soft groups and normalistic soft groups soft set theory proposed by molodtsov has been regarded as an effective mathematical tool to deal with uncertainties in this paper first we correct some of the problematic cases in a previous paper by aktas and email protected man h aktas n email protected man soft sets and soft groups inf sci 177 2007 2726 2735 moreover we introduce the concepts of normalistic soft group and normalistic soft group homomorphism study their several related properties and investigate some structures that are preserved under normalistic soft group homomorphisms

continuous time random walks on networks with vertex and time dependent forcing we have investigated the transport of particles moving as random walks on the vertices of a network subject to vertex and time dependent forcing we have derived the generalized master equations for this transport using continuous time random walks characterized by jump and waiting time densities as the underlying stochastic process the forcing is incorporated through a vertex and time dependent bias in the jump densities governing the random walking particles as a particular case we consider particle forcing proportional to the concentration of particles on adjacent vertices analogous to self chemotactic attraction in a spatial continuum our algebraic and numerical studies of this system reveal an interesting pair aggregation pattern formation in which the steady state is composed of a high concentration of particles on a small number of isolated pairs of adjacent vertices the steady states do not exhibit this pair aggregation if the transport is random on the vertices i e without forcing the manifestation of pair aggregation on a transport network may thus be a signature of self chemotactic like forcing

application of fuzzy soft set in decision making problems based on grey theory there are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets however the basis of evaluation of the decision method is single and simple the same decision problem can obtain different results from using a different evaluation basis in this paper in order to obtain the right result we discuss fuzzy soft set decision problems a new algorithm based on grey relational analysis is presented the evaluation bases of the new algorithm are multiple there is more information in a decision result based on multiple evaluation bases which is more easily accepted and logical to one s thinking for the two cases examined the results show that the new algorithm is efficient for solving decision problems

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

soft nexuses in this paper we define soft nexuses over a nexus n after that we define the notions cyclic soft nexus prime and maximal soft subnexuses and we obtain some results about the above definitions finally we define the integer number induced by soft nexus a a and denoted by a a and show that for any n there exists soft nexus a a such that a a n

applications of soft sets in ideal theory of bck bci algebras the notion of soft ideals and idealistic soft bck bci algebras is introduced and several examples are given relations between soft bck bci algebras and idealistic soft bck bci algebras are provided the intersection union and operation and or operation of soft ideals and idealistic soft bck bci algebras are established

fuzzy filters of mtl algebras characterizations of fuzzy filters in mtl algebras are given the fuzzy filter generated by a fuzzy set is considered the notion of boolean fuzzy filters and mv fuzzy filters are introduced and related properties are investigated a condition for a fuzzy filter to be boolean is provided a characterization of a boolean fuzzy filter is given a congruence relation on a mtl algebra induced by a fuzzy filter is established and we show that the set of all congruence relations induced by a fuzzy filter is a completely distributive lattice

operators that preserve semiring matrix functions abstract characterizations are obtained of those linear operators over certain semirings that preserve 1 the rth coefficient of the rook polynomial those that preserve 2 the term rank of matrices with term rank r and those that preserve 3 the rth elementary symmetric permanental function our results apply to many algebraic systems of combinatorial interest including the nonnegative integer matrices boolean matrices and fuzzy matrices

the characterizations of h hemiregular hemirings and h intra hemiregular hemirings in this paper the concepts of fuzzy h bi ideals and fuzzy h quasi ideals of a hemiring are introduced and related properties are investigated the notion of h intra hemiregularity of a hemiring which is a generalization of the notion of intra regularity of a ring is provided some characterizations of h hemiregular hemirings h intra hemiregular hemirings and hemirings that are both h hemiregular and h intra hemiregular are derived in terms of fuzzy left fuzzy right h ideals fuzzy h bi ideals and fuzzy h quasi ideals

