a class of convex fuzzy mappings based on the concept of ordering defined by goetschel and voxman fuzzy sets and systems 18 1996 31 in this paper we present the concepts of epigraph and convexity of the fuzzy mappings and describe characteristics of the convex fuzzy mappings and quasi convex fuzzy mappings then we discuss the properties of convex fuzzy optimizations

on integration of fuzzy mappings abstract in this paper we introduce the concept of an integral of a fuzzy mapping this generalises the integral introduced by matloka 10 and also extends riemann stieltjes integral over a closed interval to fuzzy mappings

invex and generalized convex fuzzy mappings in this paper we introduce the concepts of pseudo convexity invexity and pseudo invexity for fuzzy mappings of one variable based on the notion of differentiability proposed by goetschel and voxman 4 and investigate the relationship between convex fuzzy mappings preinvex fuzzy mappings and these classes of fuzzy mappings we shall prove that pseudo convex fuzzy mappings and invex fuzzy mappings are pseudo invex and that a differentiable convex resp preinvex fuzzy mapping is pseudo convex resp invex in addition sufficient optimality conditions are obtained for pseudo convex invex and pseudo invex fuzzy mappings

a note on generalized convexity for fuzzy mappings through a linear ordering in de campos ibanez and gonzalez munoz fuzzy sets syst 29 145 154 1989 6 goestschel and voxman fuzzy sets syst 18 31 43 1986 7 the authors considered a linear ordering on the space of fuzzy intervals for each fuzzy mapping fuzzy interval valued mapping f based on the aforementioned linear ordering they introduced a real valued function t f on the domain of the fuzzy mapping f recently chalco cano et al fuzzy sets syst 231 70 83 2013 4 have studied the relationship between the generalized hukuhara differentiability of a fuzzy mapping f g differentiability for short and the differentiability of t f and some properties of local global minima this paper studies such properties for fuzzy mappings using new concepts which generalize the existing ones

on the fuzzy initial value problem abstract the initial value problem x t f t x t x 0 x 0 with fuzzy initial value and with deterministic or fuzzy function f is considered two different approaches viz the extension principle and the use of extremal solutions of deterministic initial value problems are applied generalizations to fuzzy integral equations and fuzzy functional differential equations are indicated

generalized differentiability of fuzzy valued functions in the present paper using novel generalizations of the hukuhara difference for fuzzy sets we introduce and study new generalized differentiability concepts for fuzzy valued functions several properties of the new concepts are investigated and they are compared to similar fuzzy differentiabilities finding connections between them characterization and relatively simple expressions are provided for the new derivatives

convex fuzzy mapping with differentiability and its application in fuzzy optimization abstract the concepts of differentiability convexity generalized convexity and minimization of a fuzzy mapping are known in the literature the purpose of this present paper is to extend and generalize these concepts to fuzzy mappings of several variables using buckley feuring approach for fuzzy differentiation and derive karush kuhn tucker condition for the constrained fuzzy minimization problem

nonconvex fuzzy mappings and the fuzzy pre variational inequality in this paper we introduce the concepts of fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping from r n to the set of fuzzy numbers and put forward the concepts of fuzzy extended directional differential subgradient and subdifferential some properties are obtained for fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping relations are discussed between the fuzzy pre variational inequality and the fuzzy vector optimization problem

duality theory in fuzzy mathematical programming problems with fuzzy coefficients in this paper the notions of subgradient subdifferential and differential with respect to convex fuzzy mappings are investigated which provides the basis for the fuzzy extremum problem theory we consider the problems of minimizing or maximizing a convex fuzzy mapping over a convex set and develop the necessary and or sufficient optimality conditions furthermore the concept of saddle points and minimax theorems under fuzzy environment is discussed the results obtained are used to formulate the lagrangian dual of fuzzy programming under certain fuzzy convexity assumptions kkt conditions for fuzzy programming are derived and the perturbed convex fuzzy programming is considered finally these results are applied to fuzzy linear programming and fuzzy quadratic programming

generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equations the usual concept of differentiability of fuzzy number valued functions has the following shortcoming if c is a fuzzy number and g a b r is an usual real valued function differentiable on x 0 a b with g x 0 0 then f x c g x is not differentiable on x 0 in this paper we introduce and study generalized concepts of differentiability of any order n n which solves this shortcoming newton leibnitz type formula is obtained and existence of the solutions of fuzzy differential equations involving generalized differentiability is studied also some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c g x are given

directional derivatives and subdifferential of convex fuzzy mappings and application in convex fuzzy programming abstract in this paper we put forward the concepts of directional derivative differential and subdifferential of fuzzy mappings from r n into e 1 and discuss the characterizations of directional derivative and differential by respectively using the directional derivative and differential of two crisp functions that are determined by the fuzzy mapping and we also consider the problem of existence of directional derivative for convex fuzzy mappings and discuss the relations among directional derivative differential and subdifferential of fuzzy mappings at last we give two results of application in convex fuzzy programming

