are grades of membership probabilities abstract a small sample is given of the difficulties with present day fuzzy set theory with respect to the requirements of a scientific theory and a summary of some probabilistic interpretations of grades of membership to be found in the literature the tee model for grades of membership is then suggested instead of starting out from mathematical postulates such as the assumed max and min operations for or and and the tee model uses a semantic physio logical psycho logical starting point by investigating the possibilities which a person has for assigning linguistic labels and partial grades of membership in a meaningful way the assignment of partial grades of membership is explained by the assumption that humans have the ability to take errors of observation and intersubject differences into consideration a membership value uex is identified with the subject s estimate of the probability that the label e g tall would be assigned to an object of exact attribute value uex in a natural language situation this situation being a labeling or a yes no one in which at least one of three possible sources of uncertainty is present almost all the accepted formulas of fuzzy set theory as well as the shapes of the grade of membership curves are then derived instead of having to be postulated however the derived formulas for or and and reduce to the max and min operations only in a number of special cases in another special case they reduce to the summation and the zero operation respectively the generally valid formulas are presented

theoretical and semantic distinctions of fuzzy possibilistic and mixed fuzzy possibilistic optimization theoretical semantic and algorithmic distinctions among fuzzy possibilistic and mixed fuzzy possibilistic optimization are presented and illustrated the theory underlying fuzzy possibilistic and mixed fuzzy possibilistic optimization is developed and demonstrated and points to the appropriate use of distinct solution methods associated with each type of optimization dependant on the semantics of the problem semantics is key to both the input where one is obtaining the data and constructing the optimization model in the presence of uncertainty and the output where the meaning of the results is necessary for understanding solutions the case in which the optimization model arises from the data that is a combination of fuzzy and possibilistic distributions is also derived lastly examples illustrate the theory this paper is a modification and an amplification of a presentation made at ifsa 05 w a lodwich k d jamison theory and semantics for fuzzy and possibilistic optimization in fuzzy logic soft computing and computational intelligence eleventh internat fuzzy systems association world congress july 28 31 2005 beijing china vol iii pp 1805 1810 26

the concept of grade of membership abstract the concept of grade of membership is bound up with the general problem of fuzzy reasoning in this paper an approach to the latter problem is outlined and the consequences for the notion of grade of membership are described particular care is taken from the beginning to base the theory on concepts which have an immediate practical meaning for this reason assertions rather than sentences are taken as fundamental an assertion being characterized in terms of utility and decision theory fuzzy sentences and degrees of truth and then fuzzy sets and grades of membership are defined in terms of assertions the definitions being illustrated with examples the problem of defining unary and binary operations connectives for assertions sentences and fuzzy sets is discussed finally some other aspects of the logic of assertions are outlined and the extent to which the concepts of fuzzy set and grade of membership can be incorporated into the theory is discussed

interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference information systems which contain only crisp data precise and unique attribute values for all objects have been widely investigated due to the fact that in realworld applications imprecise data are abundant uncertainty is inherent in real information systems in this paper information systems are called fuzzy information systems and formalized by objects attributes f in which f is a fuzzy set and expresses some uncertainty between an object and its attribute values to interpret and extract fuzzy decision rules from fuzzy information systems the meta theory based on modal logic proposed by resconi et al is modified the modified meta theory not only expresses uncertainty between objects and their attributes but also uncertainty in the process of recognizing fuzzy information systems in addition according to perception computing proposed by zadeh granules of fuzzy information systems can be represented by fuzzy decision rules so that fuzzy inference methods can be used to obtain the decision attribute of a new object finally a novel way of combining evidences based on the modified meta theory is introduced which extends the concept of combining evidences based on dempster shafer theory

unirational threefolds with no universal codimension 2 cycle we prove that the general quartic double solid with k le 7 nodes does not admit a chow theoretic decomposition of the diagonal or equivalently has a nontrivial universal mathrm ch 0 group and the same holds if we replace in this statement chow theoretic by cohomological in particular it is not stably rational we also deduce that the general quartic double solid with seven nodes does not admit a universal codimension 2 cycle parameterized by its intermediate jacobian and even does not admit a parametrization with rationally connected fibers of its jacobian by a family of 1 cycles this finally implies that its third unramified cohomology group is not universally trivial

