Generalized intuitionistic fuzzy laplace transform and its application in electrical circuit

In this paper we describe the generalized intuitionistic fuzzy laplace transform method for solving first order generalized intutionistic fuzzy differential equation. The procedure is applied in imprecise electrical circuit theory problem. Here the initial condition of those applications is taken as Generalized Intuitionistic triangular fuzzy numbers (GITFNs).Publisher's Versio

Interval type-2 intuitionistic fuzzy logic system for time series and identification problems - a comparative study

This paper proposes a sliding mode control-based learning of interval type-2 intuitionistic fuzzy logic system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and hybrid method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of interval type-2 intuitionistic fuzzy logic systems. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted using both real world and artificially generated datasets. Analysis of results reveals that the proposed interval type-2 intuitionistic fuzzy logic system trained with sliding mode control learning algorithm (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models

Derivatives and indefinite integrals of single valued neutrosophic functions

With the continuous development of the fuzzy set theory, neutrosophic set theory can better solve uncertain, incomplete and inconsistent information. As a special subset of the neutrosophic set, the single-valued neutrosophic set has a significant advantage when the value expressing the degree of membership is a set of finite discrete numbers. Therefore, in this paper, we first discuss the change values of single-valued neutrosophic numbers when treating them as variables and classifying these change values with the help of basic operations. Second, the convergence of sequences of single-valued neutrosophic numbers are proposed based on subtraction and division operations. Further, we depict the concept of single-valued neutrosophic functions (SVNF) and study in detail their derivatives and differentials. Finally, we develop the two kinds of indefinite integrals of SVNF and give the relevant examples

Plithogeny, Plithogenic Set, Logic, Probability, and Statistics

In this book we introduce for the first time, as generalization of dialectics and neutrosophy, the philosophical concept called plithogeny. And as its derivatives: the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic logics), plithogenic probability (as generalization of classical, imprecise, and neutrosophic probabilities), and plithogenic statistics (as generalization of classical, and neutrosophic statistics). Plithogeny is the genesis or origination, creation, formation, development, and evolution of new entities from dynamics and organic fusions of contradictory and/or neutrals and/or non-contradictory multiple old entities. Plithogenic Set is a set whose elements are characterized by one or more attributes, and each attribute may have many values. An attribute’s value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x, v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set/logic/probability and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement/inclusion/equality are influenced by the attribute values’ contradiction (dissimilarity) degrees. Formal definitions of plithogenic set/logic/probability/statistics are presented into the book, followed by plithogenic aggregation operators, various theorems related to them, and afterwards examples and applications of these new concepts in our everyday life

Approximation Theory and Related Applications

In recent years, we have seen a growing interest in various aspects of approximation theory. This happened due to the increasing complexity of mathematical models that require computer calculations and the development of the theoretical foundations of the approximation theory. Approximation theory has broad and important applications in many areas of mathematics, including functional analysis, differential equations, dynamical systems theory, mathematical physics, control theory, probability theory and mathematical statistics, and others. Approximation theory is also of great practical importance, as approximate methods and estimation of approximation errors are used in physics, economics, chemistry, signal theory, neural networks and many other areas. This book presents the works published in the Special Issue "Approximation Theory and Related Applications". The research of the world’s leading scientists presented in this book reflect new trends in approximation theory and related topics

Soft Computing

Soft computing is used where a complex problem is not adequately specified for the use of conventional math and computer techniques. Soft computing has numerous real-world applications in domestic, commercial and industrial situations. This book elaborates on the most recent applications in various fields of engineering

Fuzzy Systems

This book presents some recent specialized works of theoretical study in the domain of fuzzy systems. Over eight sections and fifteen chapters, the volume addresses fuzzy systems concepts and promotes them in practical applications in the following thematic areas: fuzzy mathematics, decision making, clustering, adaptive neural fuzzy inference systems, control systems, process monitoring, green infrastructure, and medicine. The studies published in the book develop new theoretical concepts that improve the properties and performances of fuzzy systems. This book is a useful resource for specialists, engineers, professors, and students

Soft Computing

Soft computing is used where a complex problem is not adequately specified for the use of conventional math and computer techniques. Soft computing has numerous real-world applications in domestic, commercial and industrial situations. This book elaborates on the most recent applications in various fields of engineering