symmetric successive overrelaxation methods for fuzzy linear systems symmetric successive overrelaxation ssor methods for solving fuzzy linear systems are discussed and followed by convergence theorems numerical examples are given to illustrate the procedure

a new method for solving interval and fuzzy equations linear case a new approach to the solution of interval and fuzzy equations based on the generalized procedure of interval extension called interval extended zero method is proposed the central for the proposed approach is the treatment of the interval zero as an interval centered around zero it is shown that such proposition is not of heuristic nature but is the direct consequence of the interval subtraction operation some methodological problems concerned with this definition of interval zero are discussed it is shown that the resulting solution of interval linear equations based on the proposed method may be naturally treated as a fuzzy number an important advantage of a new method is that it substantially decreases the excess width effect on the other hand we show that it can be used as a reliable practical tool for solving linear interval and fuzzy equations as well as the systems of them the features of the method are illustrated by the example of the solution of the well known leontief input output problem in the interval setting

iterative solution of fuzzy linear systems abstract linear systems have important applications to many branches of science and engineering in many applications at least some of the parameters of the system are represented by fuzzy rather than crisp numbers so it is immensely important to develop numerical procedures that would appropriately treat general fuzzy linear systems will be denoted by fls and solve them in this paper firstly a general fuzzy linear system using the embedding approach has been investigated and then several well known numerical algorithms for solving system of linear equations such as richardson extrapolated richardson jacobi jor gaus seidel egs sor aor esor ssor ussor ema and msor are extended for solving fls the iterative methods are followed by convergence theorems and the presented algorithms are tested by solving some numerical examples hackbusch noticed that gauss spelling is less correct than gaus w hackbusch iterative solution of large sparse systems of equations springer verlag inc new york 1994 9

computing real solutions of fuzzy polynomial systems abstract this paper presents an efficient algorithm called solvefuzzysystem or sfs for finding real solutions of polynomial systems whose coefficients are symmetrical l r fuzzy numbers with bounded support for which the spread functions l and r are bijective the real solutions of such a system are deduced from solutions of some polynomial systems with real coefficients this algorithm is based on new results that are universal because they are independent from the spread functions these theoretical results include the management of the fuzzy system s solutions signs an implementation in the fuzzy package of the free computer algebra software sagemath and a parallel version of the algorithm are described

alternating forms and self adjoint operators abstract let k be a field and n 1 an integer we study the action of the symplectic group over k on the set of alternating forms on k 2 n we show that the action on pairs of forms can be interpreted in terms of the conjugation action on self adjoint operators and obtain some old and new results using this interpretation in particular for each k and n we determine the smallest base size for the action of pgl 2 n k on the set of non degenerate skew symmetric matrices over the field k modulo scalars

local uniqueness of generalized shalika models for so4n abstract this paper shows the uniqueness of generalized shalika model on so 4 n f n 1 where f is a p adic field or a finite field with characteristic p p 2

fuzzy symmetric solutions of fuzzy linear systems in this paper we propose a simple and practical method to solve a fuzzy linear system email protected email protected where email protected and email protected are fuzzy triangular vectors with non zero spreads and matrix a is nonsingular with real coefficients the aim of this paper is twofold first we obtain the crisp solution of a fuzzy linear system to this end we solve the 1 cut of a fuzzy linear system second we allocate some unknown symmetric spreads to any rows of fuzzy linear system in 1 cut position thus a fuzzy linear system in 1 cut will be transformed to a system of interval equations the symmetric spreads of each element of a fuzzy vector solution are derived by solving such an interval system moreover based on the obtained symmetric spreads we derive three types of solutions however one of the mentioned spreads has pessimistic optimistic attitude that is determined with a decision maker it seems that such a solution is a connection solution between tolerable solution set tss and controllable solution set css also we derive the maximal solution and the minimal solution of an original fuzzy linear system which are placed in tss and css respectively finally some numerical examples are given to illustrate the efficiency and ability of the proposed method

