Libby Heaney is a British artist and quantum physicist known for her pioneering work on AI and quantum computing. She works on the impact of future technologies and is widely known to be the first artist to use quantum computing as a functioning artistic medium. Her work has been featured internationally, including in the Victoria and Albert Museum, Tate Modern and the Science Gallery. == Early life and scientific career == Heaney is from Tamworth, Staffordshire. She lived in Amington, and went to Greenacres Primary School and Woodhouse High School, now called Landau Forte Academy Amington. She took her GCSEs in 1999. She studied physics at Imperial College London, graduating in 2005 with first class honours. Libby pursued a successful career in quantum physics, completing a PhD thesis on mode entanglement in ultra-cold atomic gases at the University of Leeds, and pursued her own research as a postdoctoral fellow at the University of Oxford and at the National University of Singapore. In 2008, Heaney was awarded the Institute of Physics Very Early Career Woman in Physics Award (now Jocelyn Bell Burnell Medal and Prize). == Artistic career == In 2013 Heaney returned to the UK and completed a master's degree at the University of the Arts London. She studied arts and science at Central Saint Martins and graduated in 2015. She then became a lecturer at the Royal College of Art, teaching Information Experience Design. In 2016, she created Lady Chatterley's Tinderbot which presented Tinder conversations between real users and AI bots programmed using Lady Chatterley's Lover. Lady Chatterley's Tinderbot was covered by BBC News, TheJournal.ie and the Irish Examiner and was exhibited internationally. In 2017, Heaney was commissioned by Sky Arts and the Barbican Centre to design Britbot, an internet bot built using artificial intelligence and the citizenship book Life in the UK: a guide for new residents. The book, a manual for the citizenship test, has been described by Heaney as being "largely a white male privileged version of British history and culture". The bot spoke to the public about what it meant to be British and learnt from their responses to become an ever changing, plural version of Britishness. She was awarded an Arts Council England grant to widen participation of the Britbot to social media. Heaney has exhibited Britbot at the Victoria and Albert Museum, at CogX, the Sheffield Documentary Festival the Edinburgh TV festival, and Art Ai in Leicester. She has been creating with quantum computing since 2019, and has created artworks using quantum computing for Light Art Space (LAS) in Berlin, Somerset House and arebyte in London. Using quantum code, storytelling, and immersive installations and performances, Libby Heaney's works such as Ent- and slimeqore explore and warn against the double-edged potential of quantum computing and its exploitation by private companies. In 2022, Ent- received the Lumen Prize immersive environment award. == Major works == === Ent- and The Evolution of Ent-: QX (2022) === In 2022, Libby Heaney was commissioned by Light Art Space to create Ent-, a 360 immersive installation that revisits Bosch's Garden of Earthly Delights through quantum. The work uses quantum computing as both a medium and a paradigm through which to conceive human and non-human relations. Ent- was exhibited at LAS, Ars Electronica, and arebyte gallery in London. The work was also modified to fit a full dome projection at the Deutsches Museum in Munich, projected onto a public facade in Seoul, and turned into a playable version for an exhibition at Nahmad Contemporary in New York. In 2022, Ent- was a winner in the Art Science Category of the Falling Walls prize and received the Lumen Prize immersive environment award. The Evolution of Ent-:QX, first displayed at arebyte gallery in London, builds on Ent- and imagines a fictional quantum computing company (QX) that appropriates, parodies and subverts the language of big tech in order to educate the viewer on current profit-oriented uses of quantum computing as well as propose new ways to think about and use the technology. In 2023, Ent- was acquired and displayed by the 0xCollection, a new media arts institution based in Basel, in their inaugural exhibition in Prague. === Touch is response-ability (2020) === Touch is response-ability is an instagram performance and touch screen installation where participants activate animations by flicking through instagram stories. The performance