Ketty Peeva

Fuzzy linear systems

Abstract Fuzzy linear systems of equations and inequalities over a bounded chain are studied both from theoretical and computational points of view. A unified approach is presented for solving such systems, completed with polynomial time algorithms. The main results are concerned with establishing the consistency of the system, computing all kinds of solutions, or marking the contradictory equations (respectively inequalities) if the system is inconsistent. Applications in fuzzy linear programming, multivalued logic, fuzzy matrix equations or inequalities, fuzzy relation equations or inclusions, fuzzy automata and medicine are presented.

Algorithm for Solving Max-product Fuzzy Relational Equations

Analytical methods are proposed for solving fuzzy linear system of equations when the composition is max-product. These methods provide universal algorithm for computing the greatest solution and the set of all minimal solutions, when the system is consistent. In case of inconsistency, the equations that can not be satisfied are obtained.

Fuzzy Relational Calculus: Theory, Applications and Software(With CD-ROM)

Fuzzy Relations. Direct Problem Resolution Fuzzy Relation Equations Fuzzy Relational Inclusions Fuzzy Linear Systems -- Dual Approach Direct and Inverse Problems in Intuitionistic Fuzzy Relational Calculus L-Fuzzy Finite Machines Fuzzy Languages in Syntactic Pattern Recognition Applications as Inference Engine Software Description

Finite L-fuzzy machines

Abstract For finite L -fuzzy machines we develop behaviour, reduction and minimization theory. Here L stands for ( L ,∨,∧,0,1), where L is a totally ordered set with universal bounds 0 and 1 and the operations are join ∨ and meet ∧. The most essential results include investigating behaviour, equivalence, reduction and minimization problems and their algorithmical decidability.

Behaviour, reduction and minimization of finite :G6-automata

Abstract Finite fuzzy automata over a bounded chain L ( L -automata) are studied in a natural manner including max-min fuzzy automata as a special case. The solvability of systems of linear equations over L is investigated. An algorithm for computing the behaviour matrix for each finite L -automaton is proposed. Using the behaviour matrices we can decide whether two L -automata have approximately the same behaviour, i.e. if an L -automaton makes an approximate model of the other. For this purpose approximate equivalence, reduction and minimization for finite L -automata are defined and completely studied. The paper arises as a refinement and natural extension of [2, 4, 7]. The results are valid for all finite L -automata and for a narrow class of stochastic automata.

Resolution of Min-Max Fuzzy Relational Equations

The paper provides methodology and polynomial time algorithm for inverse problem resolution for min-max fuzzy relational equations. An exact and universal method is presented for solving min-max fuzzy linear systems of equations, completed with polynomial time algorithm. The main results are concerned with establishing the consistency of the system, computing complete solution set if the system is consistent or marking the contradictory equations if the system is inconsistent. A method and algorithm for solving min-max fuzzy relational equations are proposed.

Optimization of Linear Objective Function under Fuzzy Equation Constraint in BL − Algebras – Theory, Algorithm and Software

We study optimization problem with linear objective function subject to fuzzy linear system of equations as constraint, when the composition is in f − − →in BL - algebra. The algorithm for solving fuzzy linear system of equations is provided by algebraic-logical properties of the solutions. We present algorithms for computing the extremal solutions of fuzzy linear system of equations and implement the results for solving the linear optimization problem.

Inverse problem resolution for min-probabilistic sum fuzzy relational equations — Method and algorithm

Analytical method and algorithm for inverse problem resolution of fuzzy linear systems of equations in case of min-probabilistic sum composition are presented.

Optimization of Linear Objective Function Under \min -Probabilistic Sum Fuzzy Linear Equations Constraint

We present here linear optimization problem resolution, when the cost function is subject to fuzzy linear systems of equations as constraint.

Intuitionistic Fuzzy Relational Equations in BL-Algebras

We investigate direct and inverse problem resolution for intuitionistic fuzzy relational equations in some \(BL-\)algebras, when the composition for the membership degrees is a \(\sup -t-\)norm and for non-membership degrees is an \(\inf -s-\)norm. Criterion for solvability of intuitionistic fuzzy relational equation is proposed and analytical expressions for maximal solution is given.