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

embedding problem of fuzzy number space part ii abstract using a concrete structure into which we embed the fuzzy number space e1 several necessary and sufficient conditions of fuzzy set valued functions are given by means of abstract function theory

the solutions of linear fuzzy stochastic differential systems as a completion of previous work of feng fuzzy sets and systems 115 2000 351 on the general theory of fuzzy stochastic differential systems the solutions of linear fuzzy stochastic differential systems for general coefficient matrix are discussed

maximal and minimal symmetric solutions of fully fuzzy linear systems in this paper we shall propose a new method to obtain symmetric solutions of a fully fuzzy linear system ffls based on a 1 cut expansion to this end we solve the 1 cut of a ffls in the present paper we assumed that the 1 cut of a ffls is a crisp linear system or equivalently the matrix coefficient and right hand side have triangular shapes then some unknown symmetric spreads are allocated to each row of a 1 cut of a ffls so after some manipulations the original ffls is transformed to solving 2n linear equations to find the symmetric spreads however our method always give us a fuzzy number vector solution moreover using the proposed method leads to determining the maximal and minimal symmetric solutions of the ffls which are placed in a tolerable solution set and a controllable solution set respectively however the obtained solutions could be interpreted as bounded symmetric solutions of the ffls which are useful for a large number of multiplications existing between two fuzzy numbers finally some numerical examples are given to illustrate the ability of the proposed method

consistency for bi skew symmetric solutions to systems of generalized sylvester equations over a finite central algebra let be a finite dimensional central algebra with an involutorial antiautomorphism and char 2 n n be the set of all n n matrices over a aij n n is called bisymmetric if aij an i 1 n j 1 aji and biskewsymmetric if aij an i 1 n j 1 aji the following systems of generalized sylvester equations over a1x yb1 c1 i asx ybs cs a1xb1 c1xd1 e1 ii asxbs csxds es are considered necessary and sufficient conditions are given for the existence of constant solutions with bi skew symmetric constrains to i and ii as a particular case auxiliary results dealing with the system of sylvester equations are also presented

fuzzy linear regression and its applications to forecasting in uncertain environment abstract linear regression has been used for many years in developing mathematical models for application in marketing management and sales forecasting in this paper two different sales forecasting techniques are discussed the first technique involves non fuzzy abstract methods of linear regression and econometrics a study of the international market sales of cameras done in 1968 by john scott armstrong utilized these non fuzzy forecasting techniques the second sales forecasting technique uses fuzzy linear regression introduced by h tanaka s uejima and k asai in 1980 in this paper a study of the computer and peripheral equipment sales in the united states is discussed using fuzzy linear regression moreover fuzzy linear regression is applied to forecasting in an uncertain environment finally some possible improvements and suggestions for further study are mentioned

numerical methods for fuzzy system of linear equations in this paper numerical algorithms for solving fuzzy system of linear equations fsle are considered schemes based on the iterative jacobi and gauss sidel methods in detail are discussed and there are followed by convergence theorems algorithms are illustrated by solving some numerical examples

tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose the oil palm frond a lignocellulosic material is a high yielding energy crop that can be utilized as a promising source of xylose it holds the potential as a feedstock for bioethanol production due to being free and inexpensive in terms of collection storage and cropping practices the aim of the paper is to calculate the concentration and yield of xylose from the acid hydrolysis of the oil palm frond through a fuzzy fractional kinetic model the approximate solution of the derived fuzzy fractional model is achieved by using a tau method based on the fuzzy operational matrix of the generalized laguerre polynomials the results validate the effectiveness and applicability of the proposed solution method for solving this type of fuzzy kinetic model a new fractional kinetic equation under uncertainty was addressed to depict the chemical reaction arising in palm oil frond an efficient numerical simulation based on a tau method was derived to solve the proposed kinetic equation different cases were solved to demonstrate the validity and efficiency of the proposed technique

solving fuzzy linear systems using a block representation of generalized inverses the group inverse abstract we present an efficient method for solving a singular n n fuzzy linear system fls a x y where the coefficient matrix a is a real matrix singular or non singular using the block structure of the group inverse or any 1 inverse a characterization of the block structure of 1 inverses in particular the group inverse but also the drazin inverse of the matrix associated to a square fls is given based on the presented necessary and sufficient condition for the existence of a solution the general solution of a square fls is obtained finally infinitely many solutions of a singular fls are presented through many interesting examples

