Fuzzy Mappings Research Articles

Algorithm of solutions for mixed implicit quasi-variational inequalities with fuzzy mappings

In this paper, by applying the auxiliary variational principle technique, some existence theorems of solutions for a class of mixed implicit quasi-variational inequalities with fuzzy mappings are proved in Hilbert spaces. A novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed. The convergence criteria is also given. As special cases of these results, the open problem put forward by Noor is answered positively. Our results are new and generalize a number of known results to mixed implicity quasi-variational inequalities with fuzzy mappings.

Random generalized nonlinear variational inclusions for random fuzzy mappings

In this paper, we introduce and study a new class of random set-valued nonlinear generalized variational inclusions with noncompact-valued random fuzzy mappings and construct a new iterative algorithm. We also discuss the existence of random solutions for this class of random fuzzy variational inclusions and the convergence of random iterative sequences generated by the algorithm.

Fubini theorem for generalized fuzzy number-valued integrals

In this paper we introduce the notion of generalized fuzzy numbers and generalized fuzzy mappings, and give Fubini theorem for integrals of generalized fuzzy mappings.

On convex and concave fuzzy mappings

In this paper we introduce the concepts of convex subsets of F 0, the set of all fuzzy numbers, and monotonic fuzzy mappings on R 2 and show that a monotonic fuzzy mapping F on a convex set C ⊆ R 1 or R 2 is quasi-convex and quasi-concave. We establish two characterizations for convex fuzzy mappings, and two characterizations for concave fuzzy mappings. We also prove the least upper bound property.

Vector quasivariational inequalities for fuzzy mappings (II)

This paper is devoted to study the vector variational inequalities for fuzzy mappings. By using the Fan-Browder fixed point theorem, the selection theorem of Yannelis-Prabhakar [13] and the scalarization method of Luc [9,10], some existence theorems for our inequalities are proved.

Preinvex fuzzy mappings

In this paper, we introduce the concepts of preinvex fuzzy mappings, quasi-preinvex fuzzy mappings, and invex sets by modifying the concepts proposed by Noor. We also give two characterization theorems for preinvex fuzzy mappings, and present some new results for preinvex fuzzy mappings, strictly preinvex fuzzy mappings, and quasi-preinvex fuzzy mappings.

Composition, cartesian and direct products of fuzzy multivalued mappings

Fuzzy multivalued mappings have been introduced as a natural extension of classical multivalued mappings. Our previous work has been devoted to the extension of the images of sets under a multivalued mapping to the fuzzy case. The direct image and the lower inverse image under a fuzzy multivalued mapping have been modelled using the degree of compatibility of fuzzy sets defined from a triangular norm. For the upper inverse image three different definitions have been proposed using the concept of a fuzzy inclusion defined from an implication operator. In this paper, we introduce composition, cartesian and direct products of fuzzy multivalued mappings and study their properties. A special attention is paid to the expressions for the images under the products of fuzzy multivalued mappings. For the composition the properties of the images in terms of cuts are also studied. The cartesian and direct products are defined for two fuzzy multivalued mappings. Using the concept of a diagonal of a fuzzy multivalued mapping, the interesting relationship between them is established. The possible extension of these products to a finite number of fuzzy multivalued mappings is discussed, as well. Finally, examples of five families of implication operators, defined from a triangular norm, and that satisfy the imposed conditions are presented.

Generalized strongly quasivariational inequalities for fuzzy mappings

In this paper, we prove an existence theorem of solutions and develop the algorithms of approximating solutions for a generalized strongly variational inequality for fuzzy mappings and a generalized strongly complementaryty problemsfor fuzzy mappings by using the projection method.

Generalized mildly nonlinear complementarity problems for fuzzy mappings

In this paper, we introduce and study a new class of generalized mildly nonlinear complementarity problems for fuzzy mappings. We use the change of variables technique to establish the equivalence between the generalized mildly nonlinear complementarity problems and the Wiener-Hopf equations. This equivalence is used to suggest and analyze a number of iterative algorithm for solving the generalized mildly nonlinear complementarity problems.

Representation of fuzzy-valued mappings by the sequence of single-valued mappings

In this paper the analysis focusses on the important classes of fuzzy-valued mappings: • - measurable fuzzy-valued mappings, • - integrable fuzzy-valued mappings. Our aim is to discuss the problem of representation of such mappings by countable family of single-valued mappings. This is a most useful result, since it provides us with a remarkable list of alternative definitions, criteria and proofs of theorems related to this type of fuzzy mappings.