investigates representations of the female body in art history and through computer vision to see how stereotypes are socially constructed and maintained. Images of the body are passed through a quantum algorithm, and as the users interact with them they progressively become fragmented and dissolve beyond recognition. The work was originally commissioned by Hervisions at LUX in 2020 and performed on the LUX instagram account. It was also exhibited at Etopia Zaragoza in 2021 and at Art SG with Gazelli Art House in 2023. === Lady Chatterley's Tinderbot (2016) === In Lady Chatterley's Tinderbot, Libby Heaney programmed a bot to engage in conversations on Tinder by using lines from the 1928 novel Lady Chatterley's Lover, by D.H. Lawrence. The work was first shown as an interactive installation in 2016 at the Dublin Science Gallery, allowing visitors to swipe left or right to navigate through various conversations. Lady Chatterley's Tinderbot was also exhibited at Sonar+D in Barcelona (2017), the Telefonica Fundacion in Lima (2017), the Lowry in Salford (2018), RMIT gallery in Melbourne (2021), Microwave Festival in Hong Kong (2022) and was shortlisted for the HEK-Basel Net-based art award in 2018. == Selected exhibitions == 2023 - Synesthetic Immersion, 0xCollection, Prague 2023 - slimeQrawl, Shoreditch Arts Club, London 2023 - ...and that's only (half) the story, PLUS ONE Gallery, Antwerp 2023–Present Futures Festival, Centre of Contemporary Art, Glasgow 2023 - Realtime: Lilypads: Mediating Exponential Systems, NXT Museum, Amsterdam 2023 - My Rhino is not a Myth, Art Encounters Biennial, Timisoara 2023 - Ent-er the Garden of Forking Paths, Gazelli Art House, London 2023 - Energeia, Etopia, Zaragoza 2022 - Every Kind of Wind: Calder and the 21st Century, Nahmad Contemporary, New York 2022 - remiQXing still, Fiumano Clase, London 2022 - the Evolution of Ent-: QX, arebyte, London 2022 - Ent-, Light Art Space x Schering Stiftung, Berlin 2022 - Among the Machines, Zabludowicz Collection, London 2022 - BioMedia, ZKM, Karlsruhe 2021 - CASCADE, Southbank Centre, London 2021 - Agency is the Ability to Act, Holden Gallery, Manchester 2021 - BIAS, Science Gallery, Dublin 2021 - Ars Electronica, Linz 2021 - AI & Music, S+T+ARTS & Sonar Festival, CCCB, Barcelona 2020 - Real Time Constraints, arebyte, London 2019 - Euro(re)visions, Goethe Institut, London 2019 - Higher Resolutions with Hyphen Labs, Tate Modern, London 2019 - Open Fest with Sky Arts, Barbican, London 2018 - Digital Design Weekend, V&A, London 2018 - FAKE, Science Gallery, Dublin 2017 - Ars Electronica, Linz 2017 - Entangled: Quantum Computer Art, Royal College of Art, London 2017 - Humans Need Not Apply, Science Gallery, Dublin == Awards and honours == Her awards include: 2022 - Lumen Prize, BCS Immersive Environment Award (for Ent-) 2022 - Mozilla Foundation Creative Media Award, USA 2022 - nominated for the S+T+ARTS prize 2021 - Adaptation Award, Artquest, London 2021 - British Council Amplify Collaboration Award 2018 - Arts Council England, National Lottery Project Grant 2018 - HeK Basel Net Based Art Award (shortlisted for Tinderbot)
Glossary of computer graphics
This is a glossary of terms relating to computer graphics. For more general computer hardware terms, see glossary of computer hardware terms. == 0–9 == 2D convolution Operation that applies linear filtering to image with a given two-dimensional kernel, able to achieve e.g. edge detection, blurring, etc. 2D image 2D texture map A texture map with two dimensions, typically indexed by UV coordinates. 2D vector A two-dimensional vector, a common data type in rasterization algorithms, 2D computer graphics, graphical user interface libraries. 2.5D Also pseudo 3D. Rendering whose result looks 3D while actually not being 3D or having great limitations, e.g. in camera degrees of freedom. 3D graphics pipeline A graphics pipeline taking 3D models and producing a 2D bitmap image result. 3D paint tool A 3D graphics application for digital painting of multiple texture map image channels directly onto a rotated 3D model, such as zbrush or mudbox, also sometimes able to modify vertex attributes. 3D scene A collection of 3D models and lightsources in world space, into which a camera may be placed, describing a scene for 3D rendering. 3D unit vector A unit vector in 3D space. 4D vector A common datatype in graphics code, holding homogeneous coordinates or RGBA data, or simply a 3D vector with unused W to benefit from alignment, naturally handled by machines with 4-element SIMD registers. 