eigen fuzzy sets and fuzzy relations abstract when r is a fuzzy relation between the elements of a finite set x the fuzzy sets a of x such that r a a max min composition are called eigen fuzzy sets the main result of this paper is the determination of the greatest eigen fuzzy set associated with a given fuzzy relation and we give three methods illustrated by an example we then state that the greatest eigen fuzzy set associated with r the transitive closure of r is exactly the one associated with r finally we describe how to obtain all fuzzy relations keeping invariant a given fuzzy set

eigen fuzzy number sets in this paper we extend certain results of sanchez resolution of eigen fuzzy sets equations fuzzy sets and systems 1 1978 69 75 to the context of fuzzy numbers a slight modification of the dubois prade definition of fuzzy numbers is used

fuzzy linear systems of the form a1x b1 a2x b2 linear systems of equations with uncertainty on the parameters play a major role in several applications in various areas such as economics finance engineering and physics this paper investigates fuzzy linear systems of the form a 1x b 1 a 2x b 2 with a 1 a 2 square matrices of fuzzy coefficients and b 1 b 2 fuzzy number vectors the aim of this paper is twofold first we clarify the link between interval linear systems and fuzzy linear systems second a generalization of the vector solution of buckley and qu solving systems of linear fuzzy equations fuzzy sets and systems 43 1991 33 43 to the fuzzy system a 1x b 1 a 2x b 2 is provided in particular we give the conditions under which the system has a vector solution and we show that the linear systems ax b and a 1x b 1 a 2x b 2 with a a 1 a 2 and b b 2 b 1 have the same vector solutions moreover in order to find the vector solution a simple algorithm is proposed

computational methods for linear matrix equations given the square matrices a b d e and the matrix c of conforming dimensions we consider the linear matrix equation a mathbf x e d mathbf x b c in the unknown matrix mathbf x our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing

steepest descent method for system of fuzzy linear equations in this paper the steepest descent method for solving system of fuzzy linear equation is considered the method in detail is discussed and followed by convergence theorem and illustrated by solving some numerical examples

conjugate gradient method for fuzzy symmetric positive definite system of linear equations in this paper the conjugate gradient method for solving fuzzy symmetric positive definite system of linear equation is considered the method in detail is discussed and followed by convergence theorem and illustrated by solving some numerical examples

solution of a fuzzy system of linear equation abstract in this paper we study the general m n fuzzy linear system using a numerical method the weak fuzzy solutions to the fuzzy system are expressed by using the generalized inverses of the coefficient matrix conditions for the existence of a fuzzy solution are derived and a numerical procedure for calculating the solution is designed a numerical method for finding the least squares solution of an overdetermined fuzzy system of linear equation by applying an orthogonal matrix to coefficients matrix that needs simple calculations is given

fuzzy prediction based on regression models abstract we use a linguistic variable to represent imprecise information to be inserted in regression models used for prediction we show how one can obtain probabilistic statements about the forecasted variables

roth s removal rule revisited abstract the theory of companion matrices is used to give explicit representations for the matrices needed in roth s removal rule these are then used to give simple proofs for the cyclic decomposition theorem as well as for roth s similarity theorem for matrices over a field

the extension of roth s theorem for matrix equations over a ring abstract this paper extends roth s similarity theorem as follows let r be a ring with identity b ki 0 bi i rm q if either r is a division ring and a rn n is algebraic or r is finitely generated as a module over its center then the matrix equation ki 0 aixbi c over r has a solution if and only if

the law of large numbers for fuzzy processes and the estimation problem abstract we study how the law of large numbers can be extended to the case of fuzzy numbers we work with l fuzzy sets where l is a cl commutative monoid with an operation we define the independence of fuzzy numbers we find when is the operation of the lattice that the arithmetical mean of independent fuzzy numbers does not converge we think that this case could be a limit one we show for particular cases of the operation that generally convergence holds we build estimators for fuzzy models we particularly consider the minimum fuzziness estimator we study the convergence of these estimators and compare them by way of the fuzzy subsets they induce we lastly study the case where we have dependent fuzzy numbers and particularly the case of linearly filtered autoindependent fuzzy processes

