distributivity equation in the class of 2 uninorms this paper is mainly devoted to solving the functional equation of distributivity between aggregation operators with 2 neutral element our investigations are motivated by the couple of distributive logical connectives and their generalizations used in fuzzy set theory e g triangular norms conorms uninorms nullnorms and implications one of the recent generalizations covering both uninorms and nullnorms are 2 uninorms which form a class of commutative associative and increasing operators on the unit interval with an absorbing element separating two subintervals having their own neutral elements in this work the distributivity of two binary operators from the class of 2 uninorms is considered in particular all possible solutions of the distributivity equation for the three defined subclasses of these operators depending on the position of its zero and neutral elements are characterized

weierstrass formula and zero finding methods classical weierstrass formula 29 has been often the subject of investigation of many authors in this paper we give some further applications of this formula for finding the zeros of polynomials and analytic functions we are concerned with the problems of localization of polynomial zeros and the construction of iterative methods for the simultaneous approximation and inclusion of these zeros conditions for the safe convergence of weierstrass method depending only on initial approximations are given in particular we study polynomials with interval coefficients using an interval version of weierstrass method enclosures in the form of disks for the complex valued set containing all zeros of a polynomial with varying coefficients are obtained we also present weierstrass like algorithm for approximating simultaneously all zeros of a class of analytic functions in a given closed region to demonstrate the proposed algorithms three numerical examples are included

some results about nullnorms on bounded lattices abstract nullnorms as a generalization of the concepts of t norms and t conorms admit a zero element to be any element in a bounded lattice in this paper we discuss the characterization of idempotent nullnorms on bounded lattices and investigate some of the main properties of them we propose some new methods yielding nullnorms in particular idempotent nullnorms on bounded lattices with the fixed zero element under some additional constraints moreover some illustrative examples are presented to demonstrate the feasibility of the proposed methods

on a class of weak triangular norm operators some basic properties associated with aggregation operators are introduced we introduce two classes of aggregation operators called weak t norm and weak t conorm operators these classes are obtained by relaxing the associativity and boundary conditions of the t norms and t conorm respectively using the fuzzy modeling technology we construct families of these operators the families developed involve a nonlinear weighted averaging of t norms and t conorms the nonlinearity results from the fact that the weights used are themselves dependent on the argument values used in the aggregation particular emphasis is given as used in this work to the possibilities of using the fuzzy systems modeling technology as a tool for constructing aggregation functions from a specification of some properties of the desired operator

distributivity equations in the class of semi t operators recently the distributivity equations have been discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms in this study we present the solutions to distributivity between semi t operators previous results related to the distributivity between nullnorms and between semi t operators and semi nullnorms can be obtained as simple corollaries

on approximate zeros and rootfinding algorithms for a complex polynomial on donne des criteres pour qu un nombre complexe soit une racine approchee d un polynome f par la methode de newton ou d euler d ordre k on construit des familles d algorithmes surement convergents

fast generalized minimum distance decoding of algebraic geometry and reed solomon codes generalized minimum distance gmd decoding is a standard soft decoding method for block codes we derive an efficient general gmd decoding scheme for linear block codes in the framework of error correcting pairs special attention is paid to reed solomon rs codes and one point algebraic geometry ag codes for rs codes of length n and minimum hamming distance d the gmd decoding complexity turns out to be in the order o nd where the complexity is counted as the number of multiplications in the field of concern for ag codes the gmd decoding complexity is highly dependent on the curve in consideration it is shown that we can find all relevant error erasure locating functions with complexity o o sub 1 nd where o sub 1 is the size of the first nongap in the function space associated with the code a full gmd decoding procedure for a one point ag code can be performed with complexity o dn sup 2

construction of nullnorms on bounded lattices and an equivalence relation on nullnorms abstract in this study we present two methods for the construction of nullnorms on bounded lattices based on the existence of t norms as well as t conorms on an arbitrary bounded lattice l we demonstrate that these methods differ from the existing approaches mainly because of their more generalized structures an equivalence relation is also defined based on a class of nullnorms and some properties of this relation are examined