4×4 matrix A matrix commonly used as a transformation of homogeneous coordinates in 3D graphics pipelines. 7e3 format A packed pixel format supported by some graphics processing units (GPUs) where a single 32-bit word encodes three 10-bit floating-point color channels, each with seven bits of mantissa and three bits of exponent. == A == AABB Axis-aligned bounding box (sometimes called "axis oriented"), a bounding box stored in world coordinates; one of the simplest bounding volumes. Additive blending A compositing operation where d s t = d s t + s r c , {\displaystyle dst=dst+src,} without the use of an alpha channel, used for various effects. Also known as linear dodge in some applications. Affine texture mapping Linear interpolation of texture coordinates in screen space without taking perspective into account, causing texture distortion. Aliasing Unwanted effect arising when sampling high-frequency signals, in computer graphics appearing e.g. when downscaling images. Antialiasing methods can prevent it. Alpha channel An additional image channel (e.g. extending an RGB image) or standalone channel controlling alpha blending. Ambient lighting An approximation to the light entering a region from a wide range of directions, used to avoid needing an exact solution to the rendering equation. Ambient occlusion (AO) Effect approximating, in an inexpensive way, one aspect of global illumination by taking into account how much ambient light is blocked by nearby geometry, adding visual clues about the shape. Analytic model A mathematical model for a phenomenon to be simulated, e.g. some approximation to surface shading. Contrasts with Empirical models based purely on recorded data. Anisotropic filtering Advanced texture filtering improving on mipmapping, preventing aliasing while reducing blur in textured polygons at oblique angles to the camera. Anti-aliasing Methods for filtering and sampling to avoid visual artifacts associated with the uniform pixel grid in 3D rendering. Array texture A form of texture map containing an array of 2D texture slices selectable by a 3rd 'W' texture coordinate; used to reduce state changes in 3D rendering. Augmented reality Computer-rendered content inserted into the user's view of the real world. AZDO Approaching zero driver overhead, a set of techniques aimed at reducing the CPU overhead in preparing and submitting rendering commands in the OpenGL pipeline. A compromise between the traditional GL API and other high-performance low-level rendering APIs. == B == Back-face culling Culling (discarding) of polygons that are facing backwards from the camera. Baking Performing an expensive calculation offline, and caching the results in a texture map or vertex attributes. Typically used for generating lightmaps, normal maps, or low level of detail models. Barycentric coordinates Three-element coordinates of a point inside a triangle. Beam tracing Modification of ray tracing which instead of lines uses pyramid-shaped beams to address some of the shortcomings of traditional ray tracing, such as aliasing. Bicubic interpolation Extension of cubic interpolation to 2D, commonly used when scaling textures. Bilinear interpolation Linear interpolation extended to 2D, commonly used when scaling textures. Binding Selecting a resource (texture, buffer, etc.) to be referenced by future commands. Billboard A textured rectangle that keeps itself oriented towards the camera, typically used e.g. for vegetation or particle effects. Binary space partitioning (BSP) A data structure that can be used to accelerate visibility determination, used e.g. in Doom engine. Bit depth The number of bits per pixel, sample, or texel in a bitmap image (holding one or more image channels, typical values being 4, 8, 16, 24, 32) Bitmap Image stored by pixels. Bit plane A format for bitmap images storing 1 bit per pixel in a contiguous 2D array; Several such parallel arrays combine to produce the a higher-bit-depth image. Opposite of packed-pixel format. Blend operation A render state controlling alpha blending, describing a formula for combining source and destination pixels. Bone Coordinate systems used to control surface deformation (via Weight maps) during skeletal animation. Typically stored in a hierarchy, controlled by key frames, and other procedural constraints. Bounding box One of the simplest type of bounding volume, consisting of axis-aligned or object-aligned extents. Bounding volume A mathematically