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

the adomian decomposition method for fuzzy system of linear equations in this paper the application of the adomian method for solving fuzzy system of linear equations fsle is considered for a fsle has been shown that the adomian decomposition method is equivalent to the jacobi iterative method appl math comput in press the algorithm is illustrated by solving some numerical examples

fuzzy linear systems a general fuzzy linear system is investigated using the embedding approach conditions for the existence of a unique fuzzy solution to n n linear system are derived and a numerical procedure for calculating the solution is designed the applicability of the proposed model is illustrated with examples

the matrix equation x axb c and an analogue of roth s theorem abstract we give a necessary and sufficient condition for the consistency of the matrix equation x axb c

approximate solution of dual fuzzy matrix equations in this paper we propose a simple and practical method to solve the dual fuzzy matrix equation ax b cx d in which a c are mxn matrices and b d are mxp lr fuzzy numbers matrices by means of the arithmetic operations on lr fuzzy numbers space the dual fuzzy matrix equation could be converted into two classical matrix equations and the lr minimal fuzzy solution and the strong weak lr minimal fuzzy solutions of the dual fuzzy matrix equation are derived by solving two classical matrix equations based on the generalized inverses of matrices meanwhile as a special case of the dual fuzzy matrix equation the fuzzy solutions of the dual fuzzy linear systems are investigated finally some numerical examples are given to illustrate the effectiveness of the proposed method

simultaneous solutions of matrix equations and simultaneous equivalence of matrices given matrices ai bi and ci i i of corresponding dimensions over a field f we prove that i if aiciobi are simultaneously similar to aioobi then there exists a simultaneous solution x to the matrix sylvester equations aix xbi ci and ii if aiciobi are simultaneously equivalent to aioobi then there exist simultaneous solutions x y to the matrix equations aix ybi ci we also show that analogous results hold for mixed pairs of matrix sylvester equations a1x1 yb1 c1 a2x2 yb2 c2 and for generalized stein equations x ayb c

uniqueness and disjointness of klyachko models we show the uniqueness and disjointness of klyachko models for gln over a non archimedean local field this completes in particular the study of klyachko models on the unitary dual our local results imply a global rigidity property for the discrete automorphic spectrum of gln

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

two sided coupled generalized sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices abstract in this paper we investigate and analyze in detail the structure and properties of a simultaneous decomposition for fifteen matrices a i c p i t i b i c s i q i c i c p i t i 1 d i c s i 1 q i and e i c p i q i i 1 2 3 we show that from this simultaneous decomposition we can derive some necessary and sufficient conditions for the existence of a solution to the system of two sided coupled generalized sylvester matrix equations with four unknowns a i x i b i c i x i 1 d i e i i 1 2 3 apart from proving an expression for the general solutions to this system we derive the range of ranks of these solutions using the ranks of the given matrices a i b i c i d i and e i we provide some numerical examples to illustrate our results moreover we present a similar approach to consider the simultaneous decomposition for 5k matrices and the system of k two sided coupled generalized sylvester matrix equations with k 1 unknowns a i x i b i c i x i 1 d i e i i 1 k k 4 the main results are also valid over the real number field and the real quaternion algebra

solving fuzzy linear systems using a block representation of generalized inverses the moore penrose inverse abstract in this paper we present a new method for solving an m n fuzzy linear system fls a x y where the coefficient matrix a is real using the block representation of generalized inverses a necessary and sufficient condition for a block matrix to be the moore penrose inverse of the full rank matrix associated to a fls is given we obtain a necessary and sufficient condition for the existence of solutions of a fls with arbitrary real coefficient matrix the exact algebraic form with respect to the moore penrose inverse of any solution of fls of this type is established a general efficient and universal method for obtaining the exact solutions is introduced some numerical examples are presented to illustrate the proposed method