involutive uninorm logic with the n potency axiom this paper investigates a class of extensions denoted c niul of the involutive uninorm logic iul which is obtained by adding the n potency axiom to iul the main result of this paper is the proof of the standard completeness for c niul which is obtained by generalizing jenei and montagna style approach for proving standard completeness for mtl in addition this result also presents a generalization of jenei s embedding method of constructing left continuous t norms which can generate a countable number of left continuous and involutive conjunctive uninorms and provides a tremendously wide spectrum of choice for e g logical and set theoretical connectives in non classical logic and in fuzzy theory

on the reversibility of uninorms and t operators although the concept of reverse is given in publ math debrecen 12 1973 21 39 not only for a t norm but also for any associative operator the definition does not work in so general a case in this paper the concept of reverse is extended in an appropriate way to some kinds of associative operators like t conorms uninorms and t operators all continuous and reversible t conorms are characterized and after some results an analogous characterization is also given for all semi continuous reversible uninorms and all continuous reversible t operators in the last case reversibility becomes a kind of transformation that converts a uninorm into a t operator and viceversa finally related to reversibility uninorms and t operators of moderate growth are studied

point estimation of simultaneous methods for solving polynomial equations a survey ii the construction of computationally verifiable initial conditions which provide both the guaranteed and fast convergence of the numerical root finding algorithm is one of the most important problems in solving nonlinear equations smale s point estimation theory from 1981 was a great advance in this topic it treats convergence conditions and the domain of convergence in solving an equation f z 0 using only the information of f at the initial point z 0 the study of a general problem of the construction of initial conditions of practical interest providing guaranteed convergence is very difficult even in the case of algebraic polynomials in the light of smale s point estimation theory an efficient approach based on some results concerning localization of polynomial zeros and convergent sequences is applied in this paper to iterative methods for the simultaneous determination of simple zeros of polynomials we state new improved initial conditions which provide the guaranteed convergence of frequently used simultaneous methods for solving algebraic equations ehrlich aberth s method ehrlich aberth s method with newton s correction borsch supan s method with weierstrass correction and halley like or wang zheng method the introduced concept offers not only a clear insight into the convergence analysis of sequences generated by the considered methods but also explicitly gives their order of convergence the stated initial conditions are of significant practical importance since they are computationally verifiable they depend only on the coefficients of a given polynomial its degree n and initial approximations to polynomial zeros

on the relationships between the orders induced by uninorms and nullnorms abstract in this paper some relationships between the orders induced by uninorms and nullnorms are discussed some relations between the sets admitting some incomparability w r t those orders are investigated also some relationships between the algebraic structures obtained from those orders are determined

linear diophantine equations over polynomials and soft decoding of reed solomon codes this paper generalizes the classical knuth schoumlnhage algorithm computing the greatest common divisor gcd of two polynomials for solving arbitrary linear diophantine systems over polynomials in time quasi linear in the maximal degree as an application the following weighted curve fitting problem is considered given a set of points in the plane find an algebraic curve satisfying certain degree conditions that goes through each point the prescribed number of times the main motivation for this problem comes from coding theory namely it is ultimately related to the list decoding of reed solomon codes this paper presents a new fast algorithm for the weighted curve fitting problem based on the explicit construction of a groebner basis this gives another fast algorithm for the soft decoding of reed solomon codes different from the procedure proposed by feng which works in time w r o 1 nlog2n where r is the rate of the code and w is the maximal weight assigned to a vertical line

a family of simultaneous zero finding methods abstract applying hansen patrick s formula for solving the single equation f z 0 to a suitable function appearing in the classical weierstrass method two one parameter families of interation functions for the simultaneous approximation of all simple and multiple zeros of a polynomial are derived it is shown that all the methods of these families have fourth order of convergence some computational aspects of the proposed methods and numerical examples are given

new list decoding algorithms for reed solomon and bch codes in this paper we devise a rational curve fitting algorithm and apply it to the list decoding of reed solomon and bose chaudhuri hocquenghen bch codes the resulting list decoding algorithms exhibit the following significant properties

