30 research outputs found
An exact algorithm for linear optimization problem subject to max-product fuzzy relational inequalities with fuzzy constraints
Fuzzy relational inequalities with fuzzy constraints (FRI-FC) are the
generalized form of fuzzy relational inequalities (FRI) in which fuzzy
inequality replaces ordinary inequality in the constraints. Fuzzy constraints
enable us to attain optimal points (called super-optima) that are better
solutions than those resulted from the resolution of the similar problems with
ordinary inequality constraints. This paper considers the linear objective
function optimization with respect to max-product FRI-FC problems. It is proved
that there is a set of optimization problems equivalent to the primal problem.
Based on the algebraic structure of the primal problem and its equivalent
forms, some simplification operations are presented to convert the main problem
into a more simplified one. Finally, by some appropriate mathematical
manipulations, the main problem is transformed into an optimization model whose
constraints are linear. The proposed linearization method not only provides a
super-optimum (that is better solution than ordinary feasible optimal
solutions) but also finds the best super-optimum for the main problem. The
current approach is compared with our previous work and some well-known
heuristic algorithms by applying them to random test problems in different
sizes.Comment: 29 pages, 8 figures, 7 table
An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases
Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation
Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists
This book introduces the concept of fuzzy super matrices and operations on
them. This book will be highly useful to social scientists who wish to work
with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy
Relational Maps, Bidirectional Associative Memories and Fuzzy Associative
Memories are defined here. The authors introduce 13 multi-expert models using
the notion of fuzzy supermatrices. These models are described with illustrative
examples. This book has three chapters. In the first chaper, the basic concepts
about super matrices and fuzzy super matrices are recalled. Chapter two
introduces the notion of fuzzy super matrices adn their properties. The final
chapter introduces many super fuzzy multi expert models.Comment: 280 page
Quantum Exotic PDE's
Following the previous works on the A. Pr\'astaro's formulation of algebraic
topology of quantum (super) PDE's, it is proved that a canonical Heyting
algebra ({\em integral Heyting algebra}) can be associated to any quantum PDE.
This is directly related to the structure of its global solutions. This allows
us to recognize a new inside in the concept of quantum logic for microworlds.
Furthermore, the Prastaro's geometric theory of quantum PDE's is applied to the
new category of {\em quantum hypercomplex manifolds}, related to the well-known
Cayley-Dickson construction for algebras. Theorems of existence for local and
global solutions are obtained for (singular) PDE's in this new category of
noncommutative manifolds. Finally the extension of the concept of exotic PDE's,
recently introduced by A.Pr\'astaro, has been extended to quantum PDE's. Then a
smooth quantum version of the quantum (generalized) Poincar\'e conjecture is
given too. These results extend ones for quantum (generalized) Poincar\'e
conjecture, previously given by A. Pr\'astaro.Comment: 52 page
Mathematical Logic: Proof Theory, Constructive Mathematics (hybrid meeting)
The Workshop "Mathematical Logic: Proof Theory,
Constructive Mathematics" focused on
proofs both as formal derivations in deductive systems as well as on
the extraction of explicit computational content from
given proofs in core areas of ordinary mathematics using proof-theoretic
methods. The workshop contributed to the following research strands: interactions between foundations and applications; proof mining; constructivity in classical logic; modal logic and provability logic; proof theory and theoretical computer science; structural proof theory