semantics and pragmatics of fuzzy sets and systems abstract a philosophical formalism of a new methodological aspect of humanistic systems design and evaluation is given a requisite concept of context dependency is highlighted and some approaches to fuzzy sets and linguistics subsequently extended it is consequently shown that a mathematical theory of pragmatic fuzzy subsets is not only conceptually possible but practically implementable in man machine studies as well thus the important context dependent implication of the subjective nature of zadeh s theory of fuzzy sets can be better exploited as a pragmatic theory the approach here is a seeming connection between pragmatism and ontology concepts that are traditionally diametrically opposed to each other the attitude adopted has been the equation of pragmatism and psychophysical measurements of ontological objects noumena pragmatism is tacitly defined as a form of empiricism whereby linguistic constructs i e linguistic variable denotions that represent any aspect s of a humanistic system are nothing more than an operational procedure used to achieve psychophysical measurements of the aspect s in this fashion pragmatism would enable the contents of assertions which are made through declarative propositions about humanistic systems to be deciphered within relevant contexts for pragmatism direct sense experience provides both the meaning and the criterion of reality judgements the context dependent nature of the physical reality of ontological entities is therefore better understood pragmatically vis a vis the appropriate evaluative criteria and interpretative conventions by emphasizing the distinction between a fuzzy system naturally fuzzified and a fuzzified mathematical structure meta mathematically fuzzified the use of the standard fuzzy topologies is justified although it is conceptually possible to develop a yet more general topology or perhaps an alternative one especially in the case of a meta mathematically fuzzified structure however for the express purpose of machine implementation a naturally fuzzified system such as a complex humanistic system is more amenable to an initial test of the philosophy of pragmatic fuzzy subsets consequently the fuzzy topology and spaces employed are intended to be devoid of extensive generalities in this instance

the folk theorem for games with private almost perfect monitoring we prove the folk theorem for discounted repeated games under private almost perfect monitoring our result covers all finite n player games that satisfy the usual full dimensionality condition mixed strategies are allowed in determining the individually rational payoffs we assume no cheap talk communication between players and no public randomization device

the value of markov chain games with lack of information on one side we consider a two player zero sum game given by a markov chain over a finite set of states and a family of matrix games indexed by states the sequence of states follows the markov chain at the beginning of each stage only player 1 is informed of the current state then the corresponding matrix game is played and the actions chosen are observed by both players before proceeding to the next stage we call such a game a markov chain game with lack of information on one side this model generalizes the model of aumann and maschler of zero sum repeated games with lack of information on one side which corresponds to the case where the transition matrix of the markov chain is the identity matrix we generalize the proof of aumann and maschler and from the definition and the study of appropriate nonrevealing auxiliary games with infinitely many stages show the existence of the uniform value an important difference with aumann and maschler s model is that here the notions for player 1 of using the information and revealing a relevant information are distinct

on the theory of infinitely repeated games with discounting presentation d un cadre systematique pour etudier des jeux repetes indefiniment avec actualisation en s attachant plus particulierement aux equilibres parfaits de strategie pure

the optimal trilinear restriction estimate for a class of hypersurfaces with curvature abstract in 4 nearly optimal l 1 trilinear restriction estimates in r n 1 are established under transversality assumptions only in this paper we show that the curvature improves the range of exponents by establishing l p estimates for any p 2 n 4 3 n 2 in the case of double conic surfaces the exponent 2 n 4 3 n 2 is shown to be the universal threshold for the trilinear estimate

on the multilinear restriction and kakeya conjectures we prove d linear analogues of the classical restriction and kakeya conjectures in rd our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of gaussians closely related to heat flow we conclude by giving some applications to the corresponding variable coefficient problems and the so called joints problem as well as presenting some n linear analogues for n d

computing supergame equilibria we present a general method for computing the set of supergame equilibria in infinitely repeated games with perfect monitoring and public randomization we present a three stage algorithm that constructs a convex set containing the set of equilibrium values constructs another convex set contained in the set of equilibrium values and produces strategies that support them we explore the properties of this algorithm by applying it to familiar games

