Results 141 to 150 of about 1,161 (186)

The logarithmic operational laws of intuitionistic fuzzy sets and intuitionistic fuzzy numbers

Journal of Intelligent & Fuzzy Systems, 2017
Intuitionistic fuzzy set (IFS) is an extension of fuzzy set. The basic element of an IFS is the ordered pair called intuitionistic fuzzy number (IFN). So far, some basic operational laws of IFNs are defined, but not including the logarithmic operation. In this paper, a logarithmic operational law about IFNs is defined, in which the
Zehua Li, Fuyi Wei
openaire   +1 more source

Intuitionistic Fuzzy Calculus Based on Einstein Operations

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2021
The intuitionistic fuzzy set (A-IFS) was introduced by Atanassov to generalize the concept of Zadeh’s fuzzy set. The basic elements of an A-IFS are the intuitionistic fuzzy numbers (IFNs). In this paper, we deal with the intuitionistic fuzzy set with the help of Einstein operations. First we introduce some operations of A-IFS, such as the Einstein sum,
Changhong Guo, Shaomei Fang
openaire   +1 more source

Induced generalized intuitionistic fuzzy operators

Knowledge-Based Systems, 2011
We study the induced generalized aggregation operators under intuitionistic fuzzy environments. Choquet integral and Dempster-Shafer theory of evidence are applied to aggregate inuitionistic fuzzy information and some new types of aggregation operators are developed, including the induced generalized intuitionistic fuzzy Choquet integral operators and ...
Zeshui Xu, Meimei Xia
openaire   +1 more source

Some operations on intuitionistic fuzzy sets

Fuzzy Sets and Systems, 2000
Let \(X\) be a nonempty fixed set (universe). An Intuitionistic Fuzzy Set (IFS) \(A\) is an object having the form \[ A=\biggl\{ \bigl\langle x, \mu_A(x), \nu_A(x) \bigr\rangle:x\in X\biggr\} \] where the functions \(\mu_A: X\to [0,1]\) and \(\nu_A: X\to[0,1]\) denote the degrees of membership and of non-membership of each element \(x\in X\) to set \(A\
Supriya Kumar De, Ranjit Biswas, Akhil Ranjan Roy   +2 more
openaire   +1 more source

Prioritized intuitionistic fuzzy aggregation operators

Information Fusion, 2013
In some multi-attribute decision making problems, distorted conclusions will be generated due to the lack of considering various relationships among the attributes of decision making. In this paper, we investigate the prioritization relationship of attributes in multi-attribute decision making with intuitionistic fuzzy information (i.e., partial or all
Xiaohan Yu 0004, Zeshui Xu
openaire   +1 more source

Intuitionistic Fuzzy Rough Approximation Operators Based on Intuitionistic Fuzzy Triangle Norm

2010 IEEE International Conference on Granular Computing, 2010
In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak’s rough approximations have been made in the literature over these years. This paper proposes a general framework for the study of intuitionistic fuzzy rough approximation operators based on
Renbing Lin, Jiyi Wang
openaire   +1 more source

On averaging operators for Atanassov’s intuitionistic fuzzy sets

Information Sciences, 2011
Let \(A =\{\langle x, \mu_{A}(x), \nu_{A}(x)\rangle\mid x \in E\}\) be an intuitionistic fuzzy set (IFS), where \(E\) is a given universe, the functions \(\mu_{A}: E \rightarrow [0,1]\) and \(\nu_{A}: E \rightarrow [0,1]\) define the degrees of membership and of non-membership of the element \(x\in E\) to the set \(A\), respectively, and for every \(x ...
Gleb Beliakov, Humberto Bustince Sola, D. P. Goswami, U. K. Mukherjee, Nikhil R. Pal   +4 more
openaire   +1 more source

Intuitionistic Fuzzy Rough Approximation Operators Determined by Intuitionistic Fuzzy Triangular Norms

2014
In this paper, relation-based intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy triangular norm T are investigated. By employing an intuitionistic fuzzy triangular norm T and its dual intuitionistic fuzzy triangular conorm, lower and upper approximations of intuitionistic fuzzy sets with respect to an ...
Wei-Zhi Wu 0001, Shen-Ming Gu, Tong-Jun Li, You-Hong Xu   +3 more
openaire   +1 more source

On Dual Intuitionistic Fuzzy Rough Approximation Operators Determined by an Intuitionistic Fuzzy Implicator

2013
In this paper, dual intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy implication operator ${\mathcal I}$ in infinite universes of discourse are investigated. Lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space in infinite universes of ...
Wei-Zhi Wu 0001, Cang-Jian Gao, Tong-Jun Li, You-Hong Xu   +3 more
openaire   +1 more source

On generalized intuitionistic fuzzy rough approximation operators

Information Sciences, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lei Zhou, Wei-Zhi Wu 0001
openaire   +2 more sources