]F filename] [/[~]R repository_database_name] [/A global_variable_name:typeid=value] [/L log_file_name] [/W NT_event_log_completion_status] [/Z] [/!X] [/!D] [/!Y] [/!C] ] When passing in parameters which are mapped to Global Variables, you are required to include the typeid. This is rather difficult to find on the Microsoft site. Below are the TypeIds used in passing in these values.
ALL-IN-1
ALL-IN-1 was an office automation product developed and sold by Digital Equipment Corporation in the 1980s. It was one of the first purchasable off the shelf electronic mail products. It was later known as Office Server V3.2 for OpenVMS Alpha and OpenVMS VAX systems before being discontinued. == Overview == ALL-IN-1 was advertised as an office automation system including functionality in Electronic Messaging, Word Processing and Time Management. It offered an application development platform and customization capabilities that ranged from scripting to code-level integration. ALL-IN-1 was designed and developed by Skip Walter, John Churin and Marty Skinner from Digital Equipment Corporation who began work in 1977. Sheila Chance was hired as the software engineering manager in 1981. The first version of the software, called CP/OSS, the Charlotte Package of Office System Services, named after the location of the developers, was released in May 1982. In 1983, the product was renamed ALL-IN-1 and the Charlotte group continued to develop versions 1.1 through 1.3. Digital then made the decision to move most of the development activity to its central engineering facility in Reading, United Kingdom, where a group there took responsibility for the product from version 2.0 (released in field test in 1984 and to customers in 1985) onward. The Charlotte group continued to work on the Time Management subsystem until version 2.3 and other contributions were made from groups based in Sophia Antipolis, France (System for Customization Management and the integration with VAX Notes), Reading (Message Router and MAILbus), and Nashua, New Hampshire (FMS). ALL-IN-1 V3.0 introduced shared file cabinets and the File Cabinet Server (FCS) to lay the foundation for an eventual integration with TeamLinks, Digital's PC office client. Previous integrations with PCs included PC ALL-IN-1, a DOS-based product introduced in 1989 that never proved popular with customers. Bob Wyman was the first product manager. He oversaw the growth of the product culminating in over $2 billion per year in revenue and market leadership in the proprietary office automation sector. Other consultants from Digital Equipment Corporation involved include Frank Nicodem, Donald Vickers and Tony Redmond.
DialogOS
DialogOS is a graphical programming environment to design computer system which can converse through voice with the user. Dialogs are clicked together in a Flowchart. DialogOS includes bindings to control Lego Mindstorms robots by voice and has bindings to SQL databases, as well as a generic plugin architecture to integrate with other types of backends. DialogOS is used in computer science courses in schools and universities to teach programming and to introduce beginners in the basic principles of human/computer interaction and dialog design. It has also been used in research systems. DialogOS was initially developed commercially by CLT Sprachtechnologie GmbH until its liquidation in 2017. The rights were then acquired by Saarland University and the software was released as open-source. == Bindings to Lego Mindstorms NXT == DialogOS can control the LEGO Mindstorms NXT Series. It uses sensor-nodes to obtain values for the following sensors: noise sensor ultrasonic sensor touch sensor luminosity sensor
Fuzzy number
A fuzzy number is a generalization of a regular real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. This weight is called the membership function. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. Just like fuzzy logic is an extension of Boolean logic (which uses absolute truth and falsehood only, and nothing in between), fuzzy numbers are an extension of real numbers. Calculations with fuzzy numbers allow the incorporation of uncertainty on parameters, properties, geometry, initial conditions, etc. The arithmetic calculations on fuzzy numbers are implemented using fuzzy arithmetic operations, which can be done by two different approaches: (1) interval arithmetic approach; and (2) the extension principle approach. A fuzzy number is equal to a fuzzy interval. The degree of fuzziness is determined by the a-cut which is also called the fuzzy spread.
