Fuzzy sets, uncertainty, and information
Fuzzy sets, uncertainty, and information
Approximate solutions of fuzzy relational equations
Fuzzy Sets and Systems
Fuzzy relation equations theory as a basis of fuzzy modelling: an overview
Fuzzy Sets and Systems - Special memorial volume on fuzzy logic and uncertainly modelling
Processing in relational structures: fuzzy relational equations
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Solving fuzzy relational equations through logical filtering
Fuzzy Sets and Systems
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Solution algorithms for fuzzy relational equations with max-product composition
Fuzzy Sets and Systems
Solving fuzzy relation equations with a linear objective function
Fuzzy Sets and Systems
Generalized solvability behaviour for systems of fuzzy equations
Discovering the world with fuzzy logic
Optimization of fuzzy relation equations with max-product composition
Fuzzy Sets and Systems
Solving nonlinear optimization problems with fuzzy relation equation constraints
Fuzzy Sets and Systems
Resolution of composite fuzzy relation equations based on Archimedean triangular norms
Fuzzy Sets and Systems
Fuzzy Control and Fuzzy Systems
Fuzzy Control and Fuzzy Systems
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Multi-objective optimization problems with fuzzy relation equation constraints
Fuzzy Sets and Systems - Special issue: Optimization and decision support systems
Generalized variational inequalities with fuzzy relation
Journal of Computational and Applied Mathematics - Special issue: Papers presented at the 1st Sino--Japan optimization meeting, 26-28 October 2000, Hong Kong, China
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 Optimization and Decision Making
Fuzzy Relation Equations (II): The Branch-point-solutions and the Categorized Minimal Solutions
Soft Computing - A Fusion of Foundations, Methodologies and Applications
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition
Fuzzy Optimization and Decision Making
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
On the relation between equations with max-product composition and the covering problem
Fuzzy Sets and Systems
An efficient solution procedure for fuzzy relation equations with max-product composition
IEEE Transactions on Fuzzy Systems
An accelerated approach for solving fuzzy relation equations with a linear objective function
IEEE Transactions on Fuzzy Systems
Matrix-pattern-based computer algorithm for solving fuzzy relation equations
IEEE Transactions on Fuzzy Systems
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This paper studies the optimization model of a linear objective function subject to a system of fuzzy relation inequalities (FRI) with the max-Einstein composition operator. If its feasible domain is non-empty, then we show that its feasible solution set is completely determined by a maximum solution and a finite number of minimal solutions. Also, an efficient algorithm is proposed to solve the model based on the structure of FRI path, the concept of partial solution, and the branch-and-bound approach. The algorithm finds an optimal solution of the model without explicitly generating all the minimal solutions. Some sufficient conditions are given that under them, some of the optimal components of the model are directly determined. Some procedures are presented to reduce the search domain of an optimal solution of the original problem based on the conditions. Then the reduced domain is decomposed (if possible) into several sub-domains with smaller dimensions that finding the components of the optimal solution in each sub-domain is very easy. In order to obtain an optimal solution of the original problem, we propose another more efficient algorithm which combines the first algorithm, these procedures, and the decomposition method. Furthermore, sufficient conditions are suggested that under them, the problem has a unique optimal solution. Also, a comparison between the recently proposed algorithm and the known ones will be made.