a theory of possibility for decision making although the problem of decision making under uncertainty is generally well defined the employment of models meets with obstacles in many situations the decision maker has less information than required to use probability theory there are cases in which one can speak in terms of possibilities but no concept of probability exists the purpose of this paper is to clarify the ideas connected with the new concept of possibilistic decision making as the concept is interpreted here it covers all the cases when we can find some explicit criterion for the evaluation of a degree of easiness with which the generic elements of a universe of discourse might be assigned to a variable we discuss a method of possibility function evaluation based upon empirical information application of possibility distribution to the valuation of decision alternatives is outlined

some more results on induced fuzzy topological spaces abstract the concept of induced fuzzy topological space introduced by weiss j math anal appl 50 1975 142 150 was defined with the notions of a lower semi continuous function the purpose of this paper is to present some new results on induced fuzzy topological spaces with the notion of open sets introduced by njastad pacific j math 15 1965 961 970 we also study the connections between some covering properties of an ordinary topological space x t and its corresponding induced fuzzy topological space x w t in the last section we also introduce a new class of fuzzy supra topological spaces induced fuzzy supra topological space ifst space and study the properties

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

fixed points for fuzzy mappings in this paper the problem of the existence and computation of fixed points for fuzzy mappings is approached a fuzzy mapping r over a set x is defined to be a function attaching to each x in x a fuzzy subset r of x an element x of x is called fixed point of r iff its membership degree to r is at least equal to the membership degree to r of any y x i e r r y y x two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described the convergence theorem of our algorithm is proved under the restrictive assumption that for any x in x the membership function of r has a complementary function examples of fuzzy mappings having this property are given but the problem of proving general criteria for a function to have a complementary remain open

an outer bound on the storage bandwidth tradeoff of exact repair cooperative regenerating codes cooperative regenerating codes are a kind of erasure codes which are optimal in terms of minimizing the repair bandwidth an n k d r cooperative regenerating code has n storage nodes where k arbitrary nodes are enough to reconstruct original data and r failed nodes can be repaired cooperatively with the help of d arbitrary surviving nodes in the regenerating code framework there exists a tradeoff between the storage capacity of each node alpha and the repair bandwidth gamma but the problem of specifying the optimal storage bandwidth tradeoff of the exact repair cooperative regenerating codes remains open a key contribution of this paper is that an outer bound on the storage bandwidth tradeoff of exact repair linear cooperative regenerating codes is proposed this result can be regarded as a generalization of the outer bound proposed by prakash et al which specifies the optimal tradeoff of exact repair regenerating codes for the case of d k n 1 the proposed outer bound suggests the alpha gamma pairs that no exact repair codes can achieve but only functional repair codes can by observing the size of the set of such alpha gamma pairs the performance of the proposed outer bound is evaluated under various parameter settings

riemann roch for homotopy invariant k theory and gysin morphisms abstract we prove the riemann roch theorem for homotopy invariant k theory and projective local complete intersection morphisms between finite dimensional noetherian schemes without smoothness assumptions we also prove a new riemann roch theorem for the relative cohomology of a morphism in order to do so we construct and characterize new gysin morphisms for regular immersions between cohomologies represented by spectra examples include homotopy invariant k theory motivic cohomology their arithmetic counterparts real absolute hodge and deligne beilinson cohomology rigid syntomic cohomology mixed weil cohomologies and we use this construction to prove a motivic version of the riemann roch

borel moore motivic homology and weight structure on mixed motives by defining and studying functorial properties of the borel moore motivic homology we identify the heart of bondarko hebert s weight structure on beilinson motives with corti hanamura s category of chow motives over a base therefore answering a question of bondarko

theory of possibility as a basis for analysing business experience process abstract the aim of this paper is to introduce the theory of possibility in the analysis of professional abilities creations by the labor market when an individual performs a job he can acquire new abilities and is able to obtain other jobs it is shown how career possibilities secure a dynamic property of the labor market structure due to the business experience process the model we have defined indicates that the labor market structure converges in possibility towards a stable state

the theory of fuzzy decisions cost distribution principle in social choice and optimal tax distribution abstract in this essay we present a method where the cost of a social decision or project can be distributed among the members of society for payment the method is fuzzy decision theoretic that allows social consensus and expert judgement to be incorporated in the design of optimal cost payment distribution the method is suggested to be applicable to the designing of optimal tax distribution we conclude with a summary of the logical steps for the cost payment distribution construct

fuzzy mathematical models in economics abstract this paper is a survey of three fuzzy mathematical models dealing with economic choice economic calculation and general economic equilibrium they are the elements of a fuzzy theory of value the aim is to test the efficiency of the application of fuzzy subsets theory to the analysis of the foundations of economics and thus to legitimate its use in the area

fuzzy expected utility abstract the aim of this paper is to state the foundations of fuzzy decision theory under uncertainty attention is focused on the analysis of a fuzzy expected utility given a fuzzy decision problem which does not rest on a borel field but on a weak borel field and according to the information available we shall use successively the probability and the possibility of a fuzzy subset when the imprecise preference structure of the decision maker verifies four axioms we can determine a function of fuzzy expected utility this latter is a numerical translation of the imprecise preferences of the decision maker in an uncertain world

