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Role of Computational Intelligence in Natural Language Processing
Published in Brojo Kishore Mishra, Raghvendra Kumar, Natural Language Processing in Artificial Intelligence, 2020
Bishwa Ranjan Das, Brojo Kishore Mishra
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 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. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by LotfiZadeh. Fuzzy logic had however been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. It is based on the observation that people make decisions based on imprecise and non-numerical information, fuzzy models or sets are mathematical means of representing vagueness and imprecise information, hence the term fuzzy. These models have the capability of recognizing, representing, manipulating, interpreting, and utilizing data and information that are vague and lack certainty.
Fuzzy Sets and Mathematical Fuzzy Logic Basics
Published in Umberto Straccia, Foundations of Fuzzy Logic and Semantic Web Languages, 2016
In the setting of many-valued logics (see also [172, 183]), the convention prescribing that a statement is either true or false is changed and is a matter of degree measured on an ordered scale that is no longer {0,1}, but [0,1]. The conceptual shift reflects the shift from classical crisp sets to fuzzy sets. For example, the compatibility of “tall” in the phrase “a tall man” with some individual of a given height is often graded: the man can be judged not quite tall, somewhat tall, rather tall, very tall, etc. Changing the usual true/false convention leads to a new concept of statements, whose compatibility with a given state of facts is a matter of degree and can be measured on an ordered scale 𝒮 that is no longer {0,1}, but, e.g., the unit interval [0,1]. This leads to identifying “fuzzy statements” ϕ with a fuzzy set of possible states of affairs; the degree of membership of a state of affairs to this fuzzy set evaluates the degree of fit between the statement and the state of facts it refers to. This degree of fit is called degree of truth of the statement ϕ in the interpretation ℐ (state of affairs). Many-valued logics provide compositional calculi of degrees of truth, including degrees between “true” and “false that correspond to the fuzzy set operations of conjunction, union, and negation. So, a sentence is now not true or false only, but may have a truth degree taken from a truth space𝒮, usually [0,1] or Ln for an integer n ≥ 3. In the sequel, we assume 𝒮 = [0,1].
FUZZY LOGIC
Published in Kumar S. Ray, Soft Computing and Its Applications, Volume One, 2014
Fuzzy logic is a polyvalent logic which is based upon another many-valued calculus. A mathematical relationship between Fuzzy Logic and many-valued logics can be stated as a fuzzy logic calculus is a logic, in which the truth-values are fuzzy subsets of the set of truth-values of a non-fuzzy many-valued logic. A simple many-valued logic has a fix number of truth values (3, 4, ..., n), while a Fuzzy Logic has a free number of truth values. It is the user's choice to select the number of truth values he wants to consider. The user finds the truth-values of the fuzzy system inside the evaluation set of the many-valued calculus, which is the basis of the fuzzy system. This freedom in the choice, of how many truth-values are to employ, makes Fuzzy Logic a very popular technique to treat the complex phenomena.
An inverse dynamics based fuzzy adaptive state-feedback controller for a nonlinear 3DOF manipulator
Published in International Journal of Modelling and Simulation, 2023
M. J. Mahmoodabadi, N. Nejadkourki
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. This branch of mathematics is employed to handle the concept of partial truth where it may change between completely true and completely false. The term fuzzy logic was introduced in 1965 with the proposal of the fuzzy set theory by Lotfi Zadeh [15]. Generally, it is based on this observation that people make decisions based on imprecise and non-numerical information. Moreover, in order to apply human knowledge for developing the control operation, the fuzzy logic is the only possible way. The following examples are only some of the research works performed in the field of fuzzy-logic-based control techniques. Ye et al. have proposed fuzzy control of hydrogen pressure in a fuel cell system [16]. Phu and Hung have investigated minimum stability control and time-optimal control problems for fuzzy linear control systems [17]. Mu et al. have introduced an intelligent position control for a pneumatic servo system based on predictive fuzzy methods [18]. Fakhr Shamloo et al. have examined indirect adaptive fuzzy control for nonlinear descriptor systems [19]. Mahmoodabadi and Ziaei have inspected an inverse dynamics based optimal fuzzy controller for a robot manipulator via particle swarm optimization [20]. Zhang et al. have studied command filter-based finite-time adaptive fuzzy control for nonlinear systems having uncertain disturbances [21].
Logical dual concepts based on mathematical morphology in stratified institutions: applications to spatial reasoning
Published in Journal of Applied Non-Classical Logics, 2019
The algebraic structures underlying many-valued logic, fuzzy (or more generally L-fuzzy) logic, are usually residuated lattices. Residuated lattices (Ward & Dilworth, 1938) generalise Boolean algebras for classical logic by considering a set of truth values which may contain more than two values or that are not necessarily scalar values.
Fusion of ASTER satellite imagery, geochemical and geology data for gold prospecting in the Astaneh granite intrusive, West Central Iran
Published in International Journal of Image and Data Fusion, 2022
Hooman Moradpour, Ghodratollah Rostami Paydar, Bakhtiar Feizizadeh, Thomas Blaschke, Amin Beiranvand Pour, Khalil Valizadeh Kamran, Aidy M Muslim, Mohammad Shawkat Hossain
The FLM is based on the fuzzy set theory, which was proposed by Zadeh (1965). It 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 (Novák et al. 1999). A fuzzy set of A is a set of ordered pairs:A={(x,μA(x))|xϵX}(3)