canonical fuzzy numbers of dimension two abstract recently several authors have dealt with interactive fuzzy numbers this paper proposes a new approach to interactions between fuzzy numbers by using canonical fuzzy numbers of dimension two

fuzzy n cell numbers and the differential of fuzzy n cell number value mappings in this paper we give the definition of a special kind of n dimension fuzzy numbers fuzzy n cell numbers discuss their operations and representation theorems define a complete metric on the fuzzy n cell number space and prove that the metric is equivalent to the supremum metric derived by the hausdorff metric between the level sets of the n dimension fuzzy numbers and obtain an embedding theorem of the fuzzy n cell number space isometrically embeds it into a concrete banach space we also consider the differential of the fuzzy mappings from an interval into the fuzzy n cell number space by using the embedding theorem

linear programming with fuzzy variables in practice there are many problems in which all decision parameters are fuzzy numbers and such problems are usually solved by either possibilistic programming or multiobjective programming methods unfortunately all these methods have shortcomings in this note using the concept of comparison of fuzzy numbers we introduce a very effective method for solving these problems then we propose a new method for solving linear programming problems with fuzzy variables

interactive fuzzy programming for multi level linear programming problems with fuzzy parameters this paper presents interactive fuzzy programming for multi level linear programming problems with fuzzy parameters in fuzzy programming for multi level linear programming problems recently developed by lai et al since the fuzzy goals are determined for both an objective function and decision variables at the upper level undesirable solutions are produced when these fuzzy goals are inconsistent in order to overcome such problems after eliminating the fuzzy goals for decision variables interactive fuzzy programming for multi level linear programming problems with fuzzy parameters is presented in our interactive method after determining the fuzzy goals of the decision makers at all levels a satisfactory solution is derived efficiently by updating the satisfactory degrees of decision makers with considerations of overall satisfactory balance among all levels illustrative numerical examples for two level and three level linear programming problems are provided to demonstrate the feasibility of the proposed method

joint canonical fuzzy numbers abstract starting from ramik and nakamura s report 1991 we introduce and fully characterize the joint canonical fuzzy numbers of arbitrary dimension the crucial part is to find the least value of the maximum of absolute values of several linear combinations surprisingly there is a formula for it based upon determinants formed by the coefficients of the linear combinations finally we give a full description of joint canonical fuzzy numbers of dimension 2 provided by 5 infinite families

on the restudy of fuzzy complex analysis part 1 the sequence and series of fuzzy complex numbers and their convergences this paper studies the convergence of the sequence and series of fuzzy complex numbers we define the metric convergence and levelwise convergence of sequences on the metric space of fuzzy complex numbers and discuss the relationship between two convergences all this may be a foundation for researching fuzzy complex analysis

solution of ordinary differential equations via nonlocal transformations the classical lie analysis provides a useful technique for the solution of ordinary differential equations via point symmetries transformations unfortunately the requirement that an nth order equation possesses at least an n dimensional solvable lie algebra of symmetries is only satisfied by a select number of equations we provide a class of second order ordinary differential equations with less than the required two lie point symmetries that can be solved via nonlocal transformations

fuzzy complex analysis ii integration abstract this paper continues the author s research in fuzzy complex analysis where we now define and study the basic properties of a fuzzy contour integral for fuzzy mappings which map a rectifiable curve in the complex plane into fuzzy complex numbers

approximate reasoning with time abstract the need to make time dependent assumptions is frequently encountered in many systems especially in dynamical systems this paper presents a theoretical study of the representation and manipulation of some vague concepts in the temporally changing world our approach to the modeling is based on zadeh s theory of possibility we introduce a concept of similarity index in reasoning with time we present two different types of widely used models one rule based and another resolution based for reasoning with time we consider simply yet concrete examples to illustrate the usefulness of the proposed models

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

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

some remarks for fuzzy complex analysis abstract this paper gives some results for fuzzy complex sets generalize and improve the corresponding work of fuzzy complex numbers in 1 we also introduce the derivative and integral of functions mapping complex numbers into the set of generalized fuzzy complex numbers and it is different to the definitions in 2 4 all this may be a foundation for researching fuzzy complex analysis

numerical solutions of fuzzy differential equations abstract numerical algorithms for solving fuzzy ordinary differential equations fode are considered a scheme based on the classical euler method is discussed in detail and this is followed by a complete error analysis the algorithm is illustrated by solving several linear and nonlinear fuzzy cauchy problems

fuzzy complex numbers abstract this paper first defines fuzzy complex numbers and shows closure under the basic arithmetic operations it is shown that arithmetic of fuzzy complex numbers may be performed in terms of cuts next two special types of fuzzy complex numbers based on the forms z x iy and z re i for regular complex numbers are investigated introducing a metric on the space of fuzzy complex numbers then allows us to discuss continuity and differentiability of fuzzy complex functions