aggregating constraint satisfaction degrees expressed by possibilistic truth values in information systems one often has to deal with constraints in order to compel the semantics and integrity of the stored information or to express some querying criteria hereby different constraints can be of different importance a method to aggregate the information about the satisfaction of a finite number of constraints for a given data instance is presented central to the proposed method is the use of extended possibilistic truth values to express the degree of satisfaction of a constraint and the use of residual implicators and residual coimplicators to model the impact and relevance of a constraint the proposed method can be applied to any constraint based system a database application is discussed and illustrated

birational automorphisms of fano hypersurfaces v v y v 0 between smooth three dimensional quartics v v4 v 0 v 0 4 in p is a projective isomorphism this is the original wording of their theorem in fact the arguments of im give a much stronger result namely they actually prove that smooth quartics are birationally superrigid the concept of birational rigidity is not visual being rather technical it makes little impression it is immediate implications of the property of being birationally super rigid that are really impressive for a projective variety x smooth in codimension 1 and a linear system jdj free from xed components we de ne the threshold of canonical adjunction or brie y just threshold of the pair x d setting

2 cycles sur les hypersurfaces cubiques de dimension 5 we study 2 cycles of a smooth cubic hypersurface of dimension 5 we show that the griffiths group of 2 cycles is trivial and the abel jacobi map induces an isomorphism between the chow group of algebraically trivial 2 cycles and the intermediate jacobian

erratum to birationally rigid hypersurfaces this note points out a gap in the proof of the main theorem of the article birationally rigid hypersurfaces published in invent math 192 2013 533 566 and provides a new proof of the theorem the statements of lemma 9 1 and lemma 9 2 in the original article are incorrect see the remarks at the end of this note for further comments on the errors the two lemmas are used in the proof of theorem a which is the main theorem of the original article more precisely they are used in the proof of theorem 7 4 from which theorem a is deduced the error in lemma 9 2 was brought to our attention by janos kollar while lemma 9 2 is not essential for the proof and can be circumvented the gap left by the error in lemma 9 1 appears to be more substantial because of the key role that lemma 9 1 plays in the application of theorem b in the proof of theorem a in this note we give a new argument to prove theoremawhich does not use theoremb this does not fix however the proof of theorem7 4 which should

stably irrational hypersurfaces of small slopes we show that over any uncountable field of characteristic different from two a very general hypersurface of dimension n 2 and degree at least log 2 n 2 is not stably rational this significantly improves earlier results of kollar and totaro as a byproduct of our proof we obtain new counterexamples to the integral hodge conjecture answering a question of voisin and colliot thelene voisin

varietes unirationnelles non rationnelles au dela de l exemple d artin et mumford keywords non rational but unirational variety grothendieck invariants rationality brauer invariants reference cma article 1989 001doi 10 1007 bf01850658 record created on 2008 12 16 modified on 2016 08 08

non additive multi attribute fuzzy target oriented decision analysis as an emerging area considering behavioral aspects of decision making target oriented decision model lies in the philosophical root of bounded rationality as well as represents the s shaped value function this paper deals with multi attribute decision analysis from target oriented viewpoint first the basic random target oriented decision model is extended to involve three types of target preferences benefit target cost target and equal target next since applying fuzzy set theory in decision analysis allows the decision maker to specify imprecise aspiration levels fuzzy target oriented decision analysis is formulated to model three typical types of fuzzy targets fuzzy min fuzzy max and fuzzy equal also different attitudes are used to derive target achievement functions which can be viewed as a support for probability as psychological distance furthermore we have proved that multi attribute target oriented decision analysis has a similar structure with discrete fuzzy measure and choquet integral hence we propose using discrete fuzzy measure and choquet integral to model non additive multi attribute target oriented decision analysis in particular the l measure is applied to reduce the difficulty of collecting information via a designed bisection search algorithm finally a new product development example is used to illustrate the effectiveness and advantages of our model the main advantages of our target oriented decision model are its abilities to model the fuzzy uncertainty of targets as well as capture the non additive behaviors among targets by means of discrete fuzzy measure and choquet integral

