Fuzzy mathematics is a branch of mathematics that extends classical set theory and logic to model reasoning under uncertainty. Initiated by Lotfi Asker Zadeh in 1965 with the introduction of fuzzy sets, the field has since evolved to include fuzzy set theory, fuzzy logic, and various fuzzy analogues of traditional mathematic structures. Unlike classical mathematics, which usually relies on binary membership (an element either belongs to a set or it does not), fuzzy mathematics allows elements to partially belong to a set, with degrees of membership represented by values in the interval [0, 1]. This framework enables more flexible modeling of imprecise or vague concepts. Fuzzy mathematics has found applications in numerous domains, including control theory, artificial intelligence, decision theory, pattern recognition, and linguistics, where the modeling of gradations and uncertainty is essential. == Definition == A fuzzy subset A of a set X is defined by a function A: X → L, where L is typically the interval [0, 1]. This function is called the membership function of the fuzzy subset and assigns to each element x in X a degree of membership A(x) in the fuzzy set A. In classical set theory, a subset of X can be represented by an indicator function (also known as a characteristic function), which maps elements to either 0 or 1, indicating non-membership or full membership, respectively. Fuzzy subsets generalize this concept by allowing any real value between 0 and 1, thereby enabling partial membership. More generally, the codomain L of the membership function can be replaced with any complete lattice, resulting in the broader framework of L-fuzzy sets. == Fuzzification == The development of fuzzification in mathematics can be broadly divided into three historical stages: Initial, straightforward fuzzifications (1960s–1970s), Expansion of generalization techniques (1980s), Standardization, axiomatization, and L-fuzzification (1990s). Fuzzification generally involves extending classical mathematical concepts from binary (crisp) logic, where membership is determined by characteristic functions, to fuzzy logic, where membership is expressed by values in the interval [0, 1] via membership functions. Let A and B be fuzzy subsets of a set X. The fuzzy versions of set-theoretic operations are commonly defined as: ( A ∩ B ) ( x ) = min ( A ( x ) , B ( x ) ) {\displaystyle (A\cap B)(x)=\min(A(x),B(x))} ( A ∪ B ) ( x ) = max ( A ( x ) , B ( x ) ) {\displaystyle (A\cup B)(x)=\max(A(x),B(x))} for all x ∈ X {\displaystyle x\in X} . These operations can be generalized using t-norms and t-conorms, respectively. For example, the minimum operation can be replaced by multiplication: ( A ∩ B ) ( x ) = A ( x ) ⋅ B ( x ) {\displaystyle (A\cap B)(x)=A(x)\cdot B(x)} Fuzzification of algebraic structures often relies on generalizing the closure property. Let ∗ {\displaystyle } be a binary operation on X, and let A be a fuzzy subset of X. Then A is said to satisfy fuzzy closure if: A ( x ∗ y ) ≥ min ( A ( x ) , A ( y ) ) {\displaystyle A(xy)\geq \min(A(x),A(y))} for all x , y ∈ X {\displaystyle x,y\in X} . If ( G , ∗ ) {\displaystyle (G,)} is a group, then a fuzzy subset A of G is a fuzzy subgroup if: A ( x ∗ y − 1 ) ≥ min ( A ( x ) , A ( y − 1 ) ) {\displaystyle A(xy^{-1})\geq \min(A(x),A(y^{-1}))} for all x , y ∈ G {\displaystyle x,y\in G} . Similar generalizations apply to relational properties. For example, for example, for fuzzification of the transitivity property, a fuzzy relation R {\displaystyle R} on X {\displaystyle X} (i.e., a fuzzy subset of X × X {\displaystyle X\times X} ) is said to be fuzzy transitive if: R ( x , z ) ≥ min ( R ( x , y ) , R ( y , z ) ) {\displaystyle R(x,z)\geq \min(R(x,y),R(y,z))} for all x , y , z ∈ X {\displaystyle x,y,z\in X} . == Fuzzy analogues == Fuzzy subgroupoids and fuzzy subgroups were introduced in 1971 by A. Rosenfeld. Analogues of other mathematical subjects have been translated to fuzzy mathematics, such as fuzzy field theory and fuzzy Galois theory, fuzzy topology, fuzzy geometry, fuzzy orderings, and fuzzy graphs.