towards a statistical theory of texture evolution in polycrystals most technologically useful materials possess polycrystalline microstructures composed of a large number of small monocrystalline grains separated by grain boundaries the energetics and connectivity of the grain boundary network play a crucial role in determining the properties of a material across a wide range of scales a central problem in materials science is to develop technologies capable of producing an arrangement of grains a texture that provides for a desired set of material properties one of the most challenging aspects of this problem is to understand the role of topological reconfigurations during coarsening here we propose an upscaling procedure suitable for large complex systems the procedure is based on numerical experimentation combined with stochastic tools and consists of large scale numerical simulations of a system at a microscopic level statistical analysis of the microscopic data and formulation of the model based on stochastic characteristics predicted by the statistical analysis this approach promises to be valuable in establishing the effective model of microstructural evolution in realistic two and three dimensional systems to test ideas we use our upscaling procedure to study the mesoscopic behavior of a reduced one dimensional network of grain boundaries despite the simplicity of its formulation this model exhibits highly nontrivial behavior characterized by growth and disappearance of grain boundaries and develops probability distributions similar to those observed in higher dimensional simulations here we focus on the grain deletion events which are common to all coarsening systems

soft p ideals of soft bci algebras molodtsov d molodtsov soft set theory first results comput math appl 37 1999 19 31 introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches jun y b jun soft bck bci algebras comput math appl 56 2008 1408 1413 applied first the notion of soft sets by molodtsov to the theory of bck bci algebras in this paper we introduce the notion of soft p ideals and p idealistic soft bci algebras and then investigate their basic properties using soft sets we give characterizations of fuzzy p ideals in bci algebras we provide relations between fuzzy p ideals and p idealistic soft bci algebras

list decoding of algebraic geometric codes we generalize sudan s see j compl vol 13 p 180 93 1997 results for reed solomon codes to the class of algebraic geometric codes designing algorithms for list decoding of algebraic geometric codes which can decode beyond the conventional error correction bound d 1 2 d being the minimum distance of the code our main algorithm is based on an interpolation scheme and factorization of polynomials over algebraic function fields for the latter problem we design a polynomial time algorithm and show that the resulting overall list decoding algorithm runs in polynomial time under some mild conditions several examples are included

a root finding algorithm for list decoding of reed muller codes let f sub q x sub 1 x sub m denote the set of polynomials over f sub q in m variables and f sub q x sub 1 x sub m sub spl les u denote the subset that consists of the polynomials of total degree at most u let h t be a nontrivial polynomial in t with coefficients in f sub q x sub 1 x sub m a crucial step in interpolation based list decoding of q ary reed muller rm codes is finding the roots of h t in f sub q x sub 1 x sub m sub spl les u in this correspondence we present an efficient root finding algorithm which finds all the roots of h t in f sub q x sub 1 x sub m sub spl les u the algorithm can be used to speed up the list decoding of rm codes

fuzzy relations and fuzzy groups abstract given a group s we consider fuzzy relations on s that is maps from s s into 0 1 of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on s s we prove that if is a fuzzy subset of s and is the strongest fuzzy relation on s that is a fuzzy relation on then is a fuzzy subgroup if and only if is a fuzzy subgroup a number of other results are obtained about the interrelationships between fuzzy relations on s including the weakest fuzzy relation and fuzzy subgroups on s s

matrices over semirings introducing the concept of semi invertibility of square matrices over semirings some sufficient conditions for semi invertibility of square matrices over various kinds of semirings are obtained also a necessary and sufficient condition for semi invertibility of square matrices over semirings is obtained

diffusion of epicenters of earthquake aftershocks omori s law and generalized continuous time random walk models the epidemic type aftershock sequence etas model is a simple stochastic process modeling seismicity based on the two best established empirical laws the omori law power law decay ensuremath sim 1 t 1 ensuremath theta of seismicity after an earthquake and gutenberg richter law power law distribution of earthquake energies in order to describe also the space distribution of seismicity we use in addition a power law distribution ensuremath sim 1 r 1 ensuremath mu of distances between triggered and triggering earthquakes the etas model has been studied for the last two decades to model real seismicity catalogs and to obtain short term probabilistic forecasts here we present a mapping between the etas model and a class of ctrw continuous time random walk models based on the identification of their corresponding master equations this mapping allows us to use the wealth of results previously obtained on anomalous diffusion of ctrw after translating into the relevant variable for the etas model we provide a classification of the different regimes of diffusion of seismic activity triggered by a mainshock specifically we derive the relation between the average distance between aftershocks and the mainshock as a function of the time from the mainshock and of the joint probability distribution of the times and locations of the aftershocks the different regimes are fully characterized by the two exponents ensuremath theta and ensuremath mu our predictions are checked by careful numerical simulations we stress the distinction between the bare omori law describing the seismic rate activated directly by a mainshock and the renormalized omori law taking into account all possible cascades from mainshocks to aftershocks of aftershock of aftershock and so on in particular we predict that seismic diffusion or subdiffusion occurs and should be observable only when the observed omori exponent is less than 1 because this signals the operation of the renormalization of the bare omori law also at the origin of seismic diffusion in the etas model we present predictions and insights provided by the etas to ctrw mapping which suggest different ways for studying seismic catalogs finally we discuss the present evidence for our predicted subdiffusion of seismicity triggered by a main shock stressing the caveats and limitations of previous empirical works