simple volume, such as a sphere or a box, containing 3D objects, used to simplify and accelerate spatial tests (e.g. for visibility or collisions). BRDF Bidirectional reflectance distribution functions (BRDFs), empirical models defining 4D functions for surface shading indexed by a view vector and light vector relative to a surface. Bump mapping Technique similar to normal mapping that instead of normal maps uses so called bump maps (height maps). BVH Bounding volume hierarchy is a tree structure on a set of geometric objects. == C == Camera A virtual camera from which rendering is performed, also sometimes referred to as 'eye'. Camera space A space with the camera at the origin, aligned with the viewer's direction, after the application of the world transformation and view transformation. Cel shading Cartoon-like shading effect. Clipping Limiting specific operations to a specific region, usually the view frustum. Clipping plane A plane used to clip rendering primitives in a graphics pipeline. These may define the view frustum or be used for other effects. Clip space Coordinate space in which clipping is performed. Clip window A rectangular region in screen space, used during clipping. A clip window may be used to enclose a region around a portal in portal rendering. CLUT A table of RGB color values to be indexed by a lower-bit-depth image (typically 4–8 bits), a form of vector quantization. Color bleeding Unwanted effect in texture mapping. A color from a border of unmapped region of the texture may appear (bleed) in the mapped result due to interpolation. Color channels The set of channels in a bitmap image representing the visible color components, i.e. distinct from the alpha channel or other information. Color resolution Command buffer A region of memory holding a set of instructions for a graphics processing unit for rendering a scene or portion of a scene. These may be generated manually in bare metal programming, or managed by low level rendering APIs, or handled internally by high level rendering APIs. Command list A group of rendering commands ready for submission to a graphics processing unit, see also Command buffer. Compute API An API for efficiently processing large amounts of data. Compute shader A compute kernel managed by a rendering API, with easy access to rendering resources. Cone tracing Modification of ray tracing which instead of lines uses cones as rays in order to achieve e.g. antialiasing or soft shadows. Connectivity information Indices defining [rendering primitive]s between vertices, possibly held in index buffers. describes geometry as a graph or hypergraph. CSG Constructive solid geometry, a method for generating complex solid models from boolean operations combining simpler modelling primitives. Cube mapping A form of environment reflection mapping in which the environment is captured on a surface of a cube (cube map). Culling Before rendering begins, culling removes objects that don't significantly contribute to the rendered result (e.g. being obscured or outside camera view). == D == Decal A "sticker" picture applied onto a surface (e.g. a
The Life and Times of Multivac
"The Life and Times of Multivac" is a science fiction short story by American writer Isaac Asimov. The story first appeared in the 5 January 1975 issue of The New York Times Magazine, and was reprinted in the collections The Bicentennial Man and Other Stories and The Best of Creative Computing in 1976. It is one of a loosely connected series of stories concerning a fictional supercomputer called Multivac. "The Life and Times of Multivac" was the first piece of fiction ever commissioned and published by The New York Times. Asimov's original title for the story was "Mathematical Games", but after the story appeared under the new title he decided he liked it. In his commentary on the story in The Bicentennial Man and Other Stories collection, Asimov stated, "More people came up to me over the next few weeks to tell me they had read that story than had ever been the case for any other story I had ever written." == Plot summary == When humanity begins to chafe under Multivac’s benevolent tyranny, one man takes matters into his own hands to destroy the great computer. By appearing to betray his fellow humans, he places himself in a position to permanently destroy Multivac. It is implied that it is not until completion of the act that he and his peers suddenly realize the enormity of their actions and the consequences it will have on humanity.