residual operations of left and right uninorms on a complete lattice uninorms are an important generalization of triangular norms and conorms having a neutral element lying anywhere in the unit interval in this paper we introduce the concepts of left and right uninorms on a complete lattice we discuss the residual operations of left and right uninorms and study some basic properties of the residual operations of infinitely distributive left right uninorms and pseudo uninorms

on the guaranteed convergence of the fourth order simultaneous method for polynomial zeros one of the most important and challenging problems in solving nonlinear equations is the construction of computationally verifiable initial conditions that provide both the guaranteed and fast convergence of the considered numerical method a suitable convergence procedure based partially on smale s point estimation theory from 1981 is applied in this paper to the fourth order iterative method for the simultaneous approximation of simple zeros of polynomials proposed by zheng and sun in 1999 we have stated initial conditions which ensure the guaranteed convergence of this method these conditions are of significant practical importance since they depend only on available data the coefficients of a given polynomial its degree n and initial approximations to polynomial zeros

reed solomon list decoding from a system theoretic perspective in this paper the sudan guruswami approach to list decoding of reed solomon rs codes is cast in a system theoretic framework with the data a set of trajectories or time series is associated which is then modeled as a so called behavior in this way a connection is made with the behavioral approach to system theory it is shown how a polynomial representation of the modeling behavior gives rise to the bivariate interpolating polynomials of the sudan guruswami approach the concept of weighted row reduced is introduced and used to achieve minimality two decoding methods are derived and a parametrization of all bivariate interpolating polynomials is given

weak uninorm aggregation operators abstract by weakening the identity condition of uninorm a general class of associative aggregation operators called weak uninorm is introduced it is proved that continuous weak uninorms are the combination of continuous t norm and continuous t conorm through a median operator the representation theorem for archimedean weak uninorm is also given finally the counting number of the identity elements of weak uninorm is also investigated

on the structure of 2 uninorms abstract in this paper we describe the structure of 2 uninorms defined on the unit interval we divide the class of 2 uninorms into five mutually exclusive subclasses based on their boundary behaviour as determined by the absorbing element and the conjunctive disjunctive nature of the underlying uninorms which every 2 uninorm is known to have for each of these subclasses we fully characterize the structure of its members albeit for two subclasses only under an additional continuity assumption a common practice in the study of associative operations

the modularity condition for semi t operators and semi uninorms abstract the aim of this paper is mainly to solve the functional equations given by the modularity condition several years ago the modularity equations for t norms t conorms uninorms and t operators which are commutative and associative have been studied our investigations are motivated by modularity condition for generalizations of these operators by removing associativity or commutativity in this work the following main conclusions are proved 1 a continuous t norm with respect to a continuous semicopula is modular if and only if they are equal the case for a semicopula with respect to a strict t norm is also the same a semicopula with respect to a co semicopula is modular if and only if the semicopula is min and the co semicopula is max the modularity condition does not hold for a co semicopula with respect to a semicopula 2 necessary and sufficient conditions are given for a semi t operator with respect to a semi uninorm a pseudo uninorm with respect to a semi t operator to satisfy the modularity condition equation new solutions to the modularity condition equations of the case 1 are characterized

a parametric approach to list decoding of reed solomon codes using interpolation in this paper we present a minimal list decoding algorithm for reed solomon rs codes minimal list decoding for a code c refers to list decoding with radius l where l is the minimum of the distances between the received word r and any codeword in c we consider the problem of determining the value of l as well as determining all the codewords at distance l our approach involves a parametrization of interpolating polynomials of a minimal grobner basis g we present two efficient ways to compute g we also show that so called re encoding can be used to further reduce the complexity we then demonstrate how our parametric approach can be solved by a computationally feasible rational curve fitting solution from a recent paper by wu besides we present an algorithm to compute the minimum multiplicity as well as the optimal values of the parameters associated with this multiplicity which results in overall savings in both memory and computation

some properties of weak uninorms a weak uninorm is not only a generalization of a uninorm but also of a nullnorm in this paper we will show that if a weak uninorm is archimedean then it is an archimedean nullnorm and if a weak uninorm is e archimedean then it is an archimedean uninorm moreover the de morgan triples of the weak uninorms will be characterized too

