new families of binary sequences with optimal three level autocorrelation in this correspondence we give several new families of binary sequences of period n with optimal three level autocorrelation where n spl equiv 2 mod 4 these sequences are either balanced or almost balanced our construction is based on cyclotomy

the set valued mapping based on ample fields ample fields play an important role in possibility theory based on the ample fields in possibility theory two new concepts such as possibilistic set and possibility mapping are presented a theoretical approach to define operations and implication operations of fuzzy sets based on the theory of falling shadows of possibilistic sets is established and the category posm of ample spaces and possibility mappings and the category x w a of possibilistic sets are built up respectively it is proved that the category x w a is a topos

theory and applications of q ary interleaved sequences a new class of q ary sequences called interleaved sequence is introduced their periods shift equivalence linear spans and autocorrelation functions are derived the interleaved sequences include a large number of popular sequences such as multiplexed sequences clock controlled sequences kasami 1966 sequences gmw sequences geometric sequences and no 1989 sequences a special class of the interleaved sequences is constructed by mapping gf q sup m sequences into gf q sequences in terms of different bases of gf q sup m over gf q as an application of the theory of interleaved sequences some new families of binary pseudo random sequences are constructed which have large linear spans optimal periodic cross autocorrelation functions balance and the rapidly hopped properties a complete comparison of the new family of sequences with the gold sequence family the kasami small and large set sequence families the bent function sequence family and the no sequence family is discussed this shows that the new sequence families have important advantages for use in spread spectrum multiple access communication systems

characterization of m sequences of lengths 2 2k 1 and 2 k 1 with three valued cross correlation considered is the distribution of the cross correlation between in sequences of length 22k 1 where m 2k and m sequences of shorter length 2k 1 new pairs of m sequences with three valued cross correlation are found and the complete correlation distribution is determined finally we conjecture that there are no more cases with a three valued cross correlation apart from the ones proven here

a note on the conditional probability of fuzzy subsets of a continuous domain abstract the notion of a mass assignment corresponding to a discrete fuzzy set is generalised to include all fuzzy sets the definition is motivated by considering a possible mechanism by which an intelligent agent could extend set theoretic operations to fuzzy sets this same mechanism also suggests an alternative definition for the conditional probability of fuzzy sets it is noted that this definition is probability possibility consistent and it is shown that in the case where the probability distribution on the domain has a density function then the conditional probability of f given g can be expressed as the probability of f calculated relative to a conditional density function dependent on g this result is used to develop an analytical method for calculating conditional probabilities of fuzzy subsets of the reals where the membership functions of f and g and the density function are continuous piecewise linear functions such a method has applications to the development of a general semantic unification in fril

a class of pseudonoise sequences over gf p with low correlation zone a new class of pseudonoise sequences over gf p based on gordon mills welch 1962 sequences is constructed the sequences have the property that in a specified zone the out of phase autocorrelation and cross correlation values are all equal to 1 such sequences with low correlation zone lcz are suitable for approximately synchronized code division multiple access cdma system

fuzzy sets induced by consensus and set operations abstract the idea of consensus is introduced to construct a fuzzy set system the two different approaches to the fuzzy set theory the falling shadow and the fuzzy set system based on consensus are shown to be closely related and the latter gives another analysis of those three types of set operations that were investigated by the former and proves them to be subject to the combinations of concerning representative consensus sets a notion of homomorphism is defined and applied to two fuzzy set systems to clarify similarity between them this notion shows itself very useful in the study of fuzzy set systems

new design of low correlation zone sequence sets in this paper we present several construction methods for low correlation zone lcz sequence sets first we propose a design scheme for binary lcz sequence sets with parameters 2n 1 2 m l 2 in this scheme we can freely set the lcz length l and the resulting lcz sequence sets have the size m which is almost optimal with respect to tang fan and matsufuji bound second given a q ary lcz sequence set with parameters n m l epsi and even q we construct another q ary lcz sequence set with parameters 2n 2m l 2epsi or 2n 2m l 1 2epsi especially the new set with parameters 2n 2m l 2 can be optimal in terms of the set size if a q ary optimal lcz sequence set with parameters n m l 1 is used

