system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

on fuzzy spaces and fuzzy group theory abstract the concept of fuzzy space is introduced this concept corresponds to the concept of the universal set in the ordinary case the algebra of fuzzy spaces and fuzzy subspaces is studied using the concept of fuzzy space and fuzzy binary operation a new approach to study fuzzy group theory is given this approach can be considered as a generalization and reformulation of the rosenfeld theory of fuzzy subgroups therefore it is an active tool to develop the theory of fuzzy groups

fuzzy ideals and semiprime fuzzy ideals in semigroups in this paper we investigate relationships between different definitions of fuzzy ideals of a fuzzy semigroup the equivalence of different definitions of fuzzy ideals of a fuzzy semigroup is obtained we show that the lattice of all f fuzzy ideals of a fuzzy semigroup x is a complete sublattice of the lattice of all fuzzy sets in x when f is an infinitely distributive weak pseudo t norm on l a definition of f semiprime fuzzy ideal of a fuzzy semigroup is given a description of all f semigroups in which every f fuzzy ideal is f semiprime is obtained

fuzzy radicals and prime fuzzy ideals of ordered semigroups let s be an ordered semigroup a fuzzy subset of s is by definition an arbitrary mapping f s 0 1 where 0 1 is the usual interval of real numbers motivated by studying prime fuzzy ideals in rings semigroups and ordered semigroups and as a continuation of kehayopulu and tsingelis s works in ordered semigroups in terms of fuzzy subsets in this paper we introduce the notion of ordered fuzzy points of an ordered semigroup s and give a characterization of prime fuzzy ideals of an ordered semigroup s we also introduce the concepts of weakly prime fuzzy ideals completely prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of an ordered semigroup s and establish the relationship between the five classes of ideals furthermore we characterize weakly prime fuzzy ideals completely semiprime fuzzy ideals and weakly completely prime fuzzy ideals of s by their level ideals finally we introduce and investigate the fuzzy radicals of ordered semigroups by means of ordered fuzzy points and prove that the fuzzy radical of every completely semiprime fuzzy ideal of an ordered semigroup s can be expressed as the intersection of all weakly completely prime fuzzy ideals containing it as an application of the results of this paper the corresponding results of semigroups without order are also obtained

on the structure of rough prime primary ideals and rough fuzzy prime primary ideals in commutative rings this paper is a continuation of ideas presented by davvaz roughness in rings inform sci 164 2004 147 163 roughness based on fuzzy ideals inform sci 176 2006 2417 2437 we introduce the notions of rough prime primary ideals and rough fuzzy prime primary ideals in a ring and give some properties of such ideals also we discuss the relations between the upper and lower rough prime primary ideals and the upper and lower approximations of their homomorphism images

applications of interval valued fuzzy n ary polygroups with respect to t norms t conorms using the triangular norm t conorm s in the context of n ary polygroups we introduce the concept of an interval valued anti fuzzy n ary subpolygroup with respect to t s respectively a necessary and sufficient condition for an interval valued fuzzy subset in order to be an interval valued anti fuzzy n ary subpolygroup is established and some important results are presented this study is useful for the most computational part of fuzzy control which is the defuzzification

fuzzy hyperrings in this paper we introduce and analyze the fuzzy hyperring notion we consider and study the subfuzzy structures of a such notion and homomorphisms between fuzzy hyperrings finally fundamental relations on fuzzy hyperrings are analyzed in all the paper we follow a connection between hyperrings and fuzzy hyperrings

some constructions of the join of fuzzy subgroups and certain lattices of fuzzy subgroups with sup property in this paper some new lattices of fuzzy substructures are constructed for a given fuzzy set m in a group g a fuzzy subgroup s m generated by m is defined which helps to establish that the set l s of all fuzzy subgroups with sup property constitutes a lattice consequently many other sublattices of the lattice l of all fuzzy subgroups of g like l s t l s n l s n t etc are also obtained the notion of infimum is used to construct a fuzzy subgroup i m generated by a given fuzzy set m in contrast to the usual practice of using supremum in the process a new fuzzy subgroup i m is defined which we shall call a shadow fuzzy subgroup of m it is established that if m has inf property then i m also has this property

fuzzy ideals and fuzzy semiprime ideals some ring theoretic analogues abstract an attempt is made to examine the algebraic nature of fuzzy semiprime ideals under homomorphisms also the fuzzy nil radical of the nth power of a fuzzy prime ideal is studied and a sufficient condition for a fuzzy ideal to be fuzzy maximal is given

