Orlovsky's concept of decision-making with fuzzy preference relation—Further results
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Fuzzy modeling with tolerances
Fuzzy Sets and Systems
On the construction of fuzzy eigen solutions in given regions
Fuzzy Sets and Systems
Fuzzy reasoning and fuzzy relational equations
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Two families of fuzzy integrals
Fuzzy Sets and Systems
Fuzzy sets, uncertainty, and information
Fuzzy sets, uncertainty, and information
Canonical form of a strongly transitive fuzzy matrix
Fuzzy Sets and Systems
On matrix equations in a class of complete and completely distributive lattices
Fuzzy Sets and Systems
On direct and inverse problems for fuzzy equation systems with tolerances
Fuzzy Sets and Systems
Further contributions to the study of finite fuzzy relations equations
Fuzzy Sets and Systems
Information Sciences: an International Journal - Application of Fuzzy Set Theory
Application of fuzzy sets of type 2 to the solution of fuzzy equation systems
Fuzzy Sets and Systems
The fuzzy relation equation with union or intersection preserving operator
Fuzzy Sets and Systems
Further relation equations with equality and difference composition operators
Fuzzy Sets and Systems
Fuzzy Sets and Systems
To what extent does `decomposable' mean `transitive' for a fuzzy relation?
Fuzzy Sets and Systems
On the existence of minimal solutions for fuzzy equations with tolerances
Fuzzy Sets and Systems
On solving relational equations in Brouwerian lattices
Fuzzy Sets and Systems
On some finite fuzzy relation equations
Information Sciences: an International Journal
A general purpose fuzzy inference mechanism based on coimplication
Fuzzy Sets and Systems
Solving linear and quadratic fuzzy 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
Coimplication and its application to fuzzy expert systems
Information Sciences: an International Journal
Solutions of algebraic equations involving generalized fuzzy numbers
Information Sciences: an International Journal
Minimax algebra and applications
Fuzzy Sets and Systems
Solving systems of linear fuzzy equations
Fuzzy Sets and Systems
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
On fuzzy implication operators
Fuzzy Sets and Systems
Strict preference relations based on weak t-norms
Fuzzy Sets and Systems - Special issue: Aggregation and best choices of imprecise opinions
Resolution of composite interval-valued fuzzy relation equations
Fuzzy Sets and Systems
A new algorithm for the greatest solution of fuzzy bilinear equations
Fuzzy Sets and Systems
Fuzzy Sets and Systems
Information Sciences: an International Journal
A new look at fuzzy connectives
Fuzzy Sets and Systems
General decomposition problem of fuzzy relations
Fuzzy Sets and Systems
s-t fuzzy relational equations
Fuzzy Sets and Systems
Strong regularity of matrices: a survey of results
Discrete Applied Mathematics
Information Sciences: an International Journal
Fuzzy Sets and Systems - Special issue on diagnostics and control through neural interpretations of fuzzy sets
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Residuation in fuzzy algebra and some applications
Fuzzy Sets and Systems
Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
Cut technique in valued relational systems: mainsprings and applications
Fuzzy Sets and Systems - Special issue: fuzzy relations, part 2
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
Equations in classes of fuzzy relations
Fuzzy Sets and Systems - Special issue: fuzzy relations, part 2
On transitive solutions of fuzzy equations, inequalities and lower approximations of fuzzy relations
Fuzzy Sets and Systems - Special issue: fuzzy relations, part 2
Fuzzy relational structures: the state-of-art
Fuzzy Sets and Systems - Special issue: fuzzy relations, part 2
Fuzzy Sets and Systems
Linear independence in bottleneck algebras
Fuzzy Sets and Systems
Structures on intuitionistic fuzzy relations
Fuzzy Sets and Systems
Convergence, eigen fuzzy sets and stability analysis of relational matrices
Fuzzy Sets and Systems
Truth-qualification and fuzzy relations in natural languages, application to medical diagnosis
Fuzzy Sets and Systems - Special issue dedicated to the memory of Professor Arnold Kaufmann
Convex combinations of generalized fuzzy relational equations
Fuzzy Sets and Systems
Some properties of minimal solutions for a fuzzy relation equation
Fuzzy Sets and Systems
The min-max composition rule and its superiority over the usual max-min composition rule
Fuzzy Sets and Systems
Composite fuzzy relational equations with non-commutative conjunctions
Information Sciences—Informatics and Computer Science: An International Journal - Special issue on modeling with soft-computing
Unattainable solutions of a fuzzy relation equation
Fuzzy Sets and Systems
Intuitionistic fuzzy sets and L-fuzzy sets
Fuzzy Sets and Systems
Generalized solvability behaviour for systems of fuzzy equations
Discovering the world with fuzzy logic
Compositions of fuzzy relations based on aggregation operator and its pseudocomplement
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - special issue on measures and aggregation: formal aspects and applications to clustering and decision
Method of solution to fuzzy equations in a complete Brouwerian lattice
Fuzzy Sets and Systems
Lattice functions and equations
Lattice functions and equations
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Contrapositive symmetry of distributive fuzzy implications
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Transitive Solutions of Relational Equations on Finite Sets and Linear Lattices
IPMU '90 Proceedings of the 3rd International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems: Uncertainty in Knowledge Bases
On the relationship between some extensions of fuzzy set theory
Fuzzy Sets and Systems - Theme: Basic notions
Pseudo-t-norms and implication operators on a complete Brouwerian lattice
Fuzzy Sets and Systems - Possibility theory and fuzzy logic
Disjunctive optimization, max-separable problems and extremal algebras
Theoretical Computer Science
Associative aggregation operators
Aggregation operators
When (S,N)-implications are (T,T1)-conditional functions?