the modularity condition for uninorms revisited abstract functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory the modularity equation is a kind of restricted general associative equations in the literature the already known results concerning the modularity equation for two uninorms are based on the assumption that both uninorms lie in one of the most studied classes of uninorms in this study we explore the modularity equation involving uninorms in a most general setting specifically we investigate the modularity between two uninorms in the cases when one uninorm belongs to any of the most studied classes of uninorms but the other one is any uninorm with no further assumptions further many new solutions appear from this new point of view that were not included in previous approaches

improved decoding of reed solomon and algebraic geometry codes given an error correcting code over strings of length n and an arbitrary input string also of length n the list decoding problem is that of finding all codewords within a specified hamming distance from the input string we present an improved list decoding algorithm for decoding reed solomon codes the list decoding problem for reed solomon codes reduces to the following curve fitting problem over a field f given n points x sub i spl middot y sub i sub i 1 sup n x sub i y sub i spl isin f and a degree parameter k and error parameter e find all univariate polynomials p of degree at most k such that y sub i p x sub i for all but at most e values of i spl isin 1 n we give an algorithm that solves this problem for e 1 3 where the result yields the first asymptotic improvement in four decades the algorithm generalizes to solve the list decoding problem for other algebraic codes specifically alternant codes a class of codes including bch codes and algebraic geometry codes in both cases we obtain a list decoding algorithm that corrects up to n spl radic n n d errors where n is the block length and d is the designed distance of the code the improvement for the case of algebraic geometry codes extends the methods of shokrollahi and wasserman see in proc 29th annu acm symp theory of computing p 241 48 1998 and improves upon their bound for every choice of n and d we also present some other consequences of our algorithm including a solution to a weighted curve fitting problem which may be of use in soft decision decoding algorithms for reed solomon codes

the modularity condition for uninorms and t operators in this work we study the functional equation given by the modularity condition f x g y z g f x y z for all z x where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

the re encoding transformation in algebraic list decoding of reed solomon codes the main computational steps in algebraic soft decoding as well as sudan type list decoding of reed solomon codes are bivariate polynomial interpolation and factorization we introduce a computational technique based upon re encoding and coordinate transformation that significantly reduces the complexity of the bivariate interpolation procedure this re encoding and coordinate transformation converts the original interpolation problem into another reduced interpolation problem which is orders of magnitude smaller than the original one a formal proof is presented to show that the two interpolation problems are indeed equivalent an efficient factorization procedure that applies directly to the reduced interpolation problem is also given

uninorm solutions and or nullnorm solutions to the modularity condition equations in this paper uninorm solutions and or nullnorm solutions to the modularity condition equations are in detail discussed and then we find that no new non trivial solutions to the equations appear where uninorms discussed lie in the set cu of uninorms continuous in 0 1 2 further the differences between elements in cu and in u have been shown

approximate zeros of quadratically convergent algorithms smale s condition for a point to be an approximate zero of a func tion for newton s method is extended to the general quadratically convergent iterative algorithm it is shown in which way the bound in the condition is affected by the characteristics of the algorithm this puts the original condition of smale for newton s method in a more general perspective the results are also discussed in the light of numerical evidence

u n implications and their characterizations recently we have presented characterizations of s n implications generated from t conorms and continuous strict strong negations uninorms were introduced by yager and rybalov in 1996 as a generalization of t norms and t conorms thus they are another fertile source based on which one can define fuzzy implications u n implications are a generalization of s n implications where a t conorm s is replaced by a disjunctive uninorm u in this work we present characterizations of u n implications obtained from disjunctive uninorms and continuous negations as well as u n operations defined from uninorms and continuous negations

aggregation operators and fuzzy systems modeling abstract a general class of aggregation operators called mica having the properties of monotonicity symmetry and an identity element are introduced we stress the significance of the choice of identity in characterizing the operator we show that the t norm and t conorm are special cases of these operators other classees of these operators are introduced notably an additive class which is very much in the spirit of the kind of aggregation used in neural networks it is shown how a general description of the fuzzy system modeling technique can be obtained using these operators