notes on interval valued intuitionistic fuzzy soft sets and their properties comput math appl 60 2010 906 918 in this paper we point out two definitions definition 18 and definition 19 in a previous paper by jiang et al y jiang y tang q chen h liu j tang interval valued intuitionistic fuzzy soft sets and their properties comput math appl 60 2010 906 918 are not appropriate accordingly the proofs of some relevant theorems are also not right we redefine the two definitions and reprove these theorems by using the new definitions

on soft equality molodtsov introduced the concept of soft sets which can be seen as a new mathematical tool for dealing with uncertainty in this paper we deal with the algebraic structure of soft sets the lattice structures of soft sets are constructed the concept of soft equality is introduced and some related properties are derived it is proved that soft equality is a congruence relation with respect to some operations and the soft quotient algebra is established

generalizations of fuzzy subalgebras in bck bci algebras more general form of the notion of quasi coincidence of a fuzzy point with a fuzzy set is considered and generalizations of results in the papers y b jun on a b fuzzy subalgebras of bck bci algebras bull korean math soc 42 4 2005 703 711 y b jun fuzzy subalgebras of type a b in bck bci algebras kyungpook math j 47 2007 403 410 are discussed the notions of q k fuzzy subalgebras and email protected q k fuzzy subalgebras in a bck bci algebra x are introduced and several properties are investigated characterizations of email protected q k fuzzy subalgebra in a bck bci algebra x are discussed

generalized fuzzy h bi ideals and h quasi ideals of hemirings a new kind of generalized fuzzy h ideals of a hemiring namely the set membership variant set membership variantlogical orq fuzzy h bi ideal resp h quasi ideal is studied and the relationships between these generalized fuzzy h ideals are described some characterization theorems of prime and semiprime set membership variant set membership variantlogical orq fuzzy h bi ideals resp h quasi ideals of a hemiring are also given in particular we show that the h hemiregular hemirings and h intra hemiregular hemirings can be described by using some of their generalized fuzzy h ideals finally the implication based fuzzy h bi ideals resp h quasi ideals of a hemiring are considered

a generalization of the berlekamp massey algorithm for multisequence shift register synthesis with applications to decoding cyclic codes a generalization of the berlekamp massey algorithm is presented for synthesizing minimum length linear feedback shift registers for generating prescribed multiple sequences a more general problem is first considered that of finding the smallest initial set of linearly dependent columns in a matrix over an arbitrary field which includes the multisequence problem as a special case a simple iterative algorithm the fundamental iterative algorithm fia is presented for solving this problem the generalized algorithm is then derived through a refinement of the fia application of this generalized algorithm to decoding cyclic codes up to the hartmann tzeng ht bound and roos bound making use of multiple syndrome sequences is considered conditions for guaranteeing that the connection polynomial of the shortest linear feedback shift register obtained by the algorithm will be the error locator polynomial are determined with respect to decoding up to the ht bound and special cases of the roos bound

involutory and invertible fuzzy bck algebras the concept of a fuzzy annihilator in a commutative bck algebra will be introduced and then we investigate some basic properties using this notion we define an involutory resp invertible fuzzy ideal we prove that i every bounded implicative bck algebra is an involutory fuzzy bck algebra and ii every categorical commutative bck algebra is an invertible fuzzy bck algebra let x be an involutory and invertible fuzzy bck algebra and let fi x denote the set of all fuzzy ideals of x we show that iii fi x is a distributive lattice and iv fi x is a quasi boolean algebra

fuzzy subinclines ideals of incline algebras the fuzzification of subinclines ideals in inclines are considered and some related properties are investigated we also state the product of fuzzy subinclines ideals and the projections of fuzzy subinclines ideals we discuss fuzzy relations fuzzy characteristic subinclines ideals

