Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1 both inclusive. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1.
In mathematics, fuzzy sets are somewhat like sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh and Dieter Klaua in 1965 as an extension of the classical notion of set. At the same time, Salii (1965) defined a more general kind of structure called an L-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are used now in different areas, such as linguistics, decision-making, and clustering, are special cases of L-relations when L is the unit interval [0, 1].
Computational archaeology describes computer-based analytical methods for the study of long-term human behaviour and behavioural evolution. As with other sub-disciplines that have prefixed 'computational' to their name, the term is reserved for methods that could not realistically be performed without the aid of a computer.
Lotfi Aliasker Zadeh was a mathematician, computer scientist, electrical engineer, artificial intelligence researcher and professor emeritus of computer science at the University of California, Berkeley.
Soft computing, as opposed to traditional computing, deals with approximate models and gives solutions to complex real-life problems. Unlike hard computing, soft computing is tolerant of imprecision, uncertainty, partial truth, and approximations. In effect, the role model for soft computing is the human mind. It was conceived by Lotfi Zadeh, pioneer of a mathematical concept known as fuzzy sets which led to many new fields such as fuzzy control systems, fuzzy graph theory, fuzzy systems, and so on. Zadeh observed that people are good at 'soft' thinking while computers typically are 'hard' thinking. People use concepts like 'some', 'most', or 'very' rather than 'hard' or precise concepts of 3.5 or 102. People want a 'warm' glass of milk, not one that is 102 degrees. In general, people are good at learning, finding patterns, adapting and are rather unpredictable. In 'hard' computing, by contrast, machines need precision, determinism and measures, and although pattern recognition happens, there is a 'brittleness' if things change - it cannot easily adapt. 'Soft' computing by contrast embraces chaotic, neural models of computing that are more pliable. Because there is no known single method that lets us compute like people, soft computing involves using a combination of methods that each bring something helpful to achieve this goal. The principal constituents of Soft Computing (SC) are Fuzzy Logic (FL), Evolutionary Computation (EC), Machine Learning (ML) and Probabilistic Reasoning (PR), with the latter subsuming belief networks and parts of learning theory.
The expression computational intelligence (CI) usually refers to the ability of a computer to learn a specific task from data or experimental observation. Even though it is commonly considered a synonym of soft computing, there is still no commonly accepted definition of computational intelligence.
Joseph Amadee Goguen was a US computer scientist. He was professor of Computer Science at the University of California and University of Oxford and held research positions at IBM and SRI International.
A fuzzy concept is a concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether. It has a definite meaning, which can be made more precise only through further elaboration and specification - including a closer definition of the context in which the concept is used. The study of the characteristics of fuzzy concepts and fuzzy language is called fuzzy semantics. The inverse of a "fuzzy concept" is a "crisp concept".
Imprecise probability generalizes probability theory to allow for partial probability specifications, and is applicable when information is scarce, vague, or conflicting, in which case a unique probability distribution may be hard to identify. Thereby, the theory aims to represent the available knowledge more accurately. Imprecision is useful for dealing with expert elicitation, because:
Mykhailo Zakharovych Zghurovskyi is a Ukrainian scientist. Mykhailo Zghurovsky is the President of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Scientific Supervisor of the Institute for Applied System Analysis, former Ukrainian education minister.
George Jiří Klir was a Czech-American computer scientist and professor of systems sciences at Binghamton University in Binghamton, New York.
Fuzzy mathematics forms a branch of mathematics related to fuzzy set theory and fuzzy logic. It started in 1965 after the publication of Lotfi Asker Zadeh's seminal work Fuzzy sets. A fuzzy subset A of a set X is a function A:X→L, where L is the interval [0,1]. This function is also called a membership function. A membership function is a generalization of a characteristic function or an indicator function of a subset defined for L = {0,1}. More generally, one can use a complete lattice L in a definition of a fuzzy subset A .
Type-2 fuzzy sets and systems generalize standard Type-1 fuzzy sets and systems so that more uncertainty can be handled. From the very beginning of fuzzy sets, criticism was made about the fact that the membership function of a type-1 fuzzy set has no uncertainty associated with it, something that seems to contradict the word fuzzy, since that word has the connotation of lots of uncertainty. So, what does one do when there is uncertainty about the value of the membership function? The answer to this question was provided in 1975 by the inventor of fuzzy sets, Prof. Lotfi A. Zadeh, when he proposed more sophisticated kinds of fuzzy sets, the first of which he called a type-2 fuzzy set. A type-2 fuzzy set lets us incorporate uncertainty about the membership function into fuzzy set theory, and is a way to address the above criticism of type-1 fuzzy sets head-on. And, if there is no uncertainty, then a type-2 fuzzy set reduces to a type-1 fuzzy set, which is analogous to probability reducing to determinism when unpredictability vanishes.
Perceptual computing is an application of Zadeh's theory of computing with words on the field of assisting people to make subjective judgments.
Probability bounds analysis (PBA) is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds. It is used to project partial information about random variables and other quantities through mathematical expressions. For instance, it computes sure bounds on the distribution of a sum, product, or more complex function, given only sure bounds on the distributions of the inputs. Such bounds are called probability boxes, and constrain cumulative probability distributions.
Cognitive city is a term which expands the concept of the smart city with the aspect of cognition or refers to a virtual environment where goal-driven communities gather to share knowledge. A physical cognitive city differs from conventional cities and smart cities in the fact that it is steadily learning through constant interaction with its citizens through advanced information and communications technologies (ICT) based ICT standards like IFGICT & ITU and that, based on this exchange of information, it becomes continuously more efficient, more sustainable and more resilient. A virtual cognitive city differs from social media platforms and project management platforms in that shared data is critical for the group’s performance, and the community consists of members spanning diverse expertise, backgrounds, motivations, and geographies but with a common desire to solve large problems. The virtual cognitive city is steadily learning through constant metadata generated by activity in the user community.
Romano Scozzafava is an Italian mathematician known for his contributions to subjective probability along the lines of Bruno de Finetti, based on the concept of coherence. He taught Probability Calculus at the Engineering Faculty of the Sapienza University of Rome from 1979 to his retirement.
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.