Object Data Management Group
The Object Data Management Group (ODMG) was conceived in the summer of 1991 at a breakfast with object database vendors that was organized by Rick Cattell of Sun Microsystems. In 1998, the ODMG changed its name from the Object Database Management Group to reflect the expansion of its efforts to include specifications for both object database and object–relational mapping products. The primary goal of the ODMG was to put forward a set of specifications that allowed a developer to write portable applications for object database and object–relational mapping products. In order to do that, the data schema, programming language bindings, and data manipulation and query languages needed to be portable. Between 1993 and 2001, the ODMG published five revisions to its specification. The last revision was ODMG version 3.0, after which the group disbanded. == Major components of the ODMG 3.0 specification == Object Model. This was based on the Object Management Group's Object Model. The OMG core model was designed to be a common denominator for object request brokers, object database systems, object programming languages, etc. The ODMG designed a profile by adding components to the OMG core object model. Object Specification Languages. The ODMG Object Definition Language (ODL) was used to define the object types that conform to the ODMG Object Model. The ODMG Object Interchange Format (OIF) was used to dump and load the current state to or from a file or set of files. Object Query Language (OQL). The ODMG OQL was a declarative (nonprocedural) language for query and updating. It used SQL as a basis, where possible, though OQL supports more powerful object-oriented capabilities. C++ Language Binding. This defined a C++ binding of the ODMG ODL and a C++ Object Manipulation Language (OML). The C++ ODL was expressed as a library that provides classes and functions to implement the concepts defined in the ODMG Object Model. The C++ OML syntax and semantics are those of standard C++ in the context of the standard class library. The C++ binding also provided a mechanism to invoke OQL. Smalltalk Language Binding. This defined the mapping between the ODMG ODL and Smalltalk, which was based on the OMG Smalltalk binding for the OMG Interface Definition Language (IDL). The Smalltalk binding also provided a mechanism to invoke OQL. Java Language Binding. This defined the binding between the ODMG ODL and the Java programming language as defined by the Java 2 Platform. The Java binding also provided a mechanism to invoke OQL. == Status == ODMG 3.0 was published in book form in 2000.[1] By 2001, most of the major object database and object-relational mapping vendors claimed conformance to the ODMG Java Language Binding. Compliance to the other components of the specification was mixed.[2] In 2001, the ODMG Java Language Binding was submitted to the Java Community Process as a basis for the Java Data Objects specification. The ODMG member companies then decided to concentrate their efforts on the Java Data Objects specification. As a result, the ODMG disbanded in 2001. In 2004, the Object Management Group (OMG) was granted the right to revise the ODMG 3.0 specification as an OMG specification by the copyright holder, Morgan Kaufmann Publishers. In February 2006, the OMG announced the formation of the Object Database Technology Working Group (ODBT WG) and plans to work on the 4th generation of an object database standard. == ODMG Compliant DBMS == Orient ODBMS: http://www.OrienTechnologies.com Objectivity/DB C++, Java and Smalltalk interfaces.
Secure Electronic Delivery
Secure Electronic Delivery (SED) is a service created in 2003 and provided by the British Library Document Supply Service (BLDSS). Its purpose is to enable faster delivery of digital materials as encrypted, copyright-compliant PDF Documents, to a personal e-mail address. These documents are supplied from the British Library via its On Demand service. When the British Library supplies articles electronically, it sends them securely in order to ensure its usage is permitted (research purposes) and copyright law is observed. == Methods == As the publishing industry, authors and creators become highly protective of their assets and intellectual property, they impose strict rules on delivery methods to prevent copyright infringement. Nowadays, DRM-enabled secure delivery appears to be the most widely used solution to address issues faced by libraries in supplying ebooks and digital materials to their users. SED, one of these solutions, is using Adobe LiveCycle Digital Rights Management (LCDRM) as an encryption method to deliver documents. == Advantages == SED offers convenience, quality and speed as documents are delivered upon request at any location and on any device. Requested articles are scanned for high quality reproduction, opened anywhere on any machine, including mobile devices. == Restrictions == The following are restrictions hold in a SED service implementation: The digital material is accessible only for 14 days via a link sent to a personal message. Due to copyright reasons, the material can be opened only once, saved for 14 days and does not allow a copy-paste action. Upon display, the material must be printed from the same device and reprinted only once. The On Demand encryption technology works best on the default Safari browser although other browsers may accommodate it.