a parallel algorithm for simple roots for polynomials abstract a method for finding simple roots of arbitrary polynomials based on divided differences is discussed theoretical background is presented for the case of simple roots numerical results are presented which show the algorithm finds simple and multiple zeros to an accuracy usually limited by the accuracy of polynomial evaluation the method is designed for a simd parallel computer the algorithm is compared to two other frequently used polynomial root finders the jenkins traub algorithm and laguerre s method

the distributivity equation for uninorms revisited abstract the distributivity equation has been widely studied involving different classes of aggregation functions from t norms and t conorms to uninorms nullnorms and generalizations of them it is important in the framework of logical connectives because of its applications in fuzzy logic and approximate reasoning as well as in image processing since uninorms have been used in these topics the study of the distributivity between two uninorms becomes specially interesting in a recent paper by the same authors the already known solutions were compiled and completed when the first uninorm is in any of the most studied classes of uninorms and the second uninorm is anyone in this paper we want to achieve this study by focusing on the reverse direction that is for the cases when the second uninorm lies in any of the most studied classes of uninorms and the first one is any uninorm we show along the paper that this new point of view leads to many new solutions

the monoid structure of e implications and pseudo e implications in this paper we consider the set of all e implications and pseudo e implications we define operators to endow these sets as monoid structures which are also complete lattices the set of all pseudo e implications becomes a de morgan algebra we introduce a class of e implications such that it becomes a de morgan algebra moreover contrapositive and self dual pseudo e implication and contrapositive e implication are also studied finally we introduce a class of pseudo e implications such that it becomes a complete sublattice of the set of all pseudo e implications which is also a de morgan algebra

lattice structure of e implications on l in this paper we consider the set of all e implications on l and define two operations on the set of all representable e implications on l thus endowing it with monoid structure which is also a distributive complete lattice

logics for residuated pseudo uninorms and their residua with the aim of capturing the logic of residuated pseudo uninorms and their residua we introduce an axiomatic extension of the system of bounded representable residuated lattices of metcalfe olivetti and gabbay since many known non commutative fuzzy logics are axiomatic extensions of their system it plays an important role among non commutative fuzzy logics by adding the so called n potency axiom to our system we prove that standard completeness can be obtained this result supports our conjecture that our system is the logic of residuated pseudo uninorms and their residua

the distributivity equations for semi t operators over uninorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms or called t operators in this paper we describe the solutions of distributivity for semi t operators over uninorms previous results about distributivity for nullnorms over uninorms can be obtained as a corollary

the distributivity condition for uninorms and t operators in this work we study the functional equation given by the distributivity condition f x g y z g f x y f x z for all x y z 0 1 where the unknown functions f g are uninorms and or t operators we characterize all the solutions in the four possible cases i when f g are t operators ii when f is a t operator and g a uninorm iii when f is a uninorm and g a t operator and finally iv when f g are uninorms

the theory of smale s point estimation and its applications abstract the main result of this paper is that we exact smale s point estimation theory i e without assuming k p z 1 p k z k k 2 being bounded by the point estimation convergence theorem of the ne method is set up by making use of the majorizing method the proof of the theorem is simple and precise while the required point estimation conditions are weaker than all those of known point estimation convergence theorems another result of this paper is an application of the above new theory to the durand kerner method we compare the point estimation conditions for the durand kerner method with other known point estimation conditions numerical results show that our results have evident advantages

migrativity property for uninorms and semi t operators in this paper the notions of migrative uninorms over semi t operators and migrative semi t operators over uninorms are introduced and investigated all solutions of the migrativity equations for all possible combinations of semi t operators and uninorms are characterized

distributivity and conditional distributivity of a uninorm and a continuous t conorm the open problem recalled by klement in the linz2000 closing session related to distributivity and conditional distributivity of a uninorm and a continuous t conorm is solved for the most usual known classes of uninorms from the obtained results it is deduced that distributivity and conditional distributivity are equivalent for these cases it is remarkable that solutions appear involving not only strict t conorms but also ordinal sums of the maximum with a strict t conorm conversely the distributivity of a t conorm over a uninorm is also studied leading only to already known solutions moreover the dual case of distributivity and conditional distributivity involving uninorms and continuous t norms is also solved proving again the equivalence of both kinds of distributivities

