Triangular norm (δ, γ) - fuzzy interior-ideals of hemi rings and its properties

2021 ◽  
Author(s):  
X. Arul Selvaraj ◽  
J. Jayaraj ◽  
S. Rexlin Jeyakumari
Keyword(s):  
Triangular Norm

scholarly journals Triangular Norm (δ, γ)-Fuzzy co-sets and Homomorphism

2021 ◽  
Vol 1724 (1) ◽  
pp. 012002
Author(s):  
J Jayaraj ◽  
X Arul Selvaraj
Keyword(s):  
Triangular Norm

A PRIMER ON SOLVING FUZZY RELATIONAL EQUATIONS ON THE UNIT INTERVAL

1994 ◽  
Vol 02 (02) ◽  
pp. 205-225 ◽  
Author(s):  
BERNARD DE BAETS ◽  
ETIENNE E. KERRE
Keyword(s):  
Unit Interval ◽  
Triangular Norm ◽  
Fuzzy Relational Equations ◽  
Number Of Publications

This paper has to be considered as a guide to solving fuzzy relational equations on the unit interval. Although the number of publications on this topic is quite impressive, there doesn't seem to exist a handy structured overview of all types of equations and their solution procedures. Our overview starts with a thorough treatment of [Formula: see text] equations and systems of [Formula: see text] equations, with [Formula: see text] a continuous triangular norm. It is shown that these are the basic problems: all other equations, image and composition equations, can be reduced to these problems. We do not only structure well-known results, we also present some new insights in the solution procedures of fuzzy relational equations.

scholarly journals Solvability of a Bounded Parametric System in Max-Łukasiewicz Algebra

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 1026 ◽  
Author(s):  
Martin Gavalec ◽  
Zuzana Němcová
Keyword(s):  
Linear System ◽  
Fuzzy Systems ◽  
Polynomial Algorithm ◽  
Sufficient Conditions ◽  
Recognition Algorithm ◽  
Triangular Norm ◽  
Binary Operations ◽  
Interval Coefficients ◽  
Necessary And Sufficient ◽  
The Given

The max-Łukasiewicz algebra describes fuzzy systems working in discrete time which are based on two binary operations: the maximum and the Łukasiewicz triangular norm. The behavior of such a system in time depends on the solvability of the corresponding bounded parametric max-linear system. The aim of this study is to describe an algorithm recognizing for which values of the parameter the given bounded parametric max-linear system has a solution—represented by an appropriate state of the fuzzy system in consideration. Necessary and sufficient conditions of the solvability have been found and a polynomial recognition algorithm has been described. The correctness of the algorithm has been verified. The presented polynomial algorithm consists of three parts depending on the entries of the transition matrix and the required state vector. The results are illustrated by numerical examples. The presented results can be also applied in the study of the max-Łukasiewicz systems with interval coefficients. Furthermore, Łukasiewicz arithmetical conjunction can be used in various types of models, for example, in cash-flow system.

FUZZY RELATION CALCULUS IN THE COMPRESSION AND DECOMPRESSION OF FUZZY RELATIONS

2002 ◽  
Vol 02 (04) ◽  
pp. 617-631 ◽  
Author(s):  
VINCENZO LOIA ◽  
WITOLD PEDRYCZ ◽  
SALVATORE SESSA
Keyword(s):  
Lossy Compression ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Triangular Norm ◽  
Fuzzy Matrix ◽  
Fuzzy Relation Equations

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.

Generalized Archimedean Intuitionistic Fuzzy Averaging Aggregation Operators and their Application to Multicriteria Decision-Making

2016 ◽  
Vol 15 (02) ◽  
pp. 311-352 ◽  
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Multiple Criteria Decision Making ◽  
Multicriteria Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Triangular Norm ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Averaging Operator ◽  
Fuzzy Aggregation

Aggregation operators play a key role in multiple criteria decision-making (MCDM). Extensions of aggregation operators to intuitionistic fuzzy sets (IFSs) usually involve replacing the standard arithmetic operations with those defined over the membership and nonmembership of IFS, which is essentially a pair of special Archimedean triangular norm (t-norm) and triangular conorm (t-conorm), called probabilistic sum t-conorm and product t-norm, on the membership and nonmembership of IFS, respectively. In this paper, we first introduce some operations on IFSs by means of Archimedean t-norm and t-conorm. Then some generalized Archimedean intuitionistic fuzzy aggregation operators are proposed, such as generalized Archimedean intuitionistic fuzzy weighted averaging operator, generalized Archimedean intuitionistic fuzzy ordered weighted averaging (GAIFOWA) operator, and generalized Archimedean intuitionistic fuzzy hybird averaging operator. Some desirable properties of these operators are investigated. The relations between these operators and the existing intuitionistic fuzzy aggregation operators are discussed. Finally, applying these proposed operators, we develop an approach for multi-criteria decision-making with intuitionistic fuzzy information, an illustrative example is used to verify the developed approach and to demonstrate its practicality and effectiveness.

Families of Triangular Norm-Based Kernel Functions and Their Application to Kernel k-Means

2017 ◽  
Vol 21 (3) ◽  
pp. 534-542
Author(s):  
Kazushi Okamoto ◽  
Keyword(s):  
Feature Space ◽  
Kernel Functions ◽  
Rand Index ◽  
Adjusted Rand Index ◽  
Data Sets ◽  
Linear Kernel ◽  
Triangular Norm ◽  
Higher Dimensional ◽  
Rbf Kernel ◽  
Map Data

This study proposes the concept of families of triangular norm (t-norm)-based kernel functions, and discusses their positive-definite property and the conditions for applicable t-norms. A clustering experiment with kernel k-means is performed in order to analyze the characteristics of the proposed concept, as well as the effects of the t-norm and parameter selections. It is evaluated that the clusters obtained in terms of the adjusted rand index and the experimental results suggested the following : (1) the adjusted rand index values obtained by the proposed method were almost the same or higher than those produced using the linear kernel for all of the data sets; (2) the proposed method slightly improved the adjusted rand index values for some data sets compared with the radial basis function (RBF) kernel; (3) the proposed method tended to map data to a higher dimensional feature space than the linear kernel but the dimension was lower than that using the RBF kernel.

Triangular norm based fuzzy $$BG$$ B G -algebras

2015 ◽  
Vol 27 (1-2) ◽  
pp. 187-199 ◽  
Author(s):  
Tapan Senapati ◽  
Monoranjan Bhowmik ◽  
Madhumangal Pal
Keyword(s):  
Triangular Norm

LIMIT T-NORMS AS A BASIS FOR THE CONSTRUCTION OF NEW T-NORMS

2001 ◽  
Vol 09 (02) ◽  
pp. 239-247 ◽  
Author(s):  
DANA SMUTNÁ
Keyword(s):  
Unit Interval ◽  
Triangular Norm ◽  
Full Characterization

Transformation of the Minimum t-norm TM by means of a non-decreasing transformation φ of the unit interval [0, 1] yielding triangular norm is studied. Full characterization of such φ is given. In the same spirit, transformations of the Drastic product TD are studied.

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