on the erdős distinct distances problem in the plane in this paper we prove that a set of n points in r 2 has at least c n log n distinct distances thus obtaining the sharp exponent in a problem of erd os we follow the setup of elekes and sharir which in the spirit of the erlangen program allows us to study the problem in the group of rigid motions of the plane this converts the problem to one of point line incidences in space we introduce two new ideas in our proof in order to control points where many lines are incident we create a cell decomposition using the polynomial ham sandwich theorem this creates a dichotomy either most of the points are in the interiors of the cells in which case we immediately get sharp results or alternatively the points lie on the walls of the cells in which case they are in the zero set of a polynomial of suprisingly low degree and we may apply the algebraic method in order to control points incident to only two lines we use the ecnode polynomial of the rev george salmon to conclude that most of the lines lie on a ruled surface then we use the geometry of ruled surfaces to complete the proof

weighted restriction estimates using polynomial partitioning we use the polynomial partitioning method of guth j amer math soc 29 2016 371 413 to prove weighted fourier restriction estimates in r3 with exponents p that range between 3 and 3 25 depending on the weight as a corollary to our main theorem we obtain new non weighted local and global restriction estimates for compact c surfaces s r3 with strictly positive second fundamental form for example we establish the global restriction estimate ef lp r3 f lq s in the full conjectured range of exponents for p 3 25 up to the sharp line and the global restriction estimate ef lp f l2 s for p 3 and certain sets r3 of infinite lebesgue measure as a corollary to our main theorem we also obtain new results on the decay of spherical means of fourier transforms of positive compactly supported measures on r3 with finite dimensional energies

extremizability of fourier restriction to the paraboloid abstract in this article we prove that nearly all valid scale invariant fourier restriction inequalities for the paraboloid in r 1 d have extremizers and that l p normalized extremizing sequences are precompact modulo symmetries this result had previously been established for the case q 2 in the range where the boundedness of the restriction operator is still an open question our result is conditional on improvements toward the restriction conjecture

l p decoupling for restricted k broadness to prove fourier restriction estimate using polynomial partitioning guth introduced the concept of k broad part of regular l p norm and obtained sharp k broad restriction estimates to go from k broad estimates to regular l p estimates guth employed l 2 decoupling result in this article similar to the technique introduced by bourgain guth we establish an analogue to go from regular l p norm to its m 1 broad part as the error terms we have the restricted k broad parts k 2 ldots m to analyze the restricted k broadness we prove an l p decoupling result which can be applied to handle the error terms and recover guth s linear restriction estimates

a bilinear approach to the restriction and kakeya conjectures the purpose of this paper is to investigate bilinear variants of the restriction and kakeya conjectures to relate them to the standard formulations of these conjectures and to give applications of this bilinear approach to existing conjectures the methods used are based on several observations and results of bourgain see 2 6 together with some refinements by moyua vargas and vega 17 18 this paper is organized as follows in the first section we discuss bilinear restriction estimates and show how one can pass back and forth between these estimates and the standard restriction estimates we also generalize the 12 7 bilinear restriction estimate of 18 to higher dimensions in the second section we give analogues of the above results for the kakeya operator in particular we give a bilinear improvement to wolff s kakeya theorem in arbitrary dimension in the third section we give applications of these bilinear estimates in three dimensions for example we are able to improve the 42 11 exponent in wolff s restriction theorem to 34 9 we are also able to prove a sharp lp lq restriction theorem which improves on the classical l2 l4 tomas stein theorem and also give some concrete progress on a bilinear restriction conjecture of klainerman and machedon we also give a non bilinear approach to these estimates which gives weaker results but is more direct and probably has a wider range of application

a fuzzy language abstract with the aim of designing and implementing programming languages that take into account the fuzzy paradigm we will modify the classical lambda calculus by adding a degree to each term and by redefining the b reduction thus for the new calculus to verify the church rosser property the degree computed with can be made through a function that is a t norm or an s conorm with this new tool we design a nondeterminist language that satisfies fuzzy data programming requirements and an example of its behaviour is shown

restriction estimates using polynomial partitioning ii we improve the estimates in the restriction problem in dimension n geqslant 4 to do so we establish a weak version of a k linear restriction estimate for any k the exponents in this weak k linear estimate are sharp for all k and n