relation between neutral element and annihilator in absorption equation abstract the absorption identities in algebra give a relationship between two associative and commutative binary operators join and meet we generalize these operators into a new class of binary operators and study their structures in the context of absorption equation and show that the study of absorption equation involving triangular norms triangular conorms uninorms and nullnorms in the literature are special cases of our study

on the distributivity property for uninorms abstract distributivity between two operations is a property that was already posed many years ago and that is especially interesting in the framework of logical connectives for this reason the distributivity property has been extensively studied for several families of operations like triangular norms and conorms some kinds of uninorms and nullnorms also called t operators and even for some generalizations of them in this paper we investigate the distributivity equation involving two uninorms lying in any one of the most studied classes of uninorms leading to many new solutions

a new fourth order family of simultaneous methods for finding polynomial zeros using a suitable fixed point relation with a complex parameter a new one parameter family of simultaneous methods of the fourth order for finding complex zeros of a polynomial is derived in ordinary complex arithmetic convergence analysis of the presented family is performed under computationally verifiable initial conditions which depend only on polynomial coefficients and initial approximations further improvements of the proposed family of methods are discussed and a modification for finding multiple zeros is presented some numerical results for various values of the parameter are given

the convergence of a family of parallelzero finding methods abstract one of the crucial problems in solving polynomial equations is to state some kind of quantitative conditions that provide both safe and fast convergence in the spirit of smale s point estimation theory introduced in 1981 we construct in this paper computationally verifiable initial conditions which guarantee the convergence of the recently proposed one parameter family of methods of the fourth order for the simultaneous finding polynomial zeros these conditions are computationally verifiable since they depend only on initial approximations polynomial coefficients and polynomial degree which is of significant practical importance

point estimation of a family of simultaneous zero finding methods abstract the construction of initial conditions which provide the safe convergence of iterative processes is one of the most important problems in solving equations in this paper we give initial conditions for a one parameter family of iterative methods for the simultaneous determination of all simple zeros of a polynomial zeros this family has the order of convergence four and generates some new methods with good convergence properties the presented initial conditions are of practical importance since depend only of available data coefficients of a polynomial and initial approximations to the zeros

on rational interpolation based list decoding and list decoding binary goppa codes we derive the wu list decoding algorithm for generalized reed solomon grs codes by using grobner bases over modules and the euclidean algorithm as the initial algorithm instead of the berlekamp massey algorithm we present a novel method for constructing the interpolation polynomial fast we give a new application of the wu list decoder by decoding irreducible binary goppa codes up to the binary johnson radius finally we point out a connection between the governing equations of the wu algorithm and the guruswami sudan algorithm immediately leading to equality in the decoding range and a duality in the choice of parameters needed for decoding both in the case of grs codes and in the case of goppa codes

structure of n uninorms in this paper we study binary operators on 0 1 which are associative monotone non decreasing in both variables and commutative amc with neutral element in this work we generalize the concept of neutral element and this generalization gives rise to a new class of amc binary operators on 0 1 called n uninorms n uninorms are denoted as u n where n comes from the generalization of the neutral element we study the structure of n uninorms the structure resembles an ordinal sum structure made up of n uninorms we characterize some special cases of them based on some continuity considerations and show that t norms t conorms uninorms and nullnorms t operators are special cases of n uninorms we also show that given n there are n 1 classes of operators in u n and each of them has many subclasses we also study the frank equation involving n uninorms and show that we need to consider only n uninorms for the study finally we show that the total number of subclasses of operators in u n follows the famous series called catalan numbers

the modularity law in some classes of aggregation operators abstract in this study we consider the functional equation of modularity in a special class of aggregation operators with an absorbing element first we focus on the modularity between commutative binary operators and their duals and then we examine the modularity for operators from the class of 2 uninorms which generalize nullnorms by extending their certain conditions in particular for these operators depending on the positions of their neutral elements and possessing the same absorbing element we obtain positive and negative results which are analogous to the results in the general case for operators with different absorbing elements