Media aggregation platform
A Media Aggregation Platform or Media Aggregation Portal (MAP) is an over the top service for distributing web-based streaming media content from multiple sources to a large audience. MAPs consist of networks of sources who host their own content which viewers can choose and access directly from a larger variety of content to choose from than a single source can offer. The service is used by content providers, looking to extend the reach of their content. Unlike multichannel video programming distributor (MVPD) or multiple-system operators (MSO), MAPs rely on the Internet rather than cables or satellite. As more network television channels have moved online in the early 21st century, joining web-native channels like Netflix, MAPs aggregate content the way that MSOs and MVPDs have used cable, and to a lesser extent satellite and IPTV infrastructure. There are companies that offer a similar service for free, including Yidio and StreamingMoviesRight, while others charge a subscription fee like as FreeCast Inc's Rabbit TV Plus. When compared with MSOs and MVPDs, MAP networks have much lower costs due to lack of physical infrastructure. The majority of revenue from MAP services are retained by the content creators, and revenue is instead collected from advertisements, pay-per-view, and subscription-based content offerings instead of licensing and reselling content. MAP service consumers interact and purchase content directly from its source, without the markup added by a middleman.
Basic Formal Ontology
Basic Formal Ontology (BFO) is a top-level ontology developed by Barry Smith and colleagues to promote interoperability among domain ontologies. The BFO methodology accomplishes this through a process of downward population. BFO is a formal ontology. The structure of BFO is based on a division of entities into two disjoint categories of continuant and occurrent, the former consists of objects and spatial regions, the latter contains processes conceived as extended through (or spanning) time. BFO thereby seeks to consolidate both time and space within a single framework A guide to building BFO-conformant domain ontologies was published by MIT Press in 2015. In 2021, the standard ISO/IEC 21838-2:2021 Information Technology — Top-level Ontologies (TLO) — Part 2: Basic Formal Ontology (BFO) was published by the Joint Technical Committee of the International Standards Organization and the International Electrotechnical Commission. ISO/IEC 21838 is a multi-part standard. Part 1 of the standard specifies the requirements that must be met if an ontology is to be classified as a top-level ontology by the standard. == History == BFO arose against the background of research in ontologies in the domain of geospatial information science by David Mark, Pierre Grenon, Achille Varzi and others, with a special role for the study of vagueness and of the ways sharp boundaries in the geospatial and other domains are created by fiat. BFO has passed through four major releases. 2001: release of BFO 1 2007: release of BFO 1.1 2015: release of BFO 2.0 2020: release of BFO 2020 2021: release of BFO 2020 as an ISO/IEC Standard The current revision was released in 2020, and this forms the basis of the standard ISO/IEC 21838-2, which was released by the Joint Committee of the International Standards Organization and International Electrotechnical Commission in 2021. == Applications == BFO has been adopted as a foundational ontology by over 650 ontology projects, principally in the areas of biomedical ontology, security and defense (intelligence) ontology, and industry ontologies. Example applications of BFO can be seen in the Ontology for Biomedical Investigations (OBI). In January 2024, BFO and the Common Core Ontologies (CCO), a suite of BFO-extension ontologies, were adopted as the "baseline standards for formal DOD and IC ontology" development work in the DOD and Intelligence Community. A memorandum to this effect was signed by the chief data officers of the DOD, the Office of the Director of National Intelligence and the Chief Digital and Artificial Intelligence Office.