roth s solvability criteria for the matrix equations ax xˆb c and x axˆb c over the skew field of quaternions with an involutive automorphism q qˆ abstract the matrix equation a x x b c has a solution if and only if the matrices a c 0 b and a 0 0 b are similar this criterion was proved over a field by w e roth 1952 and over the skew field of quaternions by huang liping 1996 h k wimmer 1988 proved that the matrix equation x a x b c over a field has a solution if and only if the matrices a c 0 i and i 0 0 b are simultaneously equivalent to a 0 0 i and i 0 0 b we extend these criteria to the matrix equations a x x b c and x a x b c over the skew field of quaternions with a fixed involutive automorphism q q

isotropic subspaces for skewforms and maximal abelian subgroups of p groups will be called a skewform a subspace w is isotropic for a if the restriction of a to w is null i e a x y 0 for all x ye w more generally if a b 1 ak is a collection of skewforms on v then a subspace w is said to be isotropic for a if it is isotropic for each a note that we could choose to think of the collection a as an alternating bilinear map a vx v fk given a collection a of k skewforms as above let m a be the dimension of the largest isotropic subspace for a let d f n k denote the minimum possible value of m a as a ranges over all k tuples of skewforms on an n dimensional vector space

fuzzy data analysis by possibilistic linear models abstract since fuzzy data can be regarded as distribution of possibility fuzzy data analysis by possibilistic linear models is proposed in this paper possibilistic linear systems are defined by the extension principle fuzzy parameter estimations are discussed in possibilistic linear systems and possibilistic linear models are employed for fuzzy data analysis with non fuzzy inputs and fuzzy outputs defined by fuzzy numbers the estimated possibilistic linear system can be obtained by solving a linear programming problem this approach can be regarded as fuzzy interval analysis

fuzzy eigenvalues and input output analysis abstract we first generalize the perron frobenius results for nonnegative matrices to nonnegative fuzzy matrices which says that these fuzzy matrices have a dominant nonnegative fuzzy eigenvalue this result is then used to extend leontief s closed input output analysis to fuzzy economies and obtain a fuzzy model of the world s economy

base sizes for simple groups and a conjecture of cameron let g be a permutation group on a finite set a base for g is a subset b with pointwise stabilizer in g that is trivial we write b g for the smallest size of a base for g in this paper we prove that b g 6 if g is an almost simple group of exceptional lie type and is a primitive faithful g set an important consequence of this result when combined with other recent work is that b g 7 for any almost simple group g in a non standard action proving a conjecture of cameron the proof is probabilistic and uses bounds on fixed point ratios

restarted global fom and gmres algorithms for the stein like matrix equation x m x c abstract in this paper we propose the restarted global full orthogonalization method gl fom and global generalized minimum residual gl gmres method to solve the stein like matrix equation x m x c with m x a x b m x a x b m x a x b or m x a x h b respectively where x is an unknown matrix to be solved first by using a real inner product in complex matrix spaces a generalized global arnoldi process is given then we demonstrate how to employ the restarted gl fom and gl gmres algorithms for solving the stein like matrix equation the proposed algorithms take advantage of the shifted structure of the matrix equation and are implemented by the original coefficient matrices finally some numerical examples are given to illustrate the effectiveness with comparison to some existing methods

intersecting two classical groups abstract a new algorithm is presented to compute the algebra of adjoints associated to a pair of forms on a common finite vector space this algebra is used in several recent and ongoing projects to study central products intersections of classical groups and automorphism groups the implementation of the new algorithms in magma greatly outperforms its predecessor and hence in restricted yet important settings increases the practicality of the various algorithms that use adjoint algebras

pairs of alternating forms and products of two skew symmetric matrices let k be a field and let s t s1 t1 be skew symmetric matrices over k with s s1 both nonsingular if k has characteristic 2 a skew symmetric matrix is a symmetric one with zero diagonal it is shown that there exists a nonsingular matrix p over k with p sp s1 p tp t1 where p denotes the transpose of p if and only if s 1t and s 11t1 are similar it is also shown that a 2m 2m matrix over k can be factored as st with s t skew symmetric and s nonsingular if and only if a is similar to a matrix direct sum b b where b is an m m matrix over k this is equivalent to saying that all elementary divisors of a occur with even multiplicity an extension of this result giving necessary and sufficient conditions for a square matrix to be so expressible without assuming that either s or t is nonsingular is included