minimal grobner bases and the predictable leading monomial property abstract we focus on grobner bases for modules of univariate polynomial vectors over a ring we identify a useful property the predictable leading monomial plm property that is shared by minimal grobner bases of modules in f x q no matter what positional term order is used the plm property is useful in a range of applications and can be seen as a strengthening of the wellknown predictable degree property row reducedness a terminology introduced by forney in the 70 s because of the presence of zero divisors minimal grobner bases over a finite ring of the type z p r where p is a prime integer and r is an integer 1 do not necessarily have the plm property in this paper we show how to derive from an ordered minimal grobner basis a so called minimal grobner p basis that does have a plm property we demonstrate that minimal grobner p bases lend themselves particularly well to derive minimal realization parametrizations over z p r applications are in coding and sequences over z p r

construction methods for idempotent nullnorms on bounded lattices abstract in this paper we discuss the presence of idempotent nullnorms on bounded lattices and investigate some properties of these operators we introduce two new methods for constructing idempotent nullnorms on bounded lattices for a zero element under a constraint that all elements incomparable with the zero element are comparable with each other in order to stress the role of this constraint satisfying that our constructions yield an idempotent nullnorm some illustrative examples are added

representations through a monoid on the set of fuzzy implications fuzzy implications are one of the most important fuzzy logic connectives in this work we conduct a systematic algebraic study on the set ii of all fuzzy implications to this end we propose a binary operation denoted by which makes i i a non idempotent monoid while this operation does not give a group structure we determine the largest subgroup ss of this monoid and using its representation define a group action of ss that partitions ii into equivalence classes based on these equivalence classes we obtain a hitherto unknown representations of the two main families of fuzzy implications viz the f and g implications

decisions and evaluations by hierarchical aggregation of information usually in preparing a decision a hierarchy of criteria for evaluating alternatives can he agreed upon by the decision makers the problem addressed in this paper is the appropriate modelling of such evaluations and their aggregation in order to arrive at a proper overall evaluation function by which the decision alternatives can be ordered easily representing the criteria subjective categories by fuzzy sets it is possible to use aggregation operators as models for the amalgamation of those criteria in the framework of an empirical research project a hierarchy of criteria was developed for the evaluation of credit worthiness of customers 50 credit applications were evaluated by a number of credit managers of banks and their judgement could be appropriately modelled by a four level hierarchy of criteria

on a certain class of aggregative operators abstract here our starting point is a study of connection with dombi aggregative operators uninorms strict t norms and t conorms we present a new representation theorem of strong negations that explicitly contains the neutral value then the relationships for aggregative operators and strong negations are verified as well as those for the t norm and t conorm using the pan operator concept we introduce the multiplicative pliant concept and give the necessary and sufficient conditions for it we study a certain class of weighted aggregative operators representable uninorms which build a self demorgan class with infinitely many negations we provide the necessary and sufficient conditions for these operators

a characterization of idempotent nullnorms nullnorms are generalization of triangular norms and conorms with a zero element anywhere in the unit interval nullnorms are built up from triangular norms and triangular conorms if nullnorm is idempotent then it is composed of a minimum and a maximum the idea of this paper is to find minimal assumptions on an operation in order to get an idempotent nullnorm

nullnorms on bounded lattices nullnorms are generalization of triangular norms and triangular conorms with a zero element in the interior of the unit interval in this paper we generalize nullnorms to an arbitrary bounded lattices we show the existence of nullnorms with zero element a for arbitrary element a l 0 1 using the fact that some t norms and t conorms on an arbitrary fixed bounded lattice l always exist as a by product we give a method of constructing nullnorms using this method we obtain also the smallest nullnorm and the greatest nullnorm with given zero element a some other construction methods for nullnorms are also added

distributivity between semi t operators and semi nullnorms recently the distributivity equation was discussed in families of certain operations e g triangular norms conorms uninorms and nullnorms in this paper we describe the solutions of distributivity between semi t operators and semi nullnorms previous results about distributivity between nullnorms can be obtained as simple corollaries