Logogen model
The logogen model of 1969 is a model of speech recognition that uses units called "logogens" to explain how humans comprehend spoken or written words. Logogens are a vast number of specialized recognition units, each able to recognize one specific word. This model provides for the effects of context on word recognition. == Overview == The word logogen can be traced back to the Greek-language word logos, which means "word", and genus, which means "birth". British scientist John Morton's logogen model was designed to explain word recognition using a new type of unit known as a logogen. A critical element of this theory is the involvement of lexicons, or specialized aspects of memory that include semantic and phonemic information about each item that is contained in memory. A given lexicon consists of many smaller, abstract items known as logogens. Logogens contain a variety of properties about given word such as their appearance, sound, and meaning. Logogens do not store words within themselves, but rather they store information that is specifically necessary for retrieval of whatever word is being searched for. A given logogen will become activated by psychological stimuli or contextual information (words) that is consistent with the properties of that specific logogen and when the logogen's activation level rises to or above its threshold level, the pronunciation of the given word is sent to the output system. Certain stimuli can affect the activation levels of more than one word at a time, usually involving words that are similar to one another. When this occurs, whichever of the words' activation levels reaches the threshold level, it is that word that is then sent to the output system with the subject remaining unaware of any partially excited logogens. This assumption was made by Marslen-Wilson and Welch (1978), who added to the model some assumptions of their own in order to account for their experimental results. They also assumed that the analysis of phonetic input can only become available to other parts of the system by process of how the input affects the logogen system. Finally, Marslen-Wilson and Welch assume that the first syllable of a given word will increase the activation level of a given logogen more than those of the latter syllables, which supported the data found at the time. == Analysis == The logogen model can be used to help linguists explain particular occurrences in the human language. The most-helpful application of the model is to show how one accesses words and their meanings in the lexicon. The word-frequency effect is best explained by the logogen model in that words (or logogens) that have a higher frequency (or are more common) have a lower threshold. This means that they require less perceptual power in the brain to be recognized and decoded from the lexicon and are recognized faster than those words that are less common. Also, with high-frequency words, the recovery from lowering the item's threshold is less fulfilled compared to low-frequency words so less sensory information is needed for that particular item's recognition. There are ways to lower thresholds, such as repetition and semantic priming. Also, each time a word is encountered through these methods, the threshold for that word is temporarily lowered partially because of its recovering ability. This model also conveys that specific concrete words are recalled better because they use images and logogens, whereas abstract words are not as easily recalled well because they only use logogens, hence showing the difference in thresholds between these two types of words. At the time of its conception, Morton's logogen model was one of the most influential models in springing up other parallel word access models and served as the essential basis for these subsequent models. Morton's model also strongly influenced other contemporary theories on lexical access. However, despite the advantages that the logogen theory presents, it also displays some negative facets. First and foremost, the logogen model does not explain all occurrences in language, such as the introduction of new words or non-words into a person's lexicon. Also, because of the distinctive model application, it may vary in its effectiveness in different languages. == Criticisms == While this model does a reasonable job of understanding the underlying semantics of many aspects in psycholinguistics, there are some flaws that have been pointed out in the logogen model. It has been argued that the prior stimulus patterns that have been seen in the logogen theory are not centrally localized in the logogen itself but are actually distributed throughout the different pathways over which the stimulus is being processed. What this directs at is that the notion and proliferation of logogens was due to modality. In essence, the logogen is unnecessary in the idea of attaining the title of being a recognition unit because of the variety of pathways that it is open to, not just logogens. Another criticism has been that this model essentially ignores larger and more critical structures in language and phonetics such as the different syntactic rules or grammatical construction that innately exists in language. Since this model overtly limits itself to the scope of lexical access then this model is seen as biased and misunderstood. To many psychologists, the logogen model does not meet the functional or representational adequacy that a theory should include to sufficiently comprehend language. Also, another criticism is that the logogen theory was supposed to predict that stimulus degradation should affect priming and word frequency in humans. However, many psychologists have conducted studies and researched the model to show that only priming and not word frequency is interacted with stimulus degradation. Priming is supposed to deteriorate a stimulus because it postulates that the semantic characteristics of previously known words are fed back into