fuzzy sets probability and measurement abstract in recent years the problem of uncertainty modeling has received much attention from scholars in artificial intelligence and decision theory various formal settings including but not restricted to fuzzy sets and possibility measures have been proposed based on different intuitions and dealing with various kinds of uncertain data the two main research directions are upper and lower probabilities which convey the idea of imprecisely estimated probability measures and distorted probabilities for the descriptive assessment of partial belief possibility measures and thereby fuzzy sets stand at the crossroads of these new approaches traditional views interpretive settings and canonical experiments for the measurement of probability such as frequentist approaches betting theories comparative uncertainty relations are currently extended to the generalized uncertainty measures these works shed new light on various interpretations of fuzzy sets and clarify their links with probability theory conversely zadeh s logical point of view on fuzzy sets suggests a set theoretic perspective on uncertainty measures that brings together numerical quantification and logic

on the rationality problem for quadric bundles we classify all positive integers n and r such that stably nonrational complex r fold quadric bundles over rational n folds exist we show in particular that for any n and r a wide class of smooth r fold quadric bundles over pcn are not stably rational if r 2n 1 1 2n 2 in our proofs we introduce a generalization of the specialization method of voisin and of colliot thelene and pirutka which avoids universally ch0 trivial resolutions of singularities

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

random models of scale free networks in this paper we study two models of network evolution and give more realistic descriptions of the local processes than barabasi albert model incorporating the addition of new nodes the addition of new links the rewiring and deleting of links to random networks model with single or double preferential attachment s we have proved that the two models are of scale free networks if the parameters are chosen properly and got the scaling exponent by the continuum theory

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

birationally rigid hypersurfaces we prove that for n 4 all smooth hypersurfaces of degree n in n are birationally superrigid first discovered in the case n 4 by iskovskikh and manin in a work that started this whole direction of research this property was later conjectured to hold in general by pukhlikov the proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals

uncertainty modelling for vague concepts a prototype theory approach an epistemic model of the uncertainty associated with vague concepts is introduced label semantics theory is proposed as a framework for quantifying an agent s uncertainty concerning what labels are appropriate to describe a given example an interpretation of label semantics is then proposed which incorporates prototype theory by introducing uncertain thresholds on the distance between elements and prototypes for description labels this interpretation naturally generates a functional calculus for appropriateness measures a more general model with distinct threshold variables for different labels is discussed and we show how different kinds of semantic dependence can be captured in this model

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

random sets and fuzzy interval analysis abstract a general expression of function with random set valued arguments is stated which encompasses zadeh s extension principle as well as functions of random variables and interval analysis a monotonicity property is derived for algebraic operations performed between random set valued variables this property extends the monotonicity of functions with set valued arguments in the sense of inclusion the application of this result to the approximate calculation of functions of random variables is suggested and illustrated by an example

a semantics for possibility theory based on likelihoods abstract in this paper a semantic basis for possibility theory based on likelihood functions is presented in some cases possibilities have been considered as approximations of shafer plausibility measures this approximation exchanges exactness of plausibility values for the simplicity of use of possibility values in this paper a different direction is followed possibility measures are considered as the supremum of a family of likelihood functions this is an exact interpretation not an approximation the minimum rule to combine possibility distributions is justified in this framework under general conditions conditions under which other rules can be applied are also studied

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

the gersten conjecture for milnor k theory we prove that the n th milnor k group of an essentially smooth local ring over an infinite field coincides with the n n motivic cohomology of the ring this implies levine s generalized bloch kato conjecture