roth s theorems and decomposition of modules it is shown that there is a connection between roth s theorems on similarity and equivalence of block triangular matrices and decomposition of modules the module property is that if m n mn then n is a summand of m this holds for any commutative ring if m is finitely presented new proofs of roth s theorems are given for commutative rings some results are established in the noncommutative case

solution of the fully fuzzy linear systems using the decomposition procedure abstract this paper tries to extend the adomian decomposition method for solving fully fuzzy linear systems shown as ffls for finding a positive fuzzy vector x that satisfies a x b where a and b are respectively a fuzzy matrix and a fuzzy vector we employ dubois and prade s approximate arithmetic operators on lr fuzzy numbers we also transform the ffls and use the adomian decomposition method for solving an ffls then we compare this method with the jacobi iterative technique additionally we give some numerical examples

character degrees and random walks in finite groups of lie type for a finite group h let irr h denote the set of irreducible characters of h and define the zeta function zeta h t sum chi in irr h chi 1 t for real t 0 we study the asymptotic behaviour of zeta h t for finite simple groups h of lie type and also of a corresponding zeta function defined in terms of conjugacy classes applications are given to the study of random walks on simple groups and on base sizes of primitive permutation groups

successive over relaxation iterative method for fuzzy system of linear equations in this paper the gauss sidel iterative method in allahviranloo appl math comput in press for solving fuzzy system of linear equations fsle is transformed to the successive over relaxation sor method this method is discussed in detail and followed by convergence theorem algorithm is compared with the gauss sidel method by solving a numerical example

block jacobi two stage method with gauss sidel inner iterations for fuzzy system of linear equations in this paper we study block two stage iterative method for finding the approximate solution of fuzzy system of linear equation fsle with convergence conditions the application of this method is solving large linear system on parallel computer algorithm is illustrated by solving some numerical examples

lu decomposition method for solving fuzzy system of linear equations in this paper lu decomposition method for solving fuzzy system of linear equations is considered we consider the method in spatial case when the coefficient matrix is symmetric positive definite the method in detail is discussed and followed by convergence theorem and illustrated by solving some numerical examples

perturbation analysis of fuzzy linear systems this paper deals with the perturbation analysis of fuzzy linear systems three cases of perturbation are considered a the right hand side is perturbed while the coefficient matrix remains unchanged b the coefficient matrix is perturbed while the right hand side remains unchanged and c both the coefficient matrix and the right hand side are perturbed for all of the three cases the respective relative error bounds for solutions of fuzzy linear system are derived the results are illustrated by numerical examples

perturbation analysis for a class of fuzzy linear systems in this paper the perturbation analysis is presented for a class of fuzzy linear systems which can be solved by an embedding method we deduce the nonlinear upper perturbation bounds for the solutions and discuss the normwise mixed and componentwise condition numbers the results show how the perturbations of the coefficient matrix and the right hand vector impact the solutions to fuzzy linear systems

fuzzy least squares abstract several models for simple least squares fitting of fuzzy valued data are developed criteria are given for when fuzzy data sets can be fitted to the models and analogues of the normal equations are derived

general fuzzy linear systems we study the general mxn fuzzy linear system using the embedding method the solution and therefore the weak fuzzy solution to the fuzzy system are expressed by using the generalized inverses of the coefficient matrix the existence of the strong fuzzy solution to the fuzzy system is also discussed some examples are presented to illustrate the theory

exponential possibility regression analysis abstract this paper aims at giving the application of possibility theory based on exponential distributions to regression analysis a general outline of the possibility theory is illustrated by exponential possibility distributions it is shown that possibility analysis is well corresponding to statistical analysis using exponential possibility analysis we propose possibility regression analysis which is suitable for rough phenomena arising from social and economic systems the spread of the given data can be directly transferred into the exponential possibility distribution of coefficients in the regression model by the proposed method