from fuzzy set theory to non additive probabilities how have economists reacted abstract in this paper we are going to try to conduct a comparative review of the two programmes devoted to the application of fuzzy sets theory in economics for the first and to nonadditive probabilities for the second while putting forward some explanations and conjecture as to their development and their future in section 1 we defend the thesis which claims that the first programme has only had a global focus on the approach in terms of generalization and we shall go deeper into the analysis of the particular area of general equilibrium as it is the programme on which ponsard worked the most in section 2 we shall seek to show that the second programme devoted to the introduction of nonadditive probabilities in decision theory on the contrary has attempted to come up with independent findings this would explain why this last programme has managed to fit into topics at a standstill or in crisis easily which is undeniably the case of the standard theory of decision making while the first programme was only envisaged as a kind of mathematical game involving the application of new rules to an old model in the case of the first programme one might thus speak of an extension principle and in the second case of a resolution principle

exact repair mds code construction using interference alignment the high repair cost of n k maximum distance separable mds erasure codes has recently motivated a new class of mds codes called repair mds codes that can significantly reduce repair bandwidth over conventional mds codes in this paper we describe n k d exact repair mds codes which allow for any failed node to be repaired exactly with access to d survivor nodes where k d n 1 we construct exact repair mds codes that are optimal in repair bandwidth for the cases of k n 1 2 and d 2k 11 b k 3 our codes are deterministic and require a finite field size of at most 2 n k our constructive codes are based on interference alignment techniques

on the locality of codeword symbols consider a linear n k d q code c we say that the ith coordinate of c has locality r if the value at this coordinate can be recovered from accessing some other r coordinates of c data storage applications require codes with small redundancy low locality for information coordinates large distance and low locality for parity coordinates in this paper we carry out an in depth study of the relations between these parameters we establish a tight bound for the redundancy n k in terms of the message length the distance and the locality of information coordinates we refer to codes attaining the bound as optimal we prove some structure theorems about optimal codes which are particularly strong for small distances this gives a fairly complete picture of the tradeoffs between codewords length worst case distance and locality of information symbols we then consider the locality of parity check symbols and erasure correction beyond worst case distance for optimal codes using our structure theorem we obtain a tight bound for the locality of parity symbols possible in such codes for a broad class of parameter settings we prove that there is a tradeoff between having good locality and the ability to correct erasures beyond the minimum distance

mixed weil cohomologies abstract we define for a regular scheme s and a given field of characteristic zero k the notion of k linear mixed weil cohomology on smooth s schemes by a simple set of properties mainly nisnevich descent homotopy invariance stability which means that the cohomology of g m behaves correctly and kunneth formula we prove that any mixed weil cohomology defined on smooth s schemes induces a symmetric monoidal realization of some suitable triangulated category of motives over s to the derived category of the field k this implies a finiteness theorem and a poincare duality theorem for such a cohomology with respect to smooth and projective s schemes which can be extended to smooth s schemes when s is the spectrum of a perfect field this formalism also provides a convenient tool to understand the comparison of such cohomology theories

some more results on completely induced fuzzy topological spaces abstract the object of the paper is to present some new results on completely induced fuzzy topological spaces and completely semi induced spaces earlier introduced by the authors in this journal when a fuzzy topological space becomes a completely induced space is discussed examples of completely induced space are also cited

an application of fuzzy subsets theory to the analysis of the consumer s spatial preferences abstract this paper discards to usual assumptions of the classical theory of consumer behaviour in mathematical economics first that the consumer is capable of perfectly discriminating between different goods second that the goods capable of satisfying needs are all supplied at a unique point actually consumer behaviour is by nature fuzzy and goods are scattered in a supply space and are transportable in this model the consumer is located at a given point of demand first a general study is made of the structures of spatial preferences in a fuzzy context next the particular properties are introduced in order to define a behaviour of attainable choice then the conditions which guarantee the existence of a completely preordered topological space are imposed in order to verify that the consumer s fuzzy behaviour is coherent these conditions permit to define the existence and continuity of a fuzzy utility as a numerical representation of the imprecise preference the resulting economic theory is neither ordinal nor cardinal but a valuation theory of preference

producer s spatial equilibrium with a fuzzy constraint the classical theory of the producer s equilibrium rests on two sets of particularly restrictive hypotheses first it is implicitely assumed that all inputs and outputs are located in a single place where the producer is also implanted and where the production is carried out next it is assumed that the producer follows a precise behaviour pattern by this we mean that the producer has complete information concerning the conditions of hisproductive activity and he has perfect command over both the set of inputs and the set of outputs he realises the maximum profit allowed by the technological constraint which limits his possible actions and by the given price system the aim of this study is to discard these two familiesof hypotheses relating first to the economic space of goods and of the agent and second to the precision of the economic agent s behaviour

cooperative regenerating codes one of the design objectives in distributed storage system is the minimization of the data traffic during the repair of failed storage nodes by repairing multiple failures simultaneously and cooperatively rather than successively and independently further reduction of repair traffic is made possible a closed form expression of the optimal tradeoff between the repair traffic and the amount of storage in each node for cooperative repair is given we show that the points on the tradeoff curve can be achieved by linear cooperative regenerating codes with an explicit bound on the required finite field size the proof relies on a max flow min cut type theorem from combinatorial optimization for submodular flows two families of explicit constructions are given

completely induced fuzzy topological spaces abstract the object of this paper is to introduce and to study the concepts of completely induced fuzzy topological spaces and completely lower semi continuous functions completely lower semi continuous functions turn out to be the natural tool for studying the completely induced fuzzy topological spaces