on the possibilistic mean value and variance of multiplication of fuzzy numbers in this paper we introduce the definitions of the possibilistic mean variance and covariance of multiplication of fuzzy numbers and show some properties of these definitions then we apply these definitions to build the possibilistic models of portfolio selection under the situations involving uncertainty over the time horizon by considering the portfolio selection problem from the point of view of possibilistic analysis moreover numerical experiments with real market data indicate that our approach results in better portfolio performance

on ordinal sums of triangular norms on bounded lattices ordinal sums have been introduced in many different contexts e g for posets semigroups t norms copulas aggregation operators or quite recently for hoops in this contribution we focus on ordinal sums of t norms acting on some bounded lattice which is not necessarily a chain or an ordinal sum of posets necessary and sufficient conditions are provided for an ordinal sum operation yielding again a t norm on some bounded lattice whereas the operation is determined by an arbitrary selection of subintervals as carriers for arbitrary summand t norms by such also the structure of the underlying bounded lattice is investigated further it is shown that up to trivial cases there are no ordinal sum t norms on product lattices in general

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

a note on the ordinal sum theorem and its consequence for the construction of triangular norms in this paper the well known ordinal sum theorem of semigroups is generalized and applied to construct new families of triangular subnorms and triangular norms t norms among them one can find several new families of left continuous t norms too

on the construction of boundary weak triangular norms through additive generators abstract recently m urbanski and j wasowski fuzzy arithmetic based on boundary weak t norms international journal of uncertainty fuzziness and knowledge based systems 13 2005 27 37 extended the triangular norm operators to a new class of operators called the boundary weak triangular norms this extension is based on the replacement of the condition t x 1 x by the weaker one t x 1 x for x 0 1 in this paper we discuss the construction of the boundary weak triangular norms based on their additive generators continuous decreasing functions f 0 1 0 which generate proper boundary weak triangular norms are completely characterized several examples are included

2 dimensional badly approximable vectors and schmidt s game we prove that for any pair s t of nonnegative numbers with s t 1 the set of s t badly approximable vectors in r 2 is 34 p 2 1 winning for schmidt s game

the canonical representation of multiplication operation on triangular fuzzy numbers the representation of multiplication operation on fuzzy numbers is very useful and important in the fuzzy system such as the fuzzy decision making in this paper we propose a new arithmetical principle and a new arithmetical method for the arithmetical operations on fuzzy numbers the new arithmetical principle is the l 1 r 1 inverse function arithmetic principle based on the l 1 r 1 inverse function arithmetic principle it is easy to interpret the multiplication operation with the membership functions of fuzzy numbers the new arithmetical method is the graded multiple integrals representation method based on the graded multiple integrals representation method it is easy to compute the canonical representation of multiplication operation on fuzzy numbers finally the canonical representation is applied to a numerical example of fuzzy decision

fibred triangular norms abstract in this paper we deal with the formula g t f x f y where f g are functions mapping from the unit interval to itself and t is a triangular norm we are interested in the conditions under which this formula yields a triangular norm the case when f is continuous is investigated in detail as a result a new method which generates new triangular norms from an arbitrary triangular norm is developed these new triangular norms are the so called fibred triangular norms which are closely related to the homomorphism of semigroups it is well known that continuous archimedean triangular norms can be generated with additive generator functions we investigate a possible generalization of the additive generator function and characterize the class of t norms which can be generated with them this class turns out to be the class of fibred continuous archimedean t norms finally some examples are given for the case when f is not continuous

matrix representation of discrete quasi copulas in this paper discrete quasi copulas defined on a square grid i n 2 of 0 1 2 are studied and it is proved that they can be represented by means of a special class of matrices with entries in 1 1 special considerations are made for the case of irreducible discrete quasi copulas those with range i n showing that they can be represented through alternating sign matrices and that they generate all discrete quasi copulas through convex sums in the process the number of irreducible quasi copulas on i n is given and those functions d for which there exists a unique copula with d as its diagonal section are characterized

cancellativity properties for t norms and t subnorms on the one hand cancellativity properties are mainly used to express to which extend the partial functions of a t subnorm t are injective on the other hand the zooms of t corresponding to its non trivial archimedean components are t subnorms that largely determine t fixing one out of four basic types of cancellativity cancellativity conditional cancellativity weak cancellativity and weak conditional cancellativity we figure out which less restrictive type of cancellativity expresses that all maximal archimedean zooms of t satisfy the given cancellativity property we lay bare the mutual relationships between all these types of cancellativity and solve an open problem posed by klement et al