new designs for signal sets with low cross correlation balance property and large linear span gf p case new designs for families of sequences over gf p with low cross correlation balance property and large linear span are presented the key idea of the new designs is to use short p ary sequences of period spl upsi with the two level autocorrelation function together with the interleaved structure to construct a set of long sequences with the desired properties the resulting sequences are interleaved sequences of period spl upsi sup 2 there are spl upsi cyclically shift distinct sequences in each family the maximal correlation value is 2 spl upsi 3 which is optimal with respect to the welch bound each sequence in the family is balanced and has large linear span in particular for binary case cross out of phase autocorrelation values belong to the set 1 spl upsi spl upsi 2 2 spl upsi 3 2 spl upsi 1 any sequence where the short sequences are quadratic residue sequences achieves the maximal linear span it is shown that some families of these sequences can be implemented efficiently in both hardware and software

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

a jordan algebraic approach to potential reduction algorithms we consider the linear monotone complementarity problem for domains obtained as the intersection of an affine subspace and the cartesian product of symmetric cones a primal dual potential reduction algorithm is described and its complexity estimates are established with the help of the jordan algebraic technique

a note on measures of fuzziness applied to nonmonotonic fuzzy propositional logic abstract we undertake a mathematical investigation of the problem of inferring a truth value s for a propositional sentence given truth values for some other set of sentences interpreting such a set of sentences and truth values as an abstraction of a fuzzy knowledge base this mathematical problem can be seen as an abstraction of the important problem of inference in fuzzy expert systems we postulate axioms for nonmonotonic fuzzy propositional logic inspired by paris and vencovska s axioms for ampliative probabilistic inference we prove simple but new results regarding the consistency of the axioms we consider one method of inference maximum fuzziness infer the truth value that is most fuzzy and yet consistent with the knowledge base we demonstrate that under certain plausible assumptions about the measure of fuzziness several of the axioms are not sound for maximum fuzziness finally we show that computing close approximations to truth values inferred by maximum fuzziness is at least as difficult as monotonic deductive propositional logic

reliability estimation and design with insufficient data based on possibility theory early in the engineering design cycle it is difficult to quantify product reliability or compliance to performance targets because of insufficient data or information for modeling the uncertainties design decisions are therefore based on fuzzy information that is vague imprecise qualitative linguistic or incomplete the uncertain information is usually available as intervals with lower and upper limits in this work the possibility theory is used to assess design reliability with incomplete information the possibility theory can be viewed as a variant of fuzzy set theory the formal theories to handle uncertainty are first introduced using the theoretical fundamentals of fuzzy measures a computationally efficient and accurate hybrid global local optimization approach is subsequently described for calculating the confidence level of fuzzy response the method combines the advantages of the commonly used vertex and discretization methods subsequently the possibility theory is used in design a possibility based design optimization method is proposed where all design constraints are expressed in a possibilistic way it is shown that the method gives a conservative solution compared with all conventional reliability based designs obtained with different probability distributions finally a general possibility based design optimization method which handles a combination of random and possibilistic design variables is presented several numerical examples demonstrate the application of possibility theory in design

binary almost perfect sequence sets sequence set with lower correlation values is highly desired for engineering applications however theoretical results e g welch bound show that max n in general that is the maximum out of phase autocorrelation and cross correlation magnitudes of a sequence set is not less than the square root of the sequence period in this paper we propose a new concept namely almost perfect sequence set apss which has the property max c except for at most m shifts where c and m are predefined small integers a uniform method is presented to construct apss and then the properties of such apss are discussed moreover a distance inequality on the apss with m 1 is obtained and several apss families such as 2p 8p 2 6 4 apss and 3p 64p2 8 3 9 9 apss for any prime p 5 are constructed based on paley and paley partial sequences finally it shows that the apss can be used to construct lcz sequences and the properties of such lcz sequences are presented