Artificial intelligence in customer experience
Artificial intelligence in customer experience is the use and development of artificial intelligence (AI) to aid and improve customer experience (sometimes abbreviated to CX AI). Chatbots are often seen as the first step in the development of AI within the industry, but more tailored offerings are slowly becoming available. The use of artificial intelligence in the space has since become more diverse than simply chatbots, with AI underpinning entire CX cloud platforms now used at major corporations. Contact center as a service (CCaaS) has become a core solution of the CX (customer experience) industry, with the CCaaS market size expected to reach $17.19 Billion by 2030 in the United States alone. == History == As with many AI applications, CX AI early implementation case studies have demonstrated that AI can increase the quality of customer interactions and therefore the overall experience that organizations can provide. This in turn has suggested a higher return on investment and/or revenue as a result. The beginning of the revolution of customer experience and the use of machine learning was with chatbots. The use of this type of AI can be traced back to Alan Turing in 1950, when the Church–Turing thesis suggested that computers could use "formal reasoning" to reach conclusions. In 2017, Meta produced one of the first breakthroughs for everyday use of AI for customer experience when it allowed Facebook users to create their own messaging bots for free on its Facebook messenger platform. The main focus of this was to both automate and improve customer experience and interaction. In 2023, CCaaS vendors began announcing the integration of ChatGPT’s generative AI into their CX solutions. Generative AI adds a layer of semantics into AI outputs. This was a major breakthrough for conversational AI. Using natural language processing and conversational AI, chatbots could enhance the level of service they could provide, speaking to customers in an easy-to-understand and conversational tone. == Applications == Currently the main location for the application of CX AI in the sector is in contact centers. Historically, contact centers were simply known as call centers, but in recent years differentiation developed between the two terms. Call centers provide phone support, while contact centers also provide support via digital channels in addition to analogue phone systems. Contact centers are therefore seen as a complete customer service solution, where as call centers simply cover one aspect of customer interactions. As a part of improving CX, AI is also improving the employee experience. AI is able to automate tasks to free up time for contact center agents to focus on higher priority tasks. For example, AI can be used for auto summarization. This means that instead of human agents having to summarize customer interactions now AI can do it, saving organizations time and money.
India AI Impact Summit 2026
The India AI Impact Summit 2026 (also abbreviated as the AI Impact Summit) was an international summit on artificial intelligence held at Bharat Mandapam, New Delhi, India, from 16 to 21 February 2026. It is the fourth in a series of global AI summits following the Bletchley Park AI Safety Summit in 2023, the AI Seoul Summit in 2024, and the AI Action Summit in Paris in 2025. Organised under the IndiaAI Mission by the Ministry of Electronics and Information Technology, it is the first summit in the series to be hosted by a Global South nation. This series of AI summits will continue with the AI Summit in Geneva to be hosted by Switzerland in 2027. The summit was inaugurated by Prime Minister Narendra Modi on 19 February 2026. The opening ceremony was also addressed by French President Emmanuel Macron and United Nations Secretary-General António Guterres. The summit was attended by over 20 heads of state and a delegation of global technology leaders including Sundar Pichai (Google), Sam Altman (OpenAI), and Demis Hassabis (DeepMind). The event faced criticism for organisational issues, misrepresentation of non-Indian products as Indian, and a perceived focus on trade fair activities over substantive governance. == Background == The AI Impact Summit was an international summit on artificial intelligence (AI) held in New Delhi from 16 to 20 February 2026. It followed the AI Action Summit in Paris in February 2025, the AI Seoul Summit in 2024 and the Bletchley Park AI Safety Summit in 2023. According to Crowell & Moring, the changing summit titles seemed to reflect a broader shift in focus away from AI safety and governance toward practical impact, implementation, and measurable outcomes. Ahead of the summit, an international panel of experts published the second International AI Safety Report. The summit was structured around three foundational pillars, termed "Sutras": People, Planet, and Progress. Seven thematic working groups were established to deliver