hypersurfaces that are not stably rational a fundamental problem of algebraic geometry is to determine which varieties are rational that is isomorphic to projective space after removing lower dimensional subvarieties from both sides in particular we want to know which smooth hypersurfaces in projective space are rational an easy case is that smooth complex hypersurfaces of degree at least n 2 in p are not covered by rational curves and hence are not rational by far the most general result on rationality of hypersurfaces is kollar s theorem that for d at least 2d n 3 3e a very general complex hypersurface of degree d in p is not ruled and therefore not rational 13 theorem v 5 14 very little is known about rationality in lower degrees except for cubic 3 folds and quintic 4 folds 4 19 chapter 3 a rational variety is also stably rational meaning that some product of the variety with projective space is rational many techniques for proving non rationality give no information about stable rationality voisin made a breakthrough in 2013 by showing that a very general quartic double solid a double cover of p ramified over a quartic surface is not stably rational 23 these fano 3 folds were known to be non rational over the complex numbers but stable rationality was an open question voisin s method was to show that the chow group of zero cycles is not universally trivial that is the chow group becomes nontrivial over some extension of the base field by degenerating the variety to a nodal 3 fold which has a resolution of singularities x with nonzero torsion in h3 x z colliot thelene and pirutka simplified and generalized voisin s degeneration method they deduced that very general quartic 3 folds are not stably rational 6 this was striking in that non rationality of smooth quartic 3 folds was the original triumph of iskovskikh manin s work on birational rigidity while stable rationality of these varieties was unknown 11 beauville applied the method to prove that very general sextic double solids quartic double 4 folds and quartic double 5 folds are not stably rational 1 2 in this paper we show that a wide class of hypersurfaces in all dimensions are not stably rational namely for all d 2d n 2 3e and n 3 a very general complex hypersurface of degree d in p is not stably rational theorem 2 1 the theorem covers all the degrees in which kollar proved non rationality in fact we get a bit more since kollar assumed d 2d n 3 3e for example very general quartic 4 folds are not stably rational whereas it was not even known whether these varieties are rational the method applies to some smooth hypersurfaces over q in each even degree section 3 gives some examples over q which are not stably rational over c the idea is that the most powerful results are obtained by degenerating a smooth complex variety to a singular variety in positive characteristic rather than to a sin

multicriteria compensability analysis abstract passive and active compensability multicriteria analysis pacman is a multicriteria methodology based on a decision maker dm oriented concept of compensation called compensability the preliminary stage of pacman is compensability analysis this is the procedure that translates information about intercriteria compensability provided by the dm into analytical form in this paper a theoretical modelization of compensability analysis is proposed codification of information is carried out by building the so called compensatory functions for each ordered pair of criteria distinguishing the compensating or active criterion from the compensated or passive one some technical features of these functions are analyzed and a methodology for their construction is presented on the basis of compensability analysis the compensatory strength of each criterion can be evaluated by computing its active and passive compensatory powers thus obtaining a partial preorder on the set of criteria moreover this type of approach to intercriteria relations allows one to estimate the dm s global aptitude to compensate among criteria

the three semantics of fuzzy sets abstract three main semantics for membership functions seem to exist in the literature similarity preference and uncertainty each semantics underlies a particular class of applications similarity notions are exploited in clustering analysis and fuzzy controllers uncertainty is captured by fuzzy sets in the framework of possibility theory the membership function of a fuzzy set is also sometimes a kind of utility function that represents flexible constraints in decision problems this paper advocates the claim that progress in operational semantics of membership functions presupposes that these distinct semantics be acknowledged and related to more basic measurement issues in terms of distance cost and frequency on which scientific traditions exist

user preferences discovery using fuzzy models user preferences discovery aims to learn the patterns of user preferences for various services or items such as movies preferences discovery is essential to the development of intelligent personalization applications based on decision and utility theories traditional approaches to preferences discovery explicitly query users about the behavior of value function or utility of every outcome with respect to each decision criterion consequently these approaches are generally error prone and labor intensive although implicit elicitation approaches have been proposed to address the above limitations extent approaches largely ignore multi valued nature of item features and uncertainty associated with item features and user preferences to address uncertainty due to vagueness and imprecision this research proposed a general framework for preferences discovery based on fuzzy set theories in addition new fuzzy models were created for preferences discovery and representation further an algorithm was developed to predict user preferences with uncertainty and visualization of item features user feedback and the discovered preferences helped improve the interpretation of the discovered knowledge the results of the simulation evaluation using a benchmark movie dataset revealed that the proposed preference discovery method 1 doubled the accuracy of preference discovery as compared to random prediction and 2 outperformed conventional techniques in making movie recommendation these findings suggest that fuzzy models are effective for preferences patterns discovery and personalized recommendation application