\(L\)-fuzzy sets and isomorphic lattices: are all the ``new results really new?

DOI10.3390/math6090146zbMath1402.03074OpenAlexW2888024370MaRDI QIDQ1634480

Publication date: 18 December 2018

Published in: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/math6090146

zbMATH Keywords

fuzzy set truth values interval-valued fuzzy set ``intuitionistic fuzzy set``Pythagorean fuzzy set isomorphic lattices

Mathematics Subject Classification ID

Theory of fuzzy sets, etc. (03E72) Other algebras related to logic (03G25) Structure theory of lattices (06B05)

Related Items

Residual implications on lattice \(\mathcal{L}\) of intuitionistic truth values based on powers of continuous t-norms ⋮ Aggregation on lattices isomorphic to the lattice of closed subintervals of the real unit interval ⋮ NEW DIRECTIONS IN FUZZY MATHEMATICS

Cites Work

A class of fuzzy multisets with a fixed number of memberships
Aggregation functions: means
Aggregation functions: construction methods, conjunctive, disjunctive and mixed classes
Structures on intuitionistic fuzzy relations
Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets
The algebra of fuzzy truth values
Uninorms in \(L^*\)-fuzzy set theory
Statistical metric spaces
Generalizing the L-fuzzy unit interval
Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued ``intuitionistic sets, ``intuitionistic fuzzy sets and topologies
Terminological difficulties in fuzzy set theory -- the case of ``intuitionistic fuzzy sets
Some notes on (Atanassov's) intuitionistic fuzzy sets
Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper ``Terminological difficulties in fuzzy set theory -- the case of ``intuitionistic fuzzy sets''
Triangle algebras: A formal logic approach to interval-valued residuated lattices
A representation of t-norms in interval-valued \(L\)-fuzzy set theory
The archimedean property for t-norms in interval-valued fuzzy set theory
Universes of fuzzy sets and axiomatizations of fuzzy set theory. II: Category theoretic approaches
A characterization of interval-valued residuated lattices
Characterizations of (weakly) Archimedean t-norms in interval-valued fuzzy set theory
Completion of L-fuzzy relations
L-fuzzy category
Intuitionistic fuzzy sets
Globalization of intuitionistic set theory
L-fuzzy normal spaces and Tietze extension theorem
Interval valued intuitionistic fuzzy sets
Representation theorems for L-fuzzy quantities
On L-fuzzy topological spaces
The concept of a linguistic variable and its application to approximate reasoning. I
Construction theorems for intuitionistic fuzzy sets
An introduction to intuitionistic fuzzy topological spaces
On the image of an \(L\)-fuzzy group
Elements of intuitionistic fuzzy logic. I
Remark on the intuitionistic fuzzy logics
Triangular norms on product lattices
On the \(L\)-fuzzy Brouwer fixed point theorem
Metamathematics of fuzzy logic
Remarks on the intuitionistic fuzzy sets
Monoidal t-norm based logic: Towards a logic for left-continuous t-norms
An equality between intuitionistic fuzzy sets
Vague sets are intuitionistic fuzzy sets
Uninorm aggregation operators
Triangular norms. Position paper I: Basic analytical and algebraic properties.
Residual implications and left-continuous t-norms which are ordinal sums of semigroups.
Triangular norms
Convergence of residuated operators and connective stability of non-classical logics
Some operations on intuitionistic fuzzy sets
Distances between intuitionistic fuzzy sets
Probabilistic topologies induced by \(L\)-fuzzy uniformities
On the predicate logics of continuous t-norm BL-algebras
Intuitionistic supra fuzzy topological spaces
A proof-theoretical investigation of global intuitionistic (fuzzy) logic
Intuitionistic fuzzy sets. Theory and applications
On the composition of intuitionistic fuzzy relations
More on intuitionistic fuzzy sets
Fuzzy addition in the L-fuzzy real line
Connectivity and the L-fuzzy unit interval
On the relationship between some extensions of fuzzy set theory
On intuitionistic gradation of openness
Observations on the monoidal t-norm logic
Triangular norms. Position paper II: General constructions and parameterized families
Triangular norms. Position paper III: Continuous t-norms
New operations defined over the intuitionistic fuzzy sets
Compactness in \(L\)-fuzzy topological spaces
\(L\)-fuzzy local compactness
Operators over interval valued intuitionistic fuzzy sets
On \(L\)-Tychonoff spaces
Remark on the cardinality of the intuitionistic fuzzy sets
Remarks on the intuitionistic fuzzy sets. III
Construction of intuitionistic fuzzy relations with predetermined properties
New family of triangular norms via contrapositive symmetrization of residuated implications
Axiomatic theory of intuitionistic fuzzy sets
Two theorems for intuitionistic fuzzy sets
Intuitionistic fuzzy sets and \(L\)-fuzzy sets
Residuated fuzzy logics with an involutive negation
The variety generated by the truth value algebra of type-2 fuzzy sets
On extensions of triangular norms on bounded lattices
New operations of picture fuzzy relations and fuzzy comprehensive evaluation
Arithmetic operators in interval-valued fuzzy set theory
Absorbent tuples of aggregation operators
Implicators based on binary aggregation operators in interval-valued fuzzy set theory
Picture fuzzy clustering: a new computational intelligence method
Universes of fuzzy sets and axiomatizations of fuzzy set theory. I: Model-based and axiomatic approaches
L-fuzzy sets
Quantitative fuzzy semantics
Sufficient triangular norms in many-valued logics with standard negation
L-Fuzzy Contiguity Relations andL-Fuzzy Closure Operators in the Case of Completely Distributive, Complete LatticesL
On theories and models in fuzzy predicate logics
Intuitionistic fuzzy logic and intuitionistic fuzzy set theory
On Fuzzy Logic II. Enriched residuated lattices and semantics of propositional calculi
Intervall-wertige Mengen
Fuzzy Membership Mapped onto Intervals and Many‐Valued Quantities
REPRESENTATION THEOREMS FOR FUZZY CONCEPTS
Vague sets
Entropy of L-fuzzy sets
A CATEGORY OF L-FUZZY CONVERGENCE SPACES
Pythagorean fuzzy Einstein weighted geometric aggregation operator and their application to multiple attribute group decision making
REPRESENTABILITY IN INTERVAL-VALUED FUZZY SET THEORY
Residuated logics based on strict triangular norms with an involutive negation
Fuzzy sets
CLASSES OF INTUITIONISTIC FUZZY T-NORMS SATISFYING THE RESIDUATION PRINCIPLE
Probabilistic Geometry
Statistical Metrics
Entropy for intuitionistic fuzzy sets.
The functional equations of Frank and Alsina for uninorms and nullnorms
An application of intuitionistic fuzzy sets in medical diagnosis
Decomposable measures and information measures for intuitionistic fuzzy sets
Aggregation operators. New trends and applications
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