Topic
Operator (computer programming)
About: Operator (computer programming) is a research topic. Over the lifetime, 40896 publications have been published within this topic receiving 671452 citations. The topic is also known as: operator symbol & operator name.
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TL;DR: A new branch of Atanassov's intuitionistic fuzzy set (AIFS) theory, where some new operations of AIFSs, such as Einstein sum, Einstein product, and Einstein scalar multiplication are introduced, are introduced as aggregation operators.
Abstract: Aggregation of fuzzy information is a new branch of Atanassov's intuitionistic fuzzy set (AIFS) theory, which has attracted significant interest from researchers in recent years. In this paper, we treat the intuitionistic fuzzy aggregation operators with the help of Einstein operations. We first introduce some new operations of AIFSs, such as Einstein sum, Einstein product, and Einstein scalar multiplication. Then, we develop some intuitionistic fuzzy aggregation operators, such as the intuitionistic fuzzy Einstein weighted averaging operator and the intuitionistic fuzzy Einstein ordered weighted averaging operator, which extend the weighted averaging operator and the ordered weighted averaging operator to aggregate Atanassov's intuitionistic fuzzy values, respectively. We further establish various properties of these operators and analyze the relations between these operators and the existing intuitionistic fuzzy aggregation operators. Moreover, we give some numerical examples to illustrate the developed aggregation operators. Finally, we apply the intuitionistic fuzzy Einstein weighted averaging operator to multiple attribute decision making with intuitionistic fuzzy information.
313 citations
Book•
31 Jan 2001
TL;DR: In this paper, the authors present a simple and direct presentation of the fundamental aspects of the theory of fractional powers of non-negative operators, which have important links with partial differential equations and harmonic analysis.
Abstract: This is a simple and direct presentation of the fundamental aspects of the theory of fractional powers of non-negative operators, which have important links with partial differential equations and harmonic analysis. The first chapters are concerned with the construction of a basic theory of fractional powers and study the classic questions in that respect. The bulk of the second part of the book is dedicated to powers with pure imaginary exponents, which have been the focus of research since the publication in 1987 of the paper by G. Dore and A. Venni. Special care has been taken to give versions of the results with more accurate hypotheses, particularly with respect to the density of the domain or the range of the operator. The authors have made a point of making the text clear and self-contained.
313 citations
TL;DR: While S- and C-operators are optimised for the representation of 1-D features such as edges and lines, the end-stopped operator responses at the key-points make explicit 2-D signal variations such as line ends, corners and segments of strong curvature.
312 citations
TL;DR: The proposed consensus operator provides an alternative consensus model for group decision making and preserves the original preference information given by the decision makers as much as possible, and supports consensus process automatically, without moderator.
311 citations
Posted Content•
TL;DR: The notion of vertex operator superalgebras was introduced in this paper, where it was shown that any local system of vertex operators on a super vector space has a natural vertex (super)algebra structure with $M$ as a module.
Abstract: We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of ``local system of vertex operators'' for a (super) vector space. We first prove that any local system of vertex operators on a (super) vector space $M$ has a natural vertex (super)algebra structure with $M$ as a module. Then we prove that for a vertex (operator) superalgebra $V$, giving a $V$-module $M$ is equivalent to giving a vertex (operator) superalgebra homomorphism from $V$ to some local system of vertex operators on $M$. As applications, we prove that certain lowest weight modules for some well-known infinite-dimensional Lie algebras or Lie superalgebras have natural vertex operator superalgebra structures. We prove the rationality of vertex operator superalgebras associated to standard modules for an affine algebra. We also give an analogue of the notion of the space of linear homomorphisms from one module to another for a Lie algebra by introducing a notion of ``generalized intertwining operators.'' We prove that $G(M^{1},M^{2})$, the space of generalized intertwining operators from one module $M^{1}$ to another module $M^{2}$ for a vertex operator superalgebra $V$, is a generalized $V$-module. Furthermore, we prove that for a fixed vertex operator superalgebra $V$ and
311 citations