self scaled barriers for irreducible symmetric cones self scaled barrier functions are fundamental objects in the theory of interior point methods for linear optimization over symmetric cones of which linear and semidefinite programming are special cases in this article we classify the special class of self scaled barriers which are defined on irreducible symmetric cones together with a decomposition theorem for general self scaled barriers this concludes the algebraic classification theory of these functions

niho type cross correlation functions via dickson polynomials and kloosterman sums suppose that n 2k is even we study the cross correlation function between two m sequences for niho type decimations d 2 sup k 1 s 1 we develop a new technique to study the value distribution of these cross correlation functions which makes use of dickson polynomials as a first application we derive here the distribution of the six valued cross correlation function for s 3 and odd k up to a term which depends on kloosterman sums in addition applying simpler methods we prove a theorem providing niho type decimations with four valued cross correlation functions and their distribution we conjecture that the latter result actually covers all such decimations

fuzzy positive implicative ideals of bck algebras based on the theory of falling shadows on the basis of the theory of a falling shadow the notion of a falling fuzzy positive implicative ideal of a bck algebra is introduced relations between falling fuzzy positive implicative ideals and falling fuzzy ideals are given relations between fuzzy positive implicative ideals and falling fuzzy positive implicative ideals are provided

a fuzzy algebraic system based on the theory of falling shadows abstract based on the concept of a falling shadow a theoretical approach of the fuzzy algebraic system is established a fuzzy subalgebraic system of an algebraic system is considered as a falling shadow of the cloud of the subalgebraic systems when an algebraic system is a ring fuzzy subrings fuzzy ideas fuzzy prime ideas of a ring are seen as falling shadows of the cloud of subrings cloud of ideas cloud of prime ideas we shall show that fuzzy algebraic systems defined int norms are consequences of our definition under certain conditions

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

almost difference sets and their sequences with optimal autocorrelation almost difference sets have interesting applications in cryptography and coding theory we give a well rounded treatment of known families of almost difference sets establish relations between some difference sets and some almost difference sets and determine the numerical multiplier group of some families of almost difference sets we also construct six new classes of almost difference sets and four classes of binary sequences of period n spl equiv 0 mod 4 with optimal autocorrelation we have also obtained two classes of relative difference sets and four classes of divisible difference sets ddss we also point out that a result due to jungnickel 1982 can be used to construct almost difference sets and sequences of period 4l with optimal autocorrelation

sampling fuzzy discretization and signal reconstruction abstract the sampling theorem provides the condition under which a continuous time signal can be precisely represented and completely recovered from its instantaneous values equally spaced in time it gives a condition for the signal reconstruction problem the importance of this theorem pertains to the necessity of knowing when a continuous time signal is uniquely represented by its discrete version so that continuous time signals can be properly converted and handled by sampled data systems like digital computers the problem of the equivalence between either continuous time or discrete time signals and their fuzzy descriptions is analyzed here this encompasses the analysis of signal reconstruction when fuzzy systems are used as sampled data systems such as fuzzy filters fuzzy models or fuzzy controllers a necessary and sufficient condition is given for ensuring that the fuzzy system processes the legitimate representations of the signal presented at its interfaces furthermore a sufficient condition suitable for automatic tuning of membership functions is proposed and discussed the discussion encompasses the outline of some requirements that membership functions at fuzzy system interfaces should meet to allow humans to assess their semantic meaning

new constructions of quaternary low correlation zone sequences in this paper given a composite integer n we propose a method of constructing quaternary low correlation zone lcz sequences of period 2 sup n 1 from binary sequences of the same length with ideal autocorrelation these new sequences are optimal with respect to the bound by tang fan and matsufuji the correlation distributions of these new quaternary lcz sequences constructed from m sequences and gordon mills welch gmw sequences are derived

a long step primal dual algorithm for the symmetric programming problem abstract based on the techniques of euclidean jordan algebras we prove complexity estimates for a long step primal dual interior point algorithm for the optimization problem of the minimization of a linear function on a feasible set obtained as the intersection of an affine subspace and a symmetric cone this result provides a meaningful illustration of a power of the technique of euclidean jordan algebras applied to problems under consideration

