An alternative approach to the resolution of fuzzy relation equations
Fuzzy Sets and Systems
Fuzzy Sets and Systems
On an algorithm for solving fuzzy linear systems
Fuzzy Sets and Systems
Unique solvability of max-min fuzzy equations and strong regularity of matrices over fuzzy algebra
Fuzzy Sets and Systems - Special issue: fuzzy relations, part 2
Solution algorithms for fuzzy relational equations with max-product composition
Fuzzy Sets and Systems
Resolution of composite fuzzy relation equations based on Archimedean triangular norms
Fuzzy Sets and Systems
New algorithms for solving fuzzy relation equations
Mathematics and Computers in Simulation
Automation and Remote Control
Some specific types of fuzzy relation equations
Information Sciences—Informatics and Computer Science: An International Journal
Fuzzy relation equations for coding/decoding processes of images and videos
Information Sciences—Informatics and Computer Science: An International Journal
Fuzzy Relation Equations (II): The Branch-point-solutions and the Categorized Minimal Solutions
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Łukasiewicz transform and its application to compression and reconstruction of digital images
Information Sciences: an International Journal
Algorithm for Solving Max-product Fuzzy Relational Equations
Soft Computing - A Fusion of Foundations, Methodologies and Applications
System of fuzzy relation equations as a continuous model of IF-THEN rules
Information Sciences: an International Journal
Solutions of fuzzy relation equations based on continuous t-norms
Information Sciences: an International Journal
Optimization of fuzzy relational equations with max-av composition
Information Sciences: an International Journal
Solution sets of fuzzy relational equations on complete Brouwerian lattices
Information Sciences: an International Journal
On the minimal solutions of max--min fuzzy relational equations
Fuzzy Sets and Systems
Information Sciences: an International Journal
An algorithm for solving fuzzy relation equations with max-T composition operator
Information Sciences: an International Journal
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition
Fuzzy Optimization and Decision Making
Information Sciences: an International Journal
Deriving minimal solutions for fuzzy relation equations with max-product composition
Information Sciences: an International Journal
A survey on fuzzy relational equations, part I: classification and solvability
Fuzzy Optimization and Decision Making
A new kind of fuzzy relation equations based on inner transformation
Computers & Mathematics with Applications
Solutions of composite fuzzy relational equations with triangular norms
Fuzzy Sets and Systems
On the relation between equations with max-product composition and the covering problem
Fuzzy Sets and Systems
Mathematical fuzzy logic as a tool for the treatment of vague information
Information Sciences: an International Journal
Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint
Information Sciences: an International Journal
On various eigen fuzzy sets and their application to image reconstruction
Information Sciences: an International Journal
A motion compression/reconstruction method based on max t-norm composite fuzzy relational equations
Information Sciences: an International Journal
An efficient solution procedure for fuzzy relation equations with max-product composition
IEEE Transactions on Fuzzy Systems
Matrix-pattern-based computer algorithm for solving fuzzy relation equations
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Novel approximate solving algorithm for fuzzy relational equations
Mathematical and Computer Modelling: An International Journal
Information Sciences: an International Journal
Resolution of a system of fuzzy polynomial equations using the Gröbner basis
Information Sciences: an International Journal
Some properties of infinite fuzzy relational equations with sup-inf composition
Information Sciences: an International Journal
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In this paper, the LU-factorization is extended to the fuzzy square matrix with respect to the max-product composition operator called L@?U-factorization. Equivalently, we will find two fuzzy (lower and upper) triangular matrices L and U for a fuzzy square matrix A such that A=L@?U, where ''@?'' is the max-product composition. An algorithm is presented to find the matrices L and U. Furthermore, some necessary and sufficient conditions are proposed for the existence and uniqueness of the L@?U-factorization for a given fuzzy square matrix A. An algorithm is also proposed to find the solution set of a square system of Fuzzy Relation Equations (FRE) using the L@?U-factorization. The algorithm finds the solution set without finding its minimal solutions and maximum solution. It is shown that the two algorithms have a polynomial-time complexity as O(n^3). Since the determination of the minimal solutions is an NP-hard problem, the algorithm can be very important from the practical point of view.