Fuzzy Sets and Systems - Implication operators
On the composition of intuitionistic fuzzy relations
Fuzzy Sets and Systems - Theme: Basic concepts
Solution Sets of Interval-Valued Min-S-Norm Fuzzy Relational Equations
Fuzzy Optimization and Decision Making
A systematic approach to the assessment of fuzzy association rules
Data Mining and Knowledge Discovery
Fuzzy Applications in Industrial Engineering (Studies in Fuzziness and Soft Computing)
Fuzzy Applications in Industrial Engineering (Studies in Fuzziness and Soft Computing)
Resolution of fuzzy relation equations (I) based on boolean-type implications
Computers & Mathematics with Applications
Dioïds and semirings: Links to fuzzy sets and other applications
Fuzzy Sets and Systems
Some properties of infinite fuzzy relational equations on complete Brouwerian lattices
Fuzzy Sets and Systems
On the characterizations of (S,N)-implications
Fuzzy Sets and Systems
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
Resolution of matrix equations over arbitrary Brouwerian lattices
Fuzzy Sets and Systems
An algorithm for solving fuzzy relation equations with max-T composition operator
Information Sciences: an International Journal
Infinite fuzzy relation equations with continuous t-norms
Information Sciences: an International Journal
Computers & Mathematics with Applications
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition
Fuzzy Optimization and Decision Making
(S, N)- and R-implications: A state-of-the-art survey
Fuzzy Sets and Systems
Graphs, Dioids and Semirings: New Models and Algorithms (Operations Research/Computer Science Interfaces Series)
System of fuzzy relation equations with inf-→ composition: Complete set of solutions
Fuzzy Sets and Systems
On the first place antitonicity in QL-implications
Fuzzy Sets and Systems
On finite relation equations with sup-conjunctor composition over a complete lattice
Fuzzy Sets and Systems
A note on solution sets of interval-valued fuzzy relational equations
Fuzzy Optimization and Decision Making
Goguen Categories: A Categorical Approach to L-fuzzy Relations
Goguen Categories: A Categorical Approach to L-fuzzy Relations
A new kind of fuzzy relation equations based on inner transformation
Computers & Mathematics with Applications
Discussion: Some notes on (Atanassov's) intuitionistic fuzzy sets
Fuzzy Sets and Systems
Decomposition and resolution of fuzzy relation equations (II) based on boolean-type implications
AI'05 Proceedings of the 18th Australian Joint conference on Advances in Artificial Intelligence
Issues on adjointness in multiple-valued logics
Information Sciences: an International Journal
On various eigen fuzzy sets and their application to image reconstruction
Information Sciences: an International Journal
Solving interval-valued fuzzy relation equations
IEEE Transactions on Fuzzy Systems
On the representation of intuitionistic fuzzy t-norms and t-conorms
IEEE Transactions on Fuzzy Systems
A Survey on Fuzzy Implication Functions
IEEE Transactions on Fuzzy Systems
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition
Fuzzy Optimization and Decision Making
Journal of Computational and Applied Mathematics
Latticized linear optimization on the unit interval
IEEE Transactions on Fuzzy Systems
Interval valued fuzzy coimplication
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
On fuzzy relational equations and the covering problem
Information Sciences: an International Journal
On the unique solvability of fuzzy relational equations
Fuzzy Optimization and Decision Making
Fuzzy Optimization and Decision Making
Spatial analysis with a tool GIS via systems of fuzzy relation equations
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part II
Randomly generating test problems for fuzzy relational equations
Fuzzy Optimization and Decision Making
Spatial analysis and fuzzy relation equations
Advances in Fuzzy Systems - Special issue on Fuzzy Functions, Relations, and Fuzzy Transforms: Theoretical Aspects and Applications to Fuzzy Systems
Fuzzy equations max-* with conditionally cancellative operations
Information Sciences: an International Journal
Mathematical and Computer Modelling: An International Journal
Novel approximate solving algorithm for fuzzy relational equations
Mathematical and Computer Modelling: An International Journal
Fuzzy relational equations with min-biimplication composition
Fuzzy Optimization and Decision Making
Supplier selection using axiomatic fuzzy set and TOPSIS methodology in supply chain management
Fuzzy Optimization and Decision Making
Linear optimization with an arbitrary fuzzy relational inequality
Fuzzy Sets and Systems
Resolution of fuzzy relational equations - Method, algorithm and software with applications
Information Sciences: an International Journal
Resolution of a system of the max-product fuzzy relation equations using LºU-factorization
Information Sciences: an International Journal
Image matching by using fuzzy transforms
Advances in Fuzzy Systems - Special issue on Fuzzy Functions, Relations, and Fuzzy Transforms 2013
An algorithm for solving optimization problems with fuzzy relational inequality constraints
Information Sciences: an International Journal
Aggregating fuzzy implications
Information Sciences: an International Journal
Interval-valued fuzzy coimplications and related dual interval-valued conjugate functions
Journal of Computer and System Sciences
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Fuzzy relational equations play an important role in fuzzy set theory and fuzzy logic systems, from both of the theoretical and practical viewpoints. The notion of fuzzy relational equations is associated with the concept of "composition of binary relations." In this survey paper, fuzzy relational equations are studied in a general lattice-theoretic framework and classified into two basic categories according to the duality between the involved composite operations. Necessary and sufficient conditions for the solvability of fuzzy relational equations are discussed and solution sets are characterized by means of a root or crown system under some specific assumptions.