Fragile Dreams: Farewell Ruins of the Moon
Fragile Dreams: Farewell Ruins of the Moon (フラジール ～さよなら月の廃墟～, Furajīru: Sayonara Tsuki no Haikyo; known in Japan as Fragile) is an action role-playing game for the Wii developed by Namco Bandai Games in co-operation with Tri-Crescendo. The game was released by Namco Bandai Games in Japan on January 22, 2009. It was later published by Xseed Games in North America on March 16, 2010, and in Europe by Rising Star Games on March 19, 2010, followed by its release in Australia on April 1, 2010. == Gameplay == In Fragile Dreams, the player character, Seto, must traverse the ruins of Tokyo and the surrounding areas, fighting off ghosts that lurk within these ruins. The game's heads-up display includes a mini-map and HP gauge for Seto's location and health, respectively. Seto will fall unconscious if his HP reaches zero, resulting in a game over. The player controls Seto from a third-person perspective with the Wii Remote and Nunchuk. Seto can use his flashlight (controlled by the Wii Remote pointer) to illuminate his surroundings or solve puzzles and interact with the environment. When searching for certain objectives or hidden enemies, pointing Seto's light in their direction picks up and plays their sounds through the Wii Remote's mini speaker. The Wii Nunchuk, meanwhile, directly controls Seto's movement: aside of basic movement, he can crouch to hide and crawl through small spaces. Seto will often come across damaged floors, which require slow movement (and for heavily damaged floors, crouching) to cross without falling through. As Seto, the player can use weapons found throughout the world to fight off ghosts, ranging from slingshots and golf clubs to crossbows and katanas. Each weapon can only take a certain amount of use: once a weapon reaches its limit, it will break after battle. The player can also find other usable and collectable items in the field, marked with fireflies. The player can only save their game by resting at small fire pits scattered throughout the world: used fire pits are marked with a bonfire. The player can also examine and identify Mystery Items, organize their inventory, as well as after encountering the Merchant, buy and sell items. As stated by the producer of the game, Kentarō Kawashima, Fragile Dreams is not strictly a survival horror: rather, its story focuses on human drama. In Fragile Dreams, aside of the main story, the player can find and examine objects and graffiti throughout the world. Objects called memory items (ranging from origami and stones to cell phones and books) hold the memories of their former owners (only accessible at bonfires), while the graffiti contains messages only seen by pointing at them in first-person. By examining these messages, the player can piece together hints to the game's backstory. == Story == === Setting and characters === Fragile Dreams is set in a post-apocalyptic version of Earth in the near-future. Almost all the world's population has vanished, leaving the surviving buildings and structures abandoned. The game is set in and near the ruins of Tokyo, Japan, where the event that nearly wiped out humanity may have originated. The protagonist, Seto, is a 15-year-old boy who searches the world for other living humans. He encounters Ren, a silver-haired girl who often leaves behind large, cryptic drawings. Other characters include: Sai, the ghost of a young woman; Crow, a mischievous and straightforward amnesiac boy; Personal Frame (P.F.), a portable computer who loves having conversations more than anything else; Chiyo, the ghost of a little girl; and the Merchant, a mysterious yet merry man who trades various goods. The game's host of enemies mainly consist of ghosts, but also include humanoid robots and security proxies. The main antagonist, Shin, is the AI of a scientist who considers speech to be an inferior means of communication. Various memory items include a greater set of characters, each giving hints to the game's backstory. === Plot === At the end of Seto's fifteenth summer, his grandfather dies. Seto buries him in front of their home, an old observatory, and that from then on he became "truly alone". At night, he searches for anything the old man had left for him and discovers a letter, along with a strange blue stone in a locket. Suddenly, a mask-like ghost appears and attacks Seto. After driving the creature off, Seto reads the old man's letter, who tells him to "reach a tall red tower" east of the observatory, where he might find other survivors. After departing for the tower, Seto reaches an old subway entrance in the Azabudai district and finds Ren sitting on a collapsed pillar, singing to the stars. He accidentally startles her and the frightened Ren flees into the subway station: getting over the shock of meeting another person, Seto follows her. While searching the station, he discovers a Personal Frame, who guides him towards Ren. Unfortunately, just as they reach the exit, P.F.'s battery dies out: Seto buries the device, keeping a screw from it in his locket. From the underground, Seto finds himself at an abandoned amusement park and encounters Crow, who steals Seto's locket. After a long chase across the park and another encounter with the masked ghost, Crow returns Seto's locket and directs him to a hotel nearby, where he saw a girl who might know something about Ren. Crow also gives Seto his skull ring to keep in his locket and kisses him. At the hotel, Seto encounters Sai and fights the masked ghost again. After laying to rest the spirit of an old woman named Chiyo, the two discover Ren's drawings by a sewer. Returning to the underground, Seto and Sai find themselves at a hydropower dam. While searching for Ren, Seto discovers that Crow is actually a robot, but his battery begins to fail and Seto mourns for him as he "die[s]". Finally, they encounter Ren in a cell: although glad to see him again, Ren runs off after Shin calls. Sai explains to Seto that most of humanity died because of a "human empathy expansion project" called Glass Cage. The project was meant to make human thoughts transparent, meaning that no one would need words to communicate. However, after Glass Cage activated, people who went to sleep never woke up again. Sai reveals that she was Glass Cage's first catalyst: this time, Shin intends to use Ren as the catalyst. After exiting the dam, a demolition crane attempts to destroy it. Hearing both Shin's and the masked ghost's voices from the crane — saying, "Any threat to the project must be eliminated." — the player realizes both are manifestations of Glass Cage. After Seto destroys the crane, Sai leads him to the facility where Ren was taken to. Entering the laboratory, Seto and Sai are confronted by Shin, who coldly dismisses Sai's attempts at reasoning with him and is adamant about proceeding with his plans. As they traverse the laboratory, they overhear a voice announcing "Glass Cage Launch Preparations Complete", strengthening their resolve to save Ren. Making it into the room where Ren is being held, Shin tells them of his intention to use Glass Cage to "obliterate corporeal beings". After Seto defeats him, Shin disappears and Seto releases Ren from the device holding her. Their reunion is cut short as Sai tells them that the backup system has "finished copying her psyche to the AI", allowing Glass Cage to proceed. Ren