characterizations of hemirings by νq k fuzzy ideals in this paper we define q k fuzzy h sub hemirings q k fuzzy h bi ideals q k fuzzy h quasi ideals we characterize h hemiregular and h intra hemiregular hemirings by the properties of their q k fuzzy h ideals q k fuzzy h bi idealsand q k fuzzy h quasi ideals some of these characterizations are generalizations of the characterizations given in 36 x ma j zhan generalized fuzzyh bi ideals and h quasi ideals of hemirings inform sci 179 2009 1249 1268

linear operators strongly preserving r potent matrices over semirings abstract we consider the problem of characterizing those linear operators l on the matrices over a semiring such that l x is idempotent if and only if x is complete characterizations are obtained for many semirings including the nonnegative reals the nonnegative integers the two element boolean algebra and the fuzzy scalars

pattern formation on networks with reactions a continuous time random walk approach we derive the generalized master equation for reaction diffusion on networks from an underlying stochastic process the continuous time random walk ctrw the nontrivial incorporation of the reaction process into the ctrw is achieved by splitting the derivation into two stages the reactions are treated as birth death processes and the first stage of the derivation is at the single particle level taking into account the death process while the second stage considers an ensemble of these particles including the birth process using this model we have investigated different types of pattern formation across the vertices on a range of networks importantly the ctrw defines the laplacian operator on the network in a non ad hoc manner and the pattern formation depends on the structure of this laplacian here we focus attention on ctrws with exponential waiting times for two cases one in which the rate parameter is constant for all vertices and the other where the rate parameter is proportional to the vertex degree this results in nonsymmetric and symmetric ctrw laplacians respectively in the case of symmetric laplacians pattern formation follows from the turing instability however in nonsymmetric laplacians pattern formation may be possible with or without a turing instability

on the equivalence between berlekamp s and euclid s algorithms corresp it is shown that berlekamp s iterative algorithm can be derived from a normalized version of euclid s extended algorithm simple proofs of the results given recently by cheng are also presented

vague soft hemirings abstract xu et al introduced the concept of vague soft sets which is an extension to the soft set and the vague set in this paper we apply the concept of vague soft sets to hemiring theory the notion of q vague soft left h ideals of a hemiring is introduced and some related properties are investigated

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

α β fuzzy ideals of hemirings we give a characterization of different types of a b fuzzy ideals of hemirings where a b q q q and a q special attention is paid to q fuzzy prime and semiprime ideals

random walk model with waiting times depending on the preceding jump length in the present paper the generalized continuous time random walk model with a coupled transition kernel is considered the coupling occurs through the dependence of the waiting time probability distribution on the preceding jump length for the description of this model a method is suggested that includes the details of the microscopic distribution over the waiting times and arrival distances at a given point a close analogy to the problem of a random walk with finite velocity is demonstrated for the particular case of coupling when a waiting time is a simple function of a preceding jump length with its help an analytical solution for the generalized random walk model is found including both effects finite velocity and jump dependent waiting times simultaneously

uncoupled continuous time random walk finite jump length probability density function in this work the uncoupled continuous time random walk model with the exponential jump length probability density function pdf is considered exact solutions for the pdf and second moment are obtained and investigated for different kinds of waiting time pdf

a hensel lifting to replace factorization in list decoding of algebraic geometric and reed solomon codes this article presents an algorithmic improvement to sudan s see j complexity vol 13 p 180 93 1997 list decoding algorithm for reed solomon codes and its generalization to algebraic geometric codes from shokrollahi and wasserman see ibid vol 45 p 432 37 1999 instead of completely factoring the interpolation polynomial over the function field of the curve we compute sufficiently many coefficients of a hensel development to reconstruct the functions that correspond to codewords we prove that these hensel developments can be found efficiently using newton s method we also describe the algorithm in the special case of reed solomon codes

normal l fuzzy ideals in semirings abstract in this paper we introduce the notion of a normal l fuzzy left resp right ideal in a semiring and investigate some properties

soft matrix theory and its decision making in this work we define soft matrices and their operations which are more functional to make theoretical studies in the soft set theory we then define products of soft matrices and their properties we finally construct a soft max min decision making method which can be successfully applied to the problems that contain uncertainties