outcomes across these pillars, covering AI for economic growth and social good; democratising AI resources; inclusion for social empowerment; safe and trusted AI; human capital; science; and resilience, innovation, and efficiency. == Programme == The summit ran over five days, later extended to six following overwhelming public response. Originally scheduled to conclude on 20 February, the event was extended to 21 February with expanded evening hours for the exhibition. === India AI Impact Expo === The India AI Impact Expo, inaugurated by Prime Minister Modi on 16 February, featured over 300 exhibitors from 30 countries across more than 10 thematic pavilions. Pavilions were organised across thematic zones aligned with the summit's three pillars, showcasing AI applications in healthcare, agriculture, education, and sustainable industry. === Leaders' Plenary and CEO Roundtable === The Leaders' Plenary on 19 February brought together heads of state, ministers, and representatives from multilateral institutions to outline national and global priorities on AI governance, infrastructure, and international cooperation. A CEO Roundtable, held the same evening, convened senior executives from global technology and industry firms with government leaders to discuss investment, research collaboration, and deployment of AI systems. === Research Symposium === A Research Symposium on AI and its Impact was held on 18 February, with the IIIT Hyderabad as knowledge partner. Discussions covered sovereign AI infrastructure, global adoption challenges, research breakthroughs, and policy priorities. == Participants == The summit drew delegations from over 100 countries, including more than 20 heads of state and 60 ministers. Notable attendees from the technology industry included Sundar Pichai (Google), Sam Altman (OpenAI), Dario Amodei (Anthropic), Demis Hassabis (Google DeepMind), and Mukesh Ambani (Reliance Industries). Representatives from multilateral institutions included Sangbu Kim of the World Bank. == Announcements and outcomes == === Indian AI models === Several Indian AI models and products were unveiled during the summit. Sarvam AI, an Indian AI laboratory, launched a new generation of large language models, including 30-billion and 105-billion parameter models using a mixture of experts architecture, as well as text-to-speech, speech-to-text, and vision models. Sarvam also introduced the Kaze smartglasses, described as the company's first hardware product, which Prime Minister Modi tested at the expo. The government-backed BharatGen Param2 model, a 17-billion parameter model supporting 22 Indian languages with multimodal capabilities, was also launched at the summit. === Infrastructure commitments === Union Minister Ashwini Vaishnaw outlined India's "whole-of-nation" AI strategy, describing plans to build a "frugal, sovereign and scalable" AI ecosystem. The government announced plans to add more than 20,000 GPUs to India's existing base of 38,000 under the IndiaAI Compute Portal. Microsoft announced at the summit that it was on track to invest US$50 billion by the end of the decade to bring AI to lower-income countries. Goa reaffirmed its commitment to artificial intelligence at the India AI Impact Summit 2026. === Guinness World Record === During the summit, India set a Guinness World Record for the most pledges received for an AI responsibility campaign in 24 hours, with 250,946 valid pledges collected between 16 and 17 February 2026. The campaign, conducted in partnership with Intel India as part of the IndiaAI Mission, exceeded its initial target of 5,000 pledges. == Controversies and criticisms == === Galgotias University incident === On 18 February, Galgotias University faced widespread criticism after a representative presented a robot dog at the university's exhibition pavilion as an indigenous development. Social media users identified the robot as the Unitree Go2, a commercially available product manufactured by Chinese company Unitree Robotics. IT Secretary S. Krishnan stated that the government did not want exhibitors to showcase items that were not their own, and the university was directed to vacate its stall. Galgotias University issued an apology, stating that the representative had been "ill-informed" and was not authorised to speak to the press. The incident drew political reactions, with the Indian National Congress using it to criticise the government. The controversy was amplified after Union IT Minister Ashwini Vaishnaw had earlier shared a video clip of the robot on social media, which was subsequently deleted. === Organisational issues === On day 1 of the Summit, Dhananjay Yadav, a Bengaluru-based entrepreneur had alleged that his product was stolen in the Summit. He called it as a pain for the people in an X post. He further wrote, "Think about this: We paid for flights, accommodation, logistics and even the booth. Only to see our wearables disappear inside a high-security