reveals Shin has escaped to the top of the Tokyo Tower and Seto asks Ren to wait at the base of the tower and for Sai to accompany her. On his way up the tower, Seto hears the voices of P.F., Chiyo and Crow wishing him luck. He confronts and defeats Shin a second time, who reveals his motivations: he had secretly used himself as the first test subject of the human empathy expansion project and gained the ability to hear the thoughts of those around him. Despite his initial belief in the project as a way for humans to empathize with one another, all he heard around him was "jealousy and contempt" and he soon grew disillusioned with the world as even his parents turned against him. Believing no person loved him, Shin wants to put an end to humanity. His words meet with a vehement response from Sai, as she tells him that she loves him, having developed those feelings while she was the catalyst and all she ever wanted was to be part of his life. Hearing this, Shin finds peace, tossing the AI mainframe away so Glass Cage can never be reactivated and vanishes together with Sai, hand-in-hand, after thanking Seto. Descending from the tower, Seto finally learns Ren's name and they resolve to look for other survivors together. == Development == Fragile Dreams was developed by the team at Namco Bandai Games. Director and producer Kentarō Kawashima came up with the concept for the game in 2003, before the Wii console was revealed. When the Wii was unveiled, it became the obvious choice as the game's platform as the Wii remote could be used to control the flashlight. Kawashima wrote the main scenario for the title, w
Document classification
Document classification or document categorization is a problem in library science, information science and computer science. The task is to assign a document to one or more classes or categories. This may be done "manually" (or "intellectually") or algorithmically. The intellectual classification of documents has mostly been the province of library science, while the algorithmic classification of documents is mainly in information science and computer science. The problems are overlapping, however, and there is therefore interdisciplinary research on document classification. The documents to be classified may be texts, images, music, etc. Each kind of document possesses its special classification problems. When not otherwise specified, text classification is implied. Documents may be classified according to their subjects or according to other attributes (such as document type, author, printing year etc.). In the rest of this article only subject classification is considered. There are two main philosophies of subject classification of documents: the content-based approach and the request-based approach. == "Content-based" versus "request-based" classification == Content-based classification is classification in which the weight given to particular subjects in a document determines the class to which the document is assigned. It is, for example, a common rule for classification in libraries, that at least 20% of the content of a book should be about the class to which the book is assigned. In automatic classification it could be the number of times given words appears in a document. Request-oriented classification (or -indexing) is classification in which the anticipated request from users is influencing how documents are being classified. The classifier asks themself: “Under which descriptors should this entity be found?” and “think of all the possible queries and decide for which ones the entity at hand is relevant” (Soergel, 1985, p. 230). Request-oriented classification may be classification that is targeted towards a particular audience or user group. For example, a library or a database for feminist studies may classify/index documents differently when compared to a historical library. It is probably better, however, to understand request-oriented classification as policy-based classification: The classification is done according to some ideals and reflects the purpose of the library or database doing the classification. In this way it is not necessarily a kind of classification or indexing based on user studies. Only if empirical data about use or users are applied should request-oriented classification be regarded as a user-based approach. == Classification versus indexing == Sometimes a distinction is made between assigning documents to classes ("classification") versus assigning subjects to documents ("subject indexing") but as Frederick Wilfrid Lancaster has argued, this distinction is not fruitful. "These terminological distinctions,” he writes, “are quite meaningless and only serve to cause confusion” (Lancaster, 2003, p. 21). The view that this distinction is purely superficial is also supported by the fact that a classification system may be transformed into a thesaurus and vice versa (cf., Aitchison, 1986, 2004; Broughton, 2008; Riesthuis & Bliedung, 1991). Therefore, assigning a subject term to a document in an index is equivalent to assigning that document to the class of documents indexed by that term (all documents indexed or classified as X belong to the same class of documents). == Automatic document classification (ADC) == Automatic document classification tasks can be divided into three sorts: supervised document classification where some external mechanism (such as human feedback) provides information on the correct classification for documents, unsupervised document classification (also known as document clustering), where the classification must be done entirely without reference to external information, and semi-supervised document classification, where parts of the documents are labeled by the external mechanism. There are several software products under various license models available. === Techniques === Automatic document classification techniques include: Artificial neural network Concept Mining Decision trees such as ID3 or C4.5 Expectation maximization (EM) Instantaneously trained neural networks Latent semantic indexing Multiple-instance learning Naive Bayes classifier Natural language processing approaches Rough set-based classifier Soft set-based classifier Support vector machines (SVM) K-nearest neighbour algorithms tf–idf == Applications == Classification techniques have been applied to spam filtering, a process which tries to discern E-mail spam messages from legitimate emails email routing, sending an email sent to a general address to a specific address or mailbox depending on topic language identification, automatically determining the language of a text genre classification, automatically determining the genre of a text readability assessment, automatically determining the degree of readability of a text, either to find suitable materials for different age groups or reader types or as part of a larger text simplification system sentiment analysis, determining the attitude of a speaker or a writer with respect to some topic or the overall contextual polarity of a document. health-related classification using social media in public health surveillance article triage, selecting articles that are relevant for manual literature curation, for example as is being done as the first step to generate manually curated annotation databases in biology
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