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

kernels and closures of soft set relations and soft set relation mappings in this paper the notions of anti reflexive kernel symmetric kernel reflexive closure and symmetric closure of a soft set relation are first introduced respectively then their accurate calculation formulae and some properties are obtained finally soft set relation mappings and inverse soft set relation mappings are proposed and some related properties are discussed

uncoupled continuous time random walks solution and limiting behavior of the master equation a detailed study is presented for a large class of uncoupled continuous time random walks ctrws the master equation is solved for the mittag leffler survival probability the properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed finally some common objections found in the literature are thoroughly reviewed

fuzzy k ideals of semirings the aim of this paper is to introduce the notions of fuzzy k ideals prime fuzzy k ideals and semiregularity of semirings and to characterize prime fuzzy k ideals semiregular semirings noetherian semirings and artinian semirings by fuzzy k ideals

on fuzzy h ideals in hemirings the fuzzy setting of a left h ideal in a hemiring is constructed and basic properties are investigated using a collection of left h ideals of a hemiring s fuzzy left h ideals of s are established the notion of a finite valued fuzzy left h ideal is introduced and its characterization is given fuzzy relations on a hemiring s are discussed

fuzzy strong implicative hyper bck ideals of hyper bck algebras the fuzzy setting of strong implicative hyper bck ideals in hyper bck algebras is considered some of their properties are investigated relations among fuzzy strong hyper bck ideals fuzzy implicative hyper bck ideals and fuzzy strong implicative hyper bck ideals are given a characterization of a fuzzy strong implicative hyper bck ideal is provided the hyper homomorphic preimage of a fuzzy strong implicative hyper bck ideal is discussed

generalized continuous time random walks master equations and fractional fokker planck equations continuous time random walks which generalize random walks by adding a stochastic time between jumps provide a useful description of stochastic transport at mesoscopic scales the continuous time random walk model can accommodate certain features such as trapping which are not manifest in the standard macroscopic diffusion equation the trapping is incorporated through a waiting time density and a fractional diffusion equation results from a power law waiting time a generalized continuous time random walk model with biased jumps has been used to consider transport that is also subject to an external force here we have derived the master equations for continuous time random walks with space and time dependent forcing for two cases when the force is evaluated at the start of the waiting time and at the end of the waiting time the differences persist in low order spatial continuum approximations however the two processes are shown to be governed by the same fokker planck equations in the diffusi

soft bck bci algebras molodtsov d molodtsov soft set theory first results comput math appl 37 1999 19 31 introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches in this paper we apply the notion of soft sets by molodtsov to the theory of bck bci algebras the notion of soft bck bci algebras and soft subalgebras are introduced and their basic properties are derived

characterizations of h intra and h quasi hemiregular hemirings the concepts of c email protected q d fuzzy h bi h quasi ideals of hemirings are introduced some new characterization theorems of these kinds of fuzzy h ideals are also given in particular some characterizations of the h intra hemiregular and h quasi hemiregular hemirings are investigated by these kinds of fuzzy h ideals

some kinds of c ccq interval valued fuzzy ideals of bci algebras in this paper we first introduce the notions of positive implicative implicative and commutative interval valued fuzzy ideals of bci algebras which are generalizations of positive implicative implicative and commutative fuzzy ideals respectively and investigate some of their related properties the concept of quasi coincidence of an interval valued fuzzy point within an interval valued fuzzy set is introduced in fact the concept is a generalized concept of quasi coincidence of a fuzzy point within a fuzzy set by using this new idea we further introduce the notions of positive implicative implicative and commutative q interval valued fuzzy ideals of bci algebras and investigate some of their related properties some characterization theorems of these generalized interval valued fuzzy ideals are derived the relationship among these generalized interval valued fuzzy ideals of bci algebras is also considered

characterizations of hemirings by their h ideals in this paper we characterize hemirings in which all h ideals or all fuzzy h ideals are idempotent it is proved among other results that every h ideal of a hemiring r is idempotent if and only if the lattice of fuzzy h ideals of r is distributive under the sum and h intrinsic product of fuzzy h ideals or equivalently if and only if each fuzzy h ideal of r is intersection of those prime fuzzy h ideals of r which contain it we also define two types of prime fuzzy h ideals of r and prove that a non constant h ideal of r is prime in the second sense if and only if each of its proper level set is a prime h ideal of r