A common fixed point theorem for a pair of fuzzy mappings

In this paper, we obtain a common fixed point theorem for a pair of fuzzy mappings, which is a generalization of the results of Bose and Sahani, and Lee and Cho.

Continuity of fuzzy multifunctions

We define the upper and lower inverse of a fuzzy multifunction and prove basic identities. Then by using these ideas we introduce the concept of hemicontinuity and obtain many interesting properties of lower and upper hemicontinuous fuzzy multifunctions. Using the notion of hemicontinuity, we also characterize closed and open fuzzy mappings.

Variational inequalities for fuzzy mappings (II)

In this paper, we establish the equivalence between the variational inequalities for fuzzy mappings and the Wiener-Hopf equations for fuzzy mappings. We use this equivalence to suggest a number of new iterative algorithms for solving the variational inequalities for fuzzy mappings. We also study the convergence criteria of these iterative algorithms. The auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution. The results proved in this paper represent an improvement of previously known results.

A new class of random completely generalized strongly nonlinear quasi-complementarity problems for random fuzzy mappings

In this paper, we introduce and study a new class of random completely generalized strongly nonlinear quasi - complementarity problems with non-compact valued random fuzzy mappings and construct some new iterative algorithms for this kind of random fuzzy quasi-complementarity problems. We also prove the existence of random solutions for this class of random fuzzy quasicomplementarity problems and the convergence of random iterative sequences generated by the algorithms.

Continuity of fuzzy multivalued mappings

Continuity of multivalued mappings is characterized by two types of semi-continuity: lower and upper semi-continuity. In this paper, different equivalent ways in which these concepts can be expressed are investigated and then used to define lower and upper semi-continuous fuzzy multivalued mappings. Some shortcomings in existing definitions of upper semi-continuous multivalued mappings are addressed. Several relationships between the lower semi-continuity of fuzzy multivalued mappings and the classical lower semi-continuity of their cuts, or the lower semi-continuity w.r.t. the level topologies are established in the setting of stratified fuzzy topological spaces. Two different types of upper semi-continuity of fuzzy multivalued mappings are introduced, inspired by the two equivalent ones in the crisp case. The relationships between these two types are studied completely. Many interesting properties of lower and upper semi-continuous fuzzy multivalued mappings are presented, including the composition and union of lower and upper semi-continuous fuzzy multivalued mappings and the compactness preserving property of upper semi-continuous and compact-valued fuzzy multivalued mappings.

Properties of b-vex fuzzy mappings and applications to fuzzy optimization

Convexity plays a key role in operations research and fuzzy optimization theory. The concept of b-vex and logarithmic b-vex for fuzzy mappings is introduced by relaxing the definition of convexity of a fuzzy mapping. Most of the basic properties of b-vex fuzzy mapping are discussed and established for the nondifferentiable case. Necessary and sufficient conditions for b-vex fuzzy mapping are presented. Several important results are given for nonlinear fuzzy optimization problems assuming that objective and constraint functions are b-vex fuzzy mappings.

A new method for a class of nonlinear variational inequalities with fuzzy mappings

In this paper, we construct a new iterative algorithm of solution for a new class of nonlinear variational inequalities with fuzzy mappings and give some convergence analysis of iterative sequences generated by algorithm.

Completely generalized mildly nonlinear complementarity problems for fuzzy mappings

In this paper, we introduce and study a new class of completely generalized mildly nonlinear complementarity problems for fuzzy mappings and construct some new iterative algorithms. We also show the existence of solution and the convergence of iterative sequences generated by the algorithms. Our results extend some recent results of Noor, Chang and Huang.

Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings

In this paper, we consider the implicit quasi-variational inequality without continuity assumptions of data mappings. Our approach here is completely different from the one based on KKM theorem in the literature. Interesting applications to generalized quasi-variational inequalities for both discontinuous mappings and discontinuous fuzzy mappings are given.

Fixed degree and fixed point theorems for fuzzy mappings in probabilistic metric spaces

This paper introduces the concept and properties of fixed degrees for fuzzy mappings in probabilistic metric spaces. By virtue of this concept, some theorems about common fixed degree of a sequence of fuzzy mappings in probabilistic metric spaces are obtained. These new results are a unified approach to generalize several fixed point theorems for fuzzy mappings.