nonlinear dynamics and loop formation in kirchhoff rods with implications to the mechanics of dna and cables the paper contributes a general dynamical formulation and numerical solution procedure for studying nonlinear and three dimensional dynamics of kirchhoff rods target applications include the dynamic formation of dna loops and supercoils as well as loops hockles in marine cables the formulation accommodates non homogeneous and non isotropic inextensible rods both with and without coupling of tension and torsion the utility of this formulation is illustrated by studying the dynamics and quasi static response of a clamped clamped rod subject to compression and or twist for slow loading rates the computed quasi static responses converge to published equilibrium solutions for a benchmark problem as loading rates increase new behaviors are observed including hysteresis in the neighborhood of equilibrium bifurcations the addition of chirality in the form of tension torsion coupling has a pronounced influence on the computed looped geometries this finding has implications for dna loops formed by dna protein binding as well as loop formation in helically wound wire and synthetic cables

canonical fuzzy numbers of dimension two and fuzzy utility difference for understanding preferential judgments abstract a notion of canonical fuzzy numbers of dimension two is introduced to represent flexible joint distributions of two fuzzy numbers whose membership functions are of a common functional type the relationships between fuzzy numbers are given by normalized scalar called relational factors in the joint distributions then the canonical fuzzy numbers are adopted to operate fuzzy utility differences and their aggregations for understanding human uncertain preferential judgments among multiattribute alternatives

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

fuzziness and branch and bound procedures applications to separation sequencing abstract the aim of the paper is to identify optimal and near optimal distillation sequences according to a particular objective function definition the potential solutions are valuated from the point of view of practical considerations rather than purely costing methods four rules of thumb addressing column sequencing expressed in vague and imprecise terms are implemented and quantified by the fuzzy set theory the integer programming problem is solved by a branch and bound procedure where the bounding and branching schemes are carried out from the four heuristic rules with fuzzy quantification furthermore the fuzzy set theory is also implemented for modelling data uncertainties particularly the partial molar flow rates from the results obtained with the fuzzy branch and bound procedure involving fuzzy data we conclude that fuzzy set theory can be considered as a promising tool for modelling uncertainty and vagueness and may have many other applications in process systems engineering

stable fuzzy logic design of point to point control for mechanical systems an approach for the development of fuzzy point to point control laws for second order mechanical systems is presented asymptotic stability of the resulting closed loop system is proved using lyapunov stability theory closed loop performance and robustness are quantified in terms of the parameters of membership functions as opposed to most existing fuzzy control laws the closed loop stability of the proposed controller does not depend on the knowledge of the entire dynamics moreover the approach does not require the plant to be open loop stable the proposed approach is demonstrated on design and simulation study of a fuzzy controller for a two link robotic arm

towards fuzzy differential calculus part 2 integration on fuzzy intervals abstract the problem of integrating mappings over fuzzy domains has already received some attention in the literature however there is not a unique approach but several definitions have been proposed each carrying its own meaning this paper tries to emphasize the relationships and the differences between the various points of view

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

fuzzy complex analysis i differentiation abstract we consider functions mapping real numbers into the set of generalized complex fuzzy numbers c we define two derivatives of such functions which are generalizations of the derivative of real fuzzy mappings presented by dubois and prade 4 5 sufficient conditions on the function are given so that derivative will be a function mapping real numbers into c if the functional value is always a rectangular complex fuzzy number made up to lr real fuzzy numbers then we show that the derivative is easily computed from the derivatives of the lr fuzzy numbers other properties of the derivatives are presented

a fuzzy relational identification algorithm and its application to predict the behaviour of a motor drive system fuzzy relational identification builds a relational model describing a system s behaviour by a nonlinear mapping between its variables in this paper we propose a new fuzzy relational algorithm based on the simplified max min relational equation the algorithm presents an adaptation method applied to the gravity centre of each fuzzy set based on the error integral value between the measured and predicted system s output and uses the concept of time variant universe of discourse the identification algorithm also includes a method to attenuate the noise influence in the extracted system s relational model using a fuzzy filtering mechanism the algorithm is applied to a one step forward prediction of a simulated and experimental motor drive system the identified model has its input output variables stator reference current and motor speed signal treated as fuzzy sets whereas the relations existing between them are described by means of a matrix r defining the relational model extracted by the algorithm the results show the good potentialities of the algorithm in predicting the behaviour of the system and in attenuating through the fuzzy filtering method possible noise distortions in the relational model