isomorphism theorems and fuzzy k ideals of k semirings we define and study the fuzzy maximal k ideal of a k semiring also we characterize the quotient k semiring r a of a k semiring r by a fuzzy maximal k ideal a and we have some isomorphism theorems in commutative k semirings and further we have some properties of the quotient k semiring r a of all cosets of a fuzzy semiprimary semiprime primary prime k ideal a in a commutative k semiring r

algebraic structures of soft sets associated with new operations recently new operations have been defined for soft sets in this paper we study some important properties associated with these new operations a collection of all soft sets with respect to new operations give rise to four idempotent monoids then with the help of these monoids we can study semiring hemiring structures of soft sets some of these semirings hemirings are actually lattices finally we show that soft sets with a fixed set of parameters are mv algebras and bck algebras

soft semirings molodtsov introduced the concept of soft sets which can be seen as a new mathematical tool for dealing with uncertainty in this paper we initiate the study of soft semirings by using the soft set theory the notions of soft semirings soft subsemirings soft ideals idealistic soft semirings and soft semiring homomorphisms are introduced and several related properties are investigated

fractional fokker planck equation solution and application recently metzler et al phys rev lett 82 3563 1999 introduced a fractional fokker planck equation ffpe describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a boltzmann thermal heat bath in this paper we present the solution of the ffpe in terms of an integral transformation the transformation maps the solution of ordinary fokker planck equation onto the solution of the ffpe and is based on levy s generalized central limit theorem the meaning of the transformation is explained based on the known asymptotic solution of the continuous time random walk ctrw we investigate in detail i a force free particle ii a particle in a uniform field and iii a particle in a harmonic field we also find an exact solution of the ctrw and compare the ctrw result with the corresponding solution of the ffpe the relation between the fractional first passage time problem in an external nonlinear field and the corresponding integer first passage time is given an example of the one dimensional fractional first passage time in an external linear field is investigated in detail the ffpe is shown to be compatible with the scher montroll approach for dispersive transport and thus is applicable in a large variety of disordered systems the simple ffpe approach can be used as a practical tool for a phenomenological description of certain types of complicated transport phenomena

combination of interval valued fuzzy set and soft set the soft set theory proposed by molodtsov can be used as a general mathematical tool for dealing with uncertainty by combining the interval valued fuzzy set and soft set models the purpose of this paper is to introduce the concept of the interval valued fuzzy soft set the complement and and or operations are defined on the interval valued fuzzy soft sets the demorgan s associative and distribution laws of the interval valued fuzzy soft sets are then proved finally a decision problem is analyzed by the interval valued fuzzy soft set some numerical examples are employed to substantiate the conceptual arguments

soft bl algebras based on fuzzy sets by means of soft sets and q soft sets some characterizations of implicative positive implicative and fantastic filteristic soft bl algebras are investigated finally we prove that a soft set is an implicative filteristic soft bl algebra if and only if it is both a positive implicative filteristic soft bl algebra and a fantastic filteristic soft bl algebra

soft hyperstructure in this paper we study soft hypergroupoids firstly we introduce the notion of soft hypergroupoids and some examples are given also we show that soft hypergroupoids are closely related to l subhypergroupoid secondly using the notion of soft hypergroupoid some new properties of soft hypergroupoids are obtained lastly we investigate some properties of soft subhypergroupoids

fuzzy prime ideals and invertible fuzzy ideals in bck algebras we state the relation between fuzzy prime ideals and invertible fuzzy ideals in commutative bck algebras

from continuous time random walks to the fractional fokker planck equation we generalize the continuous time random walk ctrw to include the effect of space dependent jump probabilities when the mean waiting time diverges we derive a fractional fokker planck equation ffpe this equation describes anomalous diffusion in an external force field and close to thermal equilibrium we discuss the domain of validity of the fractional kinetic equation for the force free case we compare between the ctrw solution and that of the ffpe

soft sets and soft rings molodtsov 1999 introduced the concept of soft sets in 1 then maji et al 2003 defined some operations on soft sets in 2 aktas and ca man 2007 defined the notion of soft groups in 3 finally soft semirings are defined by feng et al 2008 in 5 in this paper we have introduced initial concepts of soft rings