finite rationality and interpersonal complexity in repeated games a measure of complexity for repeated game strategies is studied this measure facilitates the investigation of some issues regarding finite rationality and the structure of subgame perfect equilibria of repeated games with discounting specifically the complexity of a strategy in a given repeated game is defined to be the cardinality of the induced strategy set i e the number of distinct strategies induced by the original strategy in all possible subgames we observe that this cardinality is equal to the size cardinality of the state set of the smallest automaton which can implement the strategy thus in a sense complexity is measured on the basis of the amount of computing power inherent in the strategy a measure of strategic memory is also studied the following results are obtained 1 combining two notions of bounded rationality epsilon equilibrium and finite complexity we find that every subgame perfect equilibrium of the repeated game can be approximated with regard to payoffs by a subgame perfect epsilon equilibrium of finite complexity 2 for a generic class of normal form stage games at every discount robust subgame perfect drsp equilibrium there are necessary relationships among the complexities and memories of the players strategies in the two player case strategies must be equally complex and must have equal memories 3 for a second class of two pla yer stage games we show that the payoff vectors for all drsp equilibria are obtainable via equilibria in which the players strategies are equally complex and have equal memoiies

the complexity of computing a nash equilibrium in 1951 john f nash proved that every game has a nash equilibrium ann of math 2 54 1951 pp 286 295 his proof is nonconstructive relying on brouwer s fixed point theorem thus leaving open the questions is there a polynomial time algorithm for computing nash equilibria and is this reliance on brouwer inherent many algorithms have since been proposed for finding nash equilibria but none known to run in polynomial time in 1991 the complexity class ppad polynomial parity arguments on directed graphs for which brouwer s problem is complete was introduced c papadimitriou j comput system sci 48 1994 pp 489 532 motivated largely by the classification problem for nash equilibria but whether the nash problem is complete for this class remained open in this paper we resolve these questions we show that finding a nash equilibrium in three player games is indeed ppad complete and we do so by a reduction from brouwer s problem thus establishing that the two problems are computationally equivalent our reduction simulates a stylized brouwer function by a graphical game m kearns m littman and s singh graphical model for game theory in 17th conference in uncertainty in artificial intelligence uai 2001 relying on gadgets graphical games performing various arithmetic and logical operations we then show how to simulate this graphical game by a three player game where each of the three players is essentially a color class in a coloring of the underlying graph subsequent work x chen and x deng setting the complexity of 2 player nash equilibrium in 47th annual ieee symposium on foundations of computer science focs 2006 established by improving our construction that even two player games are ppad complete here we show that this result follows easily from our proof

an improved method to construct basic probability assignment based on the confusion matrix for classification problem the determination of basic probability assignment bpa is a crucial issue in the application of dempster shafer evidence theory classification is a process of determining the class label that a sample belongs to in classification problem the construction of bpa based on the confusion matrix has been studied however the existing methods do not make full use of the available information provided by the confusion matrix in this paper an improved method to construct the bpa is proposed based on the confusion matrix the proposed method takes into account both the precision rate and the recall rate of each class an illustrative case regarding the prediction of transmembrane protein topology is given to demonstrate the effectiveness of the proposed method

computing equilibria in discounted dynamic games game theory gt is an essential formal tool for interacting entities however computing equilibria in gt is a hard problem when the same game can be played repeatedly over time the problem becomes even more complicated the existence of multiple game states makes the problem of computing equilibria in such games extremely difficult in this paper we approach this problem by first proposing a method to compute a nonempty subset of approximate up to any precision subgame perfect equilibria in repeated games we then demonstrate how to extend this method to approximate all subgame perfect equilibria in a repeated game and also to solve more complex games such as markov chain games and stochastic games we observe that in stochastic games our algorithm requires additional strong assumptions to become tractable while in repeated and markov chain games it allows approximating all subgame perfect equilibria reasonably fast and under considerably weaker assumptions than previous methods

sharp resolvent estimates outside of the uniform boundedness range in this paper we are concerned with resolvent estimates for the laplacian delta in euclidean spaces uniform resolvent estimates for delta were shown by kenig et al duke math j 55 2 329 347 1987 who established rather a complete description of the lebesgue spaces allowing such estimates however the problem of obtaining sharp l p l q bounds depending on z has not been considered in a general framework which admits all possible p q in this paper we present a complete picture of sharp l p l q resolvent estimates which may depend on z we also obtain the sharp resolvent estimates for the fractional laplacians and a new result for the bochner riesz operators of negative index