the detector of a person which in turn raises the threshold of related items. In word frequency, stimulus degradation is supposed to occur because it postulates that familiar words have lower thresholds than their low-frequency counterparts. However, in studies, priming is the only structure that does show observable and notable stimulus decadence. Even though the logogen theory has many unfilled holes, Morton was a revolutionary of his field whose speculation and research has opened up a remarkable era of psycholinguistics. == Other models to consider == cohort model – This model was proposed by Marslen-Wilson and was designed specifically to account for auditory word recognition. It works by breaking the word down and states that when a word is heard all words that begin with the first sound of the target word are activated. This set of words is considered the cohort. Once the first cohort has been activated, the other information, or sounds in the word narrow down the choices. The person recognizes the word when you are left with a single choice; this is considered the "recognition point". checking model – This model was developed by Norris in 1986. In this particular model, he took the approach that any word that partially matches the input is analyzed and checked to see if it fits with the context of the situation. interactive-activation model – This model is considered a connectionist model. Proposed by McClelland and Rumelhart in the 1981 to 1982 period, it is based around nodes, which are visual features, and positions of letters within a given word. They also act as word detectors which have inhibitory and excitatory connections between them. This model starts with first letter and suggests that all the words with that first letter are activated at first and then going through the word one can determine what the word is they are looking at. The main principle is that mental phenomena can be described by interconnected networks of simple units. verification model – The model was developed by Curtis Becker in 1970. The main idea is that a small number of candidates that are activated in parallel are subject to a serial-verification process. This model starts the word-recognition process with a basic representation of the stimulus. Then, sensory trace, consisting of line features is used to activate word detectors. When an acceptable number of detectors are activated these are used to generate a search set. These items are drawn from the lexicon on the basis of similarity to the sensory trace, which help with the identity of the stimulus. Then, in a serial process the candidates are compared to the representation of the sensory-trace input. == Related concepts == word frequency – This is the belief that the speed and accuracy with which a word is recognized is related to how frequently the word occurs in our language. Each logogen has a threshold (for identification) and words with higher frequencies have lower thresholds. Words with higher freq
Five safes
The Five Safes is a framework for helping make decisions about making effective use of data which is confidential or sensitive. It is mainly used to describe or design research access to statistical data held by government and health agencies, and by data archives such as the UK Data Service. It is not an internationally accepted standard. Two of the Five Safes refer to statistical disclosure control, and so the Five Safes is usually used to contrast statistical and non-statistical controls when comparing data management options. == Concept == The Five Safes proposes that data management decisions be considered as solving problems in five 'dimensions': projects, people, settings, data and outputs. The combination of the controls leads to 'safe use'. These are most commonly expressed as questions, for example: These dimensions are scales, not limits. That is, solutions can have a mix of more or fewer controls in each dimension, but the overall aim of 'safe use' independent of the particular mix. For example, a public use file available for open download cannot control who uses it, where or for what purpose, and so all the control (protection) must be in the data itself. In contrast, a file which is only accessed through a secure environment with certified users can contain very sensitive information: the non-statistical controls allow the data to be 'unsafe'. One academic likened the process to a graphic equalizer, where bass and treble can be combined independently to produce a sound the listener likes, which has proven to be a very useful metaphor. This 2023 Data Foundation webinar is an expert discussion of how the elements interact, including an excellent introductory representation. There is no 'order' to the Five Safes, in that one is necessarily more important than the others. However, Ritchie argued that the 'managerial' controls (projects, people, setting) should be addressed before the 'statistical' controls (data, output). The Five Safes concept is associated with other topics which developed from the same programme at ONS, although these are not necessarily implemented. Safe people is associated with 'active researcher management', while safe outputs is linked with principles-based output statistical disclosure control. The Five Safes is a positive framework, describing what is and is not. The EDRU ('evidence-based, default-open, risk-managed, user-centred') attitudinal model is sometimes used to give a normative context == The 'data access spectrum' == From 2003 the Five Safes was also represented in a simpler form as a 'Data Access Spectrum'. The non-data controls (project, people, setting, outputs) tend to work together, in that organisations often see these as a complementary set of restrictions on access. These can then be contrasted with choices about data anonymisation to present a linear representation of data access options. This presentation is consistent with the idea of 'data as a residual', as well as data protection