smooth t subnorms on finite scales in this work smooth t subnorms and boundary weak t norms bwt norms defined on a finite chain are studied in the smooth case it is proved that smooth bwt norms reduces to smooth t norms whereas a classification of smooth t subnorms as ordinal sums of a smooth t norm and an archimedean smooth t subnorm is proved in a similar way as in the case of 0 1 with respect to archimedean smooth t subnorms some cases depending on their zero region are considered classifying all of them in some cases and some specific families in others

copula like operations on finite settings this paper deals with discrete copulas considered as a class of binary aggregation operators on a finite chain a representation theorem by means of permutation matrices is given from this characterization we study the structure of associative discrete copulas and a theorem of decomposition of any discrete copula in terms of associative discrete copulas is obtained finally some aspects concerning their extension to copulas are dealt with

badly approximable points on manifolds this paper is motivated by two problems in the theory of diophantine approximation namely davenport s problem regarding badly approximable points on submanifolds of a euclidean space and schmidt s problem regarding the intersections of the sets of weighted badly approximable points the problems have been recently settled in dimension two but remain open in higher dimensions in this paper we develop new techniques that allow us to tackle them in full generality the techniques rest on lattice points counting and a powerful quantitative result of bernik kleinbock and margulis the main theorem of this paper implies that any finite intersection of the sets of weighted badly approximable points on any analytic nondegenerate submanifold of mathbb r n has full dimension one of the consequences of this result is the existence of transcendental real numbers badly approximable by algebraic numbers of any bounded degree

a fuzzy mcdm method for solving marine transshipment container port selection problems abstract transshipment is a very popular and important issue in the present international trade container transportation market in order to reduce the international trade container transportation operation cost it is very important for shipping companies to choose the best transshipment container port the aim of this paper is to present a new fuzzy multiple criteria decision making method fmcdm for solving the transshipment container port selection problem under fuzzy environment in this paper we present first the canonical representation of multiplication operation on three fuzzy numbers and then this canonical representation is applied to the selection of transshipment container port based on the canonical representation the decision maker of shipping company can determine quickly the ranking order of all candidate transshipment container ports and select easily the best one

on a problem in simultaneous diophantine approximation schmidt s conjecture for any i j 0 with i j 1 let bad i j denote the set of points x y 2 r 2 for which maxfkqxk 1 i kqyk 1 j g c q for all q 2 n here c c x y is a positive constant our main result implies that any nite intersection of such sets has full dimension this settles a conjecture of wolfgang m schmidt in the theory of simultaneous diophantine approximation

fuzzy method in group decision making abstract this paper investigates the problems of decision making with multiple judge multiple criteria in a fuzzy environment where the performance of alternatives and the importance of criteria are imprecisely defined and represented by fuzzy sets a fuzzy model associated with the solution algorithm is proposed on the basis of an level weighted fuzzy preference relation a numerical example is solved for illustration

a new fuzzy arithmetic in this paper we first present fuzzy numbers with a new parametric form based on this representation a new fuzzy arithmetic is defined and applied to fuzzy linear equations and fuzzy calculus

on a canonical representation of fuzzy numbers abstract fuzzy numbers and more generally linguistic values are approximate assessments given by experts and accepted by decision makers when obtaining more accurate values is impossible or unnecessary to simplify the task of representing and handling fuzzy numbers several authors have introduced real indices in order to capture the information contained in a fuzzy number in this paper we propose two parameters value and ambiguity for this purpose we use these parameters to obtain canonical representations and to deal with fuzzy numbers in decision making problems several examples illustrate these ideas

flows on homogeneous spaces and diophantine properties of matrices we generalize the notions of badly approximable resp singular systems of m linear forms in n variables and relate these generalizations to certain bounded resp divergent trajectories in the space of lattices in rm n

a fuzzy multi criteria decision making model by associating technique for order preference by similarity to ideal solution with relative preference relation generally classical multi criteria decision making mcdm methods were extended to encompass uncertainty and vagueness of messages under fuzzy environment for solving decision making problems especially for technique for order preference by similarity to ideal solution topsis in the fuzzy extension of topsis fuzzy numbers comparison and aggregation based on fuzzy preference relation are important issues to compute distance values between alternatives and ideal or anti ideal solution or rank feasible alternatives because lots of messages are reserved by fuzzy preference relation however fuzzy preference relation on pair wise comparison is commonly too complex to calculate to avoid the drawback we use a relative preference relation improved from fuzzy preference relation in the fuzzy extension of topsis for computing distance values between alternatives and ideal or anti ideal solution or obtaining relative closeness coefficients of alternatives thus the relative preference relation on fuzzy numbers will be associated with topsis under fuzzy environment to develop a fuzzy multi criteria decision making fmcdm model through the association above fmcdm problems can be easily solved by the model further we compare the proposed model with other methods to demonstrate the model s feasibility and rationality