zone". Later, the stolen devices were recovered by The Delhi Police. Bloomberg reported that delegates were left stranded without food or water during a security lockdown ahead of the Prime Minister's visit on 19 February. The summit venue was closed to the public on 19 February for the Prime Minister's visit, leading to criticism from attendees who had registered for that day. === Protests by the Indian Youth Congress (IYC) === On 20 February, some members of the Indian Youth Congress (IYC) carried out protests inside the venue with slogans such as "PM is compromised" and the criticism of the recent trade deal between India and the US. 4 of these members were sent to police custody by the court on 22 February. While Bharatiya Janta Party condemned these protests, with its spokesperson Shehzad Poonawalla saying, "From being anti-BJP, you have gone to being anti-national? If you have a problem with the BJP, then protest at the BJP office, Jantar Mantar, or outside the PM's office. But the people of the country and their alliance partners condemn them for their attempt to defame India in front of the entire world at the AI Summit." Congress leader Harish Rawat defended the protests, saying "it's also a fact that AI might become a tool in the hands of a few individuals… It's the opposition's job to warn against that… It's not the first time such international events have been opposed. I know how the BJP protested during the Commonwealth Games… To say that such opposition has happened for the first time is not correct. The BJP has been doing this while in the opposition." These protestors were granted bail by the Delhi high court on 2 March. == Reception and analysis == Bloomberg News reported that Prime Minister Modi used the summit to assert India's global AI ambitions following a challenging year in foreign policy. TechPolicy.Press published several critical analyses of the summit. One article argued that the summit's structure granted "multinational corporations parity with sovereign governments
Himmat (app)
Himmat is a women's safety mobile application of Delhi Police. It was launched by Home Minister Rajnath Singh on 1 January 2015. The app is freely available for Android mobile phones and can be downloaded from Delhi Police website. Delhi Police plans to launch app for other platforms in future. Low registrations and other problems resulted in a parliamentary panel calling the app a failure in 2018. Himmat has gone on to be called as one of India's best safety apps for women.
Random-fuzzy variable
In measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed. But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. This systematic error can be approximately modeled based on our past data about the measuring instrument and the process. Statistical methods can be used to calculate the total uncertainty from both systematic and random contributions in a measurement. However, the computational complexity is very high, and hence not desirable. L.A.Zadeh introduced the concepts of fuzzy variables and fuzzy sets. Fuzzy variables are based on the theory of possibility and hence are possibility distributions. This makes them suitable to handle any type of uncertainty, i.e., both systematic and random contributions to the total uncertainty. Random-fuzzy variable (RFV) is a type 2 fuzzy variable, defined using the mathematical possibility theory, used to represent the entire information associated to a measurement result. It has an internal possibility distribution and an external possibility distribution called membership functions. The internal distribution is the uncertainty contributions due to the systematic uncertainty and the bounds of the RFV are because of the random contributions. The external distribution gives the uncertainty bounds from all contributions. == Definition == A random-fuzzy Variable (RFV) is defined as a type 2 fuzzy variable which satisfies the following conditions: Both the internal and the external functions of the RFV can be identified. Both the internal and the external functions are modeled as possibility distributions (PD). Both the internal and external functions have a unitary value for possibility to the same interval of values. An RFV can be seen in the figure. The external membership function is the distribution in blue and the internal membership function is the distribution in red. Both the membership functions are possibility distributions. Both the internal and external membership functions have a unitary value of possibility only in the rectangular part of the RFV. Therefore, all three conditions have been satisfied. If there are only systematic errors in the measurement, then the RFV simply becomes a fuzzy variable which consists of just the internal membership function. Similarly, if there is no systematic error, then the RFV becomes a fuzzy variable with just the random contributions and therefore, is just the possibility distribution of the