soft polygroups soft set theory introduced by molodtsov has been considered as an effective mathematical tool for modeling uncertainties in this paper we initiate the study of algebraic hyperstructures of soft sets the concepts of soft polygroups normal soft polygroups soft subpolygroups and normal soft subpolygroups are introduced and some related properties are investigated furthermore we propose the homomorphism and isomorphism of soft polygroups and establish three isomorphism theorems for soft polygroups

application of level soft sets in decision making based on interval valued fuzzy soft sets molodtsov s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty research on fuzzy soft set based decision making has received much attention in recent years this paper aims to give deeper insights into decision making involving interval valued fuzzy soft sets a hybrid model combining soft sets with interval valued fuzzy sets the concept called reduct fuzzy soft sets of interval valued fuzzy soft sets is introduced using reduct fuzzy soft sets and level soft sets flexible schemes for decision making based on weighted interval valued fuzzy soft sets are proposed and some illustrative examples are employed to show that the proposals presented here are not only more reasonable but more efficient in practical applications

soft subsets and soft product operations molodtsov s soft set theory provides a general mathematical framework for dealing with uncertainty it is known that soft subsets and soft equal relations are of vital importance in soft set theory this paper aims to give a systematic study on several types of soft subsets and various soft equal relations induced by them we give some equivalent characterizations of different soft subsets and endeavor to ascertain the interrelations among these notions illustrated by a number of concrete examples we also consider ontology based soft sets and show that soft l subsets generalize both soft m subsets and ontology based soft subsets moreover by means of soft l subsets and some related notions we give a theoretical study concerning soft product operations such as products and products we consummate some incomplete results concerning soft product operations existing in the literature and investigate the algebraic properties of soft product operations in detail finally we consider free soft algebras associated with soft product operations it is shown that soft l equal relations are congruence relations over free soft algebras and the corresponding quotient structures form commutative semigroups

bci implicative ideals of bci algebras abstract this paper introduces the notion of bci implicative ideals and characterizes bci implicative ideals and closed bci implicative ideals using these characterizations the connections between bci implicative ideals and other ideals in bci bck algebras are investigated additionally the extension property of bci implicative ideals is established finally the implicative bci algebras are completely described using bci implicative ideals the above work generalizes the corresponding results in bck algebras

fuzzy implicative and boolean filters of r 0 algebras the notions of fuzzy filters fuzzy implicative filters and fuzzy boolean filters are introduced in r0 algebras respectively some of their properties are investigated the relations between fuzzy implicative filters and fuzzy boolean filters are discussed the characterizations of fuzzy implicative filters are studied and the following is proved to be equivalent 1 a fuzzy filter f is implicative 2 f is a fuzzy boolean filter 3 x y z l f x z f x z y f y z 4 x y l f x y f x y y 5 x l n 1 f nx f x

lattice structure on fuzzy congruence relations of a hypergroupoid in this manuscript we first define the notion of fuzzy left right congruence relation on a hypergroupoid and then we investigate the lattice structure of the set of these fuzzy relations finally we show that a special class of fuzzy equivalence relations on the hypergroupoid forms a distributive lattice

fuzzy positive implicative and fuzzy associative filters of lattice implication algebras we fuzzify the concept of positive implicative filters and associative filters in lattice implication algebras we prove that i every fuzzy positive implicative filter is a fuzzy implicative filter and ii every fuzzy associative filter is a fuzzy filter we provide equivalent conditions for both fuzzy positive implicative filter and fuzzy associative filter

soft rough fuzzy sets and soft fuzzy rough sets fuzzy set theory soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related feng et al introduced the notions of rough soft set soft rough set and soft rough fuzzy set by combining fuzzy set rough set and soft set all together this paper is devoted to the further discussion of the combinations of fuzzy set rough set and soft set a new soft rough set model is proposed and its properties are derived furthermore fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established the lower and upper approximation operators are presented and their related properties are surveyed

