Solvability of fuzzy relational equations and manipulation of fuzzy data
Fuzzy Sets and Systems
Quotients with respect to similarity relations
Fuzzy Sets and Systems - Mathematics and Fuzziness, Part 1
Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
On fuzzy implication operators
Fuzzy Sets and Systems
Fuzzy sets and residuated logic
Fuzzy Sets and Systems
Algebraic structures in fuzzy logic
Fuzzy Sets and Systems
A new look at fuzzy connectives
Fuzzy Sets and Systems
Combination of rules or their consequences in fuzzy expert systems
Fuzzy Sets and Systems - Special issue on expert decision support systems
Contrapositive symmetry of fuzzy implications
Fuzzy Sets and Systems
The three semantics of fuzzy sets
Fuzzy Sets and Systems - Special issue: fuzzy sets: where do we stand? Where do we go?
Fuzzy Sets and Systems
Elements of intuitionistic fuzzy logic. Part I
Fuzzy Sets and Systems
Axiomatics for fuzzy rough sets
Fuzzy Sets and Systems
On generalized modus ponens with multiple rules and a residuated implication
Fuzzy Sets and Systems - Data bases and approximate reasoning
Propositional calculus under adjointness
Fuzzy Sets and Systems - Possibility theory and fuzzy logic
Observations on the monoidal t-norm logic
Fuzzy Sets and Systems - Possibility theory and fuzzy logic
A general method for constructing left-continuous t-norms
Fuzzy Sets and Systems - Theme: Basic concepts
Associatively tied implications
Fuzzy Sets and Systems - Theme: Basic concepts
A unified and extended framework for operator selection in generalized modus ponens type fuzzy reasoning
A small set of axioms for residuated logic
Information Sciences: an International Journal
Fuzzy relational equations with generalized connectives and their applications
Fuzzy Sets and Systems
Solutions of composite fuzzy relational equations with triangular norms
Fuzzy Sets and Systems
Multi-dimensional fuzzy reasoning
Fuzzy Sets and Systems
Mathematical fuzzy logic as a tool for the treatment of vague information
Information Sciences: an International Journal
Fuzzy modus ponens: A new model suitable for applications in knowledge-based systems
International Journal of Intelligent Systems
Implication operators in fuzzy logic
IEEE Transactions on Fuzzy Systems
Fuzzy Sets and Systems
Implication triples versus adjoint triples
IWANN'11 Proceedings of the 11th international conference on Artificial neural networks conference on Advances in computational intelligence - Volume Part II
A comparative study of adjoint triples
Fuzzy Sets and Systems
Simple proof of basic theorem for general concept lattices by cartesian representation
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
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A conjunction T ties an implication operator A if the identity A(a,A(b,z))=A(T(a,b),z) holds [A.A. Abdel-Hamid, N.N. Morsi, Associatively tied implications, Fuzzy Sets and Systems 136 (2003) 291-311]. We study the class of tied adjointness algebras (which are five-connective algebras on two partially ordered sets), in which the implications are tied by triangular norms. This class contains, besides residuated implications, several other implications employed in fuzzy logic. Nevertheless, we show that the algebraic inequalities of residuated algebras remain true for our tied implications, but in forms that distribute roles over the five connectives of the algebra. We apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules. We prove its equivalence to a scheme with one compound rule, when both schemata are interpreted by the compositional rule of inference, and all connectives are taken from one tied adjointness algebra. Then we quote another application of this rich theory, a notion of many-valued rough sets, which exhibit the basic mathematical behaviour of the rough sets of Pawlak. A comparator H is said to be prelinear if it satisfies H(y,z)@?H(z,y)=1 for all y,z (Hajek). We introduce prelinear tied adjointness algebras, in which two comparators are prelinear. We provide a representation of those algebras, as subdirect products of tied adjointness chains, on the lines of Hajek's representation of BL-algebras. But our representations are more economical, because we employ minimal prime filters (on residuated lattices) only; rather than all prime filters.