laws of the time which often characterised data simply as anonymous or not anonymous. A similar idea had already been developed independently in 2001 by Chuck Humphrey of the Canadian RDC network, the 'continuum of access'. More recently, The Open Data Institute has developed a 'Data Spectrum toolkit' which includes industry-specific examples. == History and terminology == The Five Safes was devised in the winter of 2002/2003 by Felix Ritchie at the UK Office for National Statistics (ONS) to describe its secure remote-access Virtual Microdata Laboratory (VML). It was described at this time as the 'VML Security Model'. This was adopted by the NORC data enclave, and more widely in the US, as the 'portfolio model' (although this is now also used to refer to a slightly different legal/statistical/educational breakdown). In 2012 the framework as was still being referred to as the 'VML security model', but its increasing use among non-UK organisations led to the adoption of the more general and informative phrase 'Five Safes'. The original framework only had four safes (projects, people, settings and outputs): the framework was used to describe highly detailed data access through a secure environment, and so the 'data' dimension was irrelevant. From 2007 onwards, 'safe data' was included as the framework was used to a describe a wider range of ONS activities. As the US version was based upon the 2005 specification, some US iterations uses have the original four dimensions (eg). Some discussions, such as the OECD, use the term 'secure' instead 'safe'. However, the use of both these terms can cause presentational problems: less control in a particular dimension could be seen to imply 'unsafe users' or 'insecure settings', for example, which distracts from the main message. Hence, the Australian government uses the term "five data sharing principles". The 'Anonymisation Decision-Making Framework' uses a framework based on the Five Safes but relabelling "projects", "people", and "settings" as "governance", "agency" and "infrastructure", respectively; "Output" is omitted, and "safe use" becomes "functional anonymisation". There is no reference to the Five Safes or any associated literature. The Australian version was required to include references to the Five Safes, and presented it as an alternative without comment. == Application == The framework has had three uses: pedagogical, descriptive, and design. Since 2016, it has also been used, directly and indirectly in legislation. See for more detailed examples. === Pedagogy === The first significant use of the framework, other than internal administrative use, was to structure researcher training courses at the UK Office for National Statistics from 2003. UK Data Archive, Administrative Data Research Network, Eurostat, Statistics New Zealand, the Mexican National Institute of Statistics and Geography, NORC, Statistics Canada and the Australian Bureau of Statistics, amongst others, have also used this framework. Most of these courses are for researchers using restricted-access facilities; the Eurostat courses are unusual in that they are designed for all users of sensitive data. === Description === The framework is often used to describe existing data access solutions (e.g. UK HMRC Data Lab, UK Data Service, Statistics New Zealand) or planned/conceptualised ones (e.g. Eurostat in 2011). An early use was to help identify areas where ONS' still had 'irreducible risks' in its provision of secure remote access. The framework is mostly used for confidential social science data. To date it appears to have made little impact on medical research planning, although it is now included in the revised guidelines on implementing HIPAA regulations in the US, and by Cancer Research UK and the Health Foundation in the UK. It has also been used to describe a security model for the Scottish Health Informatics Programme. === Design === In general the Five Safes has been used to describe solutions post-factum, and to explain/justify choices made, but an increasing number of organisations have used the framework to design data access solutions. For example, the Hellenic Statistical Agency developed a data strategy built around the Five Safes in 2016; the UK Health Foundation used the Five Safes to design its data management and training programmes. Use in the private sector is less common but some organisations have incorporated the Five Safes into consulting services. In 2015 the UK Data Service organized a workshop to encourage data users from the academic and private sectors to think about how to manage confidential research data, using the Five Safes to demonstrate alternative options and best practice. Early adopters for strategic design use were in Australia: both the Australian Bureau of Statistics and the Australian Department of Social Service used the Five Safes as an ex ante design tool. In 2017 the Australian Productivity Commission recommended adopting a version of the framework to support cross-government data sharing and re-use. This underwent extensive consultation and culminated in the DAT Act 2022. Since 2020 the Five Safes has been the overriding framework for the design of new secure facilities and data sharing arrangements in the UK for public health and social sciences. This has been promoted by the Office for Statistics Regulation, the UK Statistics Authority, NHS DIgital, and the research funding bodies Administrative Data Research UK and DARE UK. === Regulation and legislation === Three laws have incorporated the Fives Safes. They are explicit in the South Australian Public Sector (Data Sharing) Act 2016, and implicit in the research provisions of the UK Digital Economy Act 2017. The Australian Data Availability and Transparency Act 2022 renames the Five Safes as the Five Data Sharing Principles.A 2025 statutory review of the DAT Act 2022 found "that the DAT Act has not been effective in achieving its objectives.". The review includes specific referen