primal dual algorithms and infinite dimensional jordan algebras of finite rank we consider primal dual algorithms for certain types of infinite dimensional optimization problems our approach is based on the generalization of the technique of finite dimensional euclidean jordan algebras to the case of infinite dimensional jb algebras of finite rank this generalization enables us to develop polynomial time primal dual algorithms for infinite dimensional second order cone programs we consider as an example a long step primal dual algorithm based on the nesterov todd direction it is shown that this algorithm can be generalized along with complexity estimates to the infinite dimensional situation under consideration an application is given to an important problem of control theory multi criteria analytic design of the linear regulator the calculation of the nesterov todd direction requires in this case solving one matrix differential riccati equation plus solving a finite dimensional system of linear algebraic equations on each iteration the number of equations and unknown variables of this algebraic system is m 1 where m is a number of quadratic performance criteria

almost perfect autocorrelation sequences almost perfect autocorrelation sequences are defined as complex periodic sequences such that all the out of phase autocorrelation coefficients are zero except one the study is restricted to 1 1 sequences in this case such sequences exist only if the period n is a multiple of 4 after setting up theoretical results several sequences are constructed for every period n multiple of 4 in the range 8

new sets of optimal p ary low correlation zone sequences in this correspondence three methods of constructing low correlation zone lcz sequences are proposed in the first method we constructed binary lcz sequence sets of period 2n 1 using the legendre sequences of period 2m 1 as a column sequence when m n in the second method we devise a column sequence set of length 2m 1 1 from a binary sequence of period 2m 1 having ideal autocorrelation property and this column sequence set is used to construct binary lcz sequence sets of period 2 n 1 when m 1 n in the third method p ary lcz sequence sets are constructed by adopting p ary sequence of period pm 1 with ideal autocorrelation for integers n and m such that m n as a column sequence the second and third methods give us the optimal sets with respect to the bound by tang fan and matsufuji finally a construction method of pntimespn p ary hadamard matrices from optimal lcz sequence sets is proposed

a note on low correlation zone signal sets in this correspondence we present a connection between designing low correlation zone lcz sequences and the results of correlation of sequences with subfield decompositions presented in a recent book by the first two authors this results in lcz signal sets with huge sizes over three different alphabetic sets finite field of size integer residue ring modulo and the subset in the complex field which consists of powers of a primitive th root of unity we show a connection between these sequence designs and ldquocompletely noncyclicrdquo hadamard matrices and a construction for those sequences we also provide some open problems along this direction

fuzzifications of generalized tarski filters in tarski algebras the fuzzification of generalized tarski filters of generalized tarski algebras is considered and related properties are investigated characterizations of a fuzzy generalized tarski filter are established based on the theory of a falling shadow the notion of a falling fuzzy generalized tarski filter of a generalized tarski algebra is introduced relations between fuzzy generalized tarski filters and falling fuzzy generalized tarski filters are provided a characterization of a falling fuzzy generalized tarski filter is established

linear systems in jordan algebras and primal dual interior point algorithms we discuss a possibility of the extension of a primal dual interior point algorithm suggested recently by alizadeh et al 1994 we consider optimization problems defined on the intersection of a symmetric cone and an affine subspace the question of solvability of a linear system arising in the implementation of the primal dual algorithm is analyzed a nondegeneracy theory for the considered class of problems is developed the jordan algebra technique suggested by faybusovich 1995 plays major role in the present paper

fuzzy inference relation based on the theory of falling shadows abstract in this paper we establish a theoretical approach to define a fuzzy inference relation based on the theory of falling shadows the main characteristic of our definition of fuzzy inference relation is that it is semantically dependent in the sense that the formula of our definition will vary according to the correlation of the antecedent and the consequence of the given implication we shall show that the formulae of fuzzy inference relation given by ukasiewicz zadeh and the probability formula are consequences of our definition under three different correlations of the propositions