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

evaluate fuzzy optimization problems based on biobjective programming problems abstract the embedding theorem shows that the set of fuzzy numbers can be embedded into a banach space inspired by this embedding theorem we propose a solution concept of the fuzzy optimization problem by solving a biobjective optimization problem which is transformed from the original fuzzy optimization problem using the embedding theorem we then also consider the fuzzy optimization problem with fuzzy coefficients i e the coefficients are assumed to be fuzzy numbers under a setting of core values of fuzzy numbers we show that the optimal solution of its corresponding crisp optimization problem the usual optimization problem is also an optimal solution of the original fuzzy optimization problem

convexity and local lipschitz continuity of fuzzy valued mappings abstract two concepts of a convexity and a local lipschitz continuity are introduced into the class of fuzzy valued mappings the convexity is defined through the fuzzy max order on the class of fuzzy numbers the local lipschitz continuity of the fuzzy valued mapping cannot be defined in the same manner as in the case of the real valued function since the space of values of the fuzzy valued mapping is not a linear space owing to this reason the local lipschitz continuity is defined in a new formula through the fuzzy max order a fundamental theorem concerning the local lipschitz continuity of the fuzzy valued convex mapping is given

fuzzy weirstrass theorem and convex fuzzy mappings the convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers the local global minimum property of real valued convex functions is extended to convex fuzzy mappings it is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given in addition the weirstrass theorem is extended from real valued functions to fuzzy mappings

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

a subjective approach for ranking fuzzy numbers abstract starting from a subjective assignation of weights related to the relative importance of the different level sets we define a new method of comparison of fuzzy numbers this procedure is an extension of some well known indices adamo tsumura et al yager some properties of our index are studied in this paper as well as its behaviour on several particular cases

duality theorems in fuzzy mathematical programming problems based on the concept of necessity the fuzzy valued lagrangian function for the fuzzy mathematical programming problem via the concept of the fuzzy scalar inner product is proposed a solution concept of fuzzy optimization problems which is essentially similar to the notion of pareto solution in multiobjective programming problems is also introduced by ranking the fuzzy numbers using the necessity indices under these settings the weak and strong duality theorems can be elicited we show that the primal and dual fuzzy mathematical programming problems have no duality gap under suitable convexity assumptions for fuzzy valued functions

generalized hukuhara differentiability of interval valued functions and interval differential equations abstract in the present paper we use a recently proposed generalization of the hukuhara difference for compact convex sets to introduce and study a generalization of the hukuhara differentiability to the case of interval valued functions we also consider several possible definitions for the derivative of an interval valued function recently proposed in the literature and we study connections between them and their properties using these concepts we study interval differential equations local existence and uniqueness of two solutions is obtained together with characterizations of the solutions of an interval differential equation by ode systems several examples are also shown

on multiindices and multivariables presentation of the voigt functions this paper aims at presenting multiindices and multivariables study of the unified or generalized voigt functions which play an important role in the several diverse field of physics such as astrophysical spectroscopy and the theory of neutron reactions some expressions representations of these functionl are given in terms of familiar special functions of multivariables further representations and series expansions involving multidimensional classical polynomials laguerre and hermite of mathematical physics are established

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

embedding of level continuous fuzzy sets on banach spaces abstract in this paper we present an extension of the minkowski embedding theorem showing the existence of an isometric embedding between the class f c x of compact convex and level continuous fuzzy sets on a real separable banach space x and c 0 1 b x the banach space of real continuous functions defined on the cartesian product between 0 1 and the unit ball b x in the dual space x also by using this embedding we give some applications to the characterization of relatively compact subsets of f c x in particular an ascoli arzela type theorem is proved and applied to solving the cauchy problem x t f t x t x t0 x0 on f c x

generalized derivative and π derivative for set valued functions in this paper we study the generalized derivative and the p derivative for interval valued functions we show the connections between these derivatives some illustrative examples and applications to interval differential equations and fuzzy functions are presented

convex fuzzy mappings abstract in this note the concept of convexity and logarithmic convexity for fuzzy mappings are introduced and some applications to optimization are discussed