stochastic calculus for uncoupled continuous time random walks the continuous time random walk ctrw is a pure jump stochastic process with several applications not only in physics but also in insurance finance and economics a definition is given for a class of stochastic integrals driven by a ctrw which includes the it and stratonovich cases an uncoupled ctrw with zero mean jumps is a martingale it is proved that as a consequence of the martingale transform theorem if the ctrw is a martingale the it integral is a martingale too it is shown how the definition of the stochastic integrals can be used to easily compute them by monte carlo simulation the relations between a ctrw its quadratic variation its stratonovich integral and its it integral are highlighted by numerical calculations when the jumps in space of the ctrw have a symmetric levy alpha stable distribution and its waiting times have a one parameter mittag leffler distribution remarkably these distributions have fat tails and an unbounded quadratic variation in the diffusive limit of vanishing scale parameters the probability density of this kind of ctrw satisfies the space time fractional diffusion equation fde or more in general the fractional fokker planck equation which generalizes the standard diffusion equation solved by the probability density of the wiener process and thus provides a phenomenologic model of anomalous diffusion we also provide an analytic expression for the quadratic variation of the stochastic process described by the fde and check it by monte carlo

a parabolic problem with a fractional time derivative we study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative our main result is a de giorgi nash moser holder regularity theorem for solutions in a divergence form equation we also prove results regarding existence uniqueness and higher regularity in time

on representations of algebraic geometry codes we show that all algebraic geometric codes possess a succinct representation that allows for list decoding algorithms to run in polynomial time we do this by presenting a root finding algorithm for univariate polynomials over function fields when their coefficients lie in finite dimensional linear spaces and proving that there is a polynomial size representation given which the root finding algorithm runs in polynomial time

on operations of soft sets soft set theory proposed by molodtsov has been regarded as an effective mathematical tool to deal with uncertainties in this paper first we prove that certain de morgan s law hold in soft set theory with respect to different operations on soft sets then we discuss the basic properties of operations on soft sets such as intersection extended intersection restricted union and restricted difference moreover we illustrate their interconnections between each other also we define the notion of restricted symmetric difference of soft sets and investigate its properties the main purpose of this paper is to extend the theoretical aspect of operations on soft sets

fuzzy soft set theory applied to bck bci algebras abstract in the paper p k maji r biswas a r roy fuzzy soft sets j fuzzy math 9 3 2001 589 602 maji et al introduced the concept of fuzzy soft sets as a generalization of the standard soft sets and presented an application of fuzzy soft sets in a decision making problem the aim of this manuscript is to apply fuzzy soft set for dealing with several kinds of theories in bck bci algebras the notions of fuzzy soft bck bci algebras closed fuzzy soft ideals and fuzzy soft p ideals are introduced and related properties are investigated

soft set theory applied to ideals in d algebras the notions of transitive soft d algebras soft edge d algebras soft d algebras soft d ideals soft d ideals soft d ideals and d idealistic d idealistic or d idealistic soft d algebras are introduced also their related properties are surveyed

generalized master equations for random walks with time dependent jump sizes in this work we develop a unified generalized master equation gme framework that extends the theory of continuous time random walks to include the cases when the jump sizes may have a delayed dependence on time and are not restricted to any particular class of distributions we compare and contrast analytical and numerical behavior of the corresponding master equations including the instantaneous vs delayed jump dependence on time and exponential vs mittag leffler interarrival times with the latter leading to fractional evolution equation we provide existence and uniqueness proofs for the resulting gmes

quotient structures of some implicative algebras via fuzzy implicative filters in this paper we discuss quotient implicative algebras induced by fuzzy implicative filters and establish the fuzzy fundamental homomorphism theorem for some implicative algebras

fuzzy h ideals of hemirings a characterization of an h hemiregular hemiring in terms of a fuzzy h ideal is provided some properties of prime fuzzy h ideals of h hemiregular hemirings are investigated it is proved that a fuzzy subset z of a hemiring s is a prime fuzzy left right h ideal of s if and only if z is two valued z 0 1 and the set of all x in s such that z x 1 is a prime left right h ideal of s finally the similar properties for maximal fuzzy left right h ideals of hemirings are considered

on fuzzy ideals in bcc algebras the purpose of this paper is description of properties of fuzzy bcc ideals in bcc algebras and its images we describe also an extension of a fuzzy bcc ideal of a given bcc subalgebra s of x to a fuzzy bcc ideal of x such that and have the same image

soft set relations and functions the traditional soft set is a mapping from a parameter to the crisp subset of universe molodtsov introduced the theory of soft sets as a generalized tool for modeling complex systems involving uncertain or not clearly defined objects in this paper the concepts of soft set relations are introduced as a sub soft set of the cartesian product of the soft sets and many related concepts such as equivalent soft set relation partition composition function etc are discussed