random contributions. == Construction == A random-fuzzy variable can be constructed using an internal possibility distribution (rinternal) and a random possibility distribution (rrandom). === The random distribution (rrandom) === rrandom is the possibility distribution of the random contributions to the uncertainty. Any measurement instrument or process suffers from random error contributions due to intrinsic noise or other effects. This is completely random in nature and is a normal probability distribution when several random contributions are combined according to the central limit theorem. However, there can also be random contributions from other probability distributions, such as a uniform distribution, gamma distribution and so on. The probability distribution can be modeled from the measurement data. Then, the probability distribution can be used to model an equivalent possibility distribution using the maximally specific probability-possibility transformation. Some common probability distributions and the corresponding possibility distributions can be seen in the figures. === The internal distribution (rinternal) === rinternal is the internal distribution in the RFV which is the possibility distribution of the systematic contribution to the total uncertainty. This distribution can be built based on the information that is available about the measuring instrument and the process. The largest possible distribution is the uniform or rectangular possibility distribution. This means that every value in the specified interval is equally possible. This actually represents the state of total ignorance according to the theory of evidence which means it represents a scenario in which there is maximum lack of information. This distribution is used for the systematic error when we have absolutely no idea about the systematic error except that it belongs to a particular interval of values. This is quite common in measurements. However, in certain cases, it may be known that certain values have a higher or lower degrees of belief than certain other values. In this case, depending on the degrees of belief for the values, an appropriate possibility distribution could be constructed. === The construction of the external distribution (rexternal) and the RFV === After modeling the random and internal possibility distribution, the external membership function, rexternal, of the RFV can be constructed by using the following equation: where x ∗ {\displaystyle x^{}} is the mode of r random {\displaystyle r_{\textit {random}}} , which is the peak in the membership function of r r a n d o m {\displaystyle r_{random}} and Tmin is the minimum triangular norm. RFV can also be built from the internal and random distributions by considering the α-cuts of the two possibility distributions (PDs). An α-cut of a fuzzy variable F can be defined as Therefore, essentially an α-cut is the set of values for which the value of the membership function μ F ( a ) {\displaystyle \mu _{\rm {F}}(a)} of the fuzzy variable is greater than α. This gives the upper and lower bounds of the fuzzy variable F for each α-cut. The α-cut of an RFV, however, has 4 specific bounds and is given by R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} . X a α {\displaystyle X_{a}^{\alpha }} and X d α {\displaystyle X_{d}^{\alpha }} are the lower and upper bounds respectively of the external membership function (rexternal) which is a fuzzy variable on its own. X b α {\displaystyle X_{b}^{\alpha }} and X c α {\displaystyle X_{c}^{\alpha }} are the lower and upper bounds respectively of the internal membership function (rinternal) which is a fuzzy variable on its own. To build the RFV, let us consider the α-cuts of the two PDs i.e., rrandom and rinternal for the same value of α. This gives the lower and upper bounds for the two α-cuts. Let them be [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} and [ X L I α , X U I α ] {\displaystyle [X_{LI}^{\alpha },X_{UI}^{\alpha }]} for the random and internal distributions respectively. [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} can be again divided into two sub-intervals [ X L R α , x ∗ ] {\displaystyle [X_{LR}^{\alpha },x^{}]} and [ x ∗ , X U R α ] {\displaystyle [x^{},X_{UR}^{\alpha }]} where x ∗ {\displaystyle x^{}} is the mode of the fuzzy variable. Then, the α-cut for the RFV for the same value of α, R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} can be defined by Using the above equations, the α-cuts are calculated for every value of α which gives us the final plot of the RFV. A random-fuzzy variable is capable of giving a complete picture of the random and systematic contributions to the total uncertainty from the α-cuts for any confidence level as the confidence level is nothing but 1-α. An example for the construction of the corresponding external membership function (rexternal) and the RFV from a random PD and an internal PD can be seen in the following figure.