fuzzy h v groups in this paper we introduce the concept of fuzzy subhypergroup of a hypergroup as well as the fuzzy hv group we prove some results in this respect we also consider the fundamental relation defined on an hv group h and for a fuzzy subset of h we define the fuzzy subset of h and prove a fundamental theorem concerning the group h

a new view of fuzzy hypernear rings in this survey article we first introduce the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set this concept is a generalized concept of quasi coincidence of a fuzzy point within a fuzzy set by using this new idea we consider the interval valued q fuzzy sub hypernear rings hyperideals of a hypernear ring and hence a generalization of a fuzzy sub near ring ideal is given some related properties of fuzzy hypernear rings are described finally we consider the concept of implication based interval valued fuzzy sub hypernear rings hyperideals in a hypernear ring in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

distributivity in lattices of fuzzy subgroups the main goal of this paper is to study the finite groups whose lattices of fuzzy subgroups are distributive we obtain a characterization of these groups which is similar to a well known result of group theory

fuzzy hyperrings hv rings based on fuzzy universal sets the aim of this paper is to define and study the concept of a fuzzy hyperring which depends on the concept of a fuzzy universal set a correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of davvaz is obtained

the lower and upper approximations in a hypergroup this paper presents a relationship between rough sets and hypergroup theory we analyze the lower and upper approximations of a subset with respect to an invertible subhypergroup and we consider some particular situations moreover the notion of a rough subhypergroup is introduced finally fuzzy rough subhypergroups are introduced and characterized

regular fuzzy duo rings in this paper we shall introduce the concept of a fuzzy bi ideal a fuzzy quasi ideal in a ring and give some properties of such fuzzy ideals we also give a characterization of a regular fuzzy duo ring in terms of fuzzy ideals

an inexact interior point method for system analysis in this article a primal dual interior point algorithm for semidefinite programming that can be used for analysing e g polytopic linear differential inclusions is tailored in order to be more computationally efficient the key to the speedup is to allow for inexact search directions in the interior point algorithm these are obtained by aborting an iterative solver for computing the search directions prior to convergence a convergence proof for the algorithm is given two different preconditioners for the iterative solver are proposed the speedup is in many cases more than an order of magnitude moreover the proposed algorithm can be used to analyse much larger problems as compared to what is possible with off the shelf interior point solvers

roughness based on fuzzy ideals the theory of rough set proposed by pawlak and the theory of fuzzy set proposed by zadeh are complementary generalizations of classical set theory many sets are naturally endowed with two binary operations addition and multiplication one concept which does this is a ring this paper concerns a relationship between rough sets fuzzy sets and ring theory it is a continuation of ideas presented by kuroki and wang n kuroki p p wang the lower and upper approximations in a fuzzy group inform sci 90 1996 203 220 we consider a ring as a universal set and we assume that the knowledge about objects is restricted by a fuzzy ideal in fact we apply the notion of fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring some characterizations of the above approximations are made and some examples are presented

convex optimization problems involving finite autocorrelation sequences we discuss convex optimization problems in which some of the variables are constrained to be finite autocorrelation sequences problems of this form arise in signal processing and communications and we describe applications in filter design and system identification autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density which results in a set of linear inequalities they can also be cast as linear matrix inequalities via the kalman yakubovich popov lemma the linear matrix inequality formulation is exact and results in convex optimization problems that can be solved using interior point methods for semidefinite programming however it has an important drawback to represent an autocorrelation sequence of length n it requires the introduction of a large number n n 1 2 of auxiliary variables this results in a high computational cost when general purpose semidefinite programming solvers are used we present a more efficient implementation based on duality and on interior point methods for convex problems with generalized linear inequalities

on probabilistic n ary hypergroups abstract the t fuzzy n ary subhypergroups of an n ary hypergroup are defined by using triangular norms and some related properties are hence obtained in particular we consider the probabilistic version of n ary hypergroups by using random sets and show that the fuzzy n ary hypergroups defined by triangular norms are consequences of some probabilistic n ary hypergroups under certain conditions some results on n ary hypergroups recently given by davvaz and corsini are extended

a polynomial time algorithm for the equivalence of probabilistic automata two probabilistic automata are equivalent if for any string x the two automata accept x with equal probability this paper presents an o n 1 n 2 4 algorithm for determining whether two probabilistic automata u 1 and u 2 are equivalent where n 1 and n 2 are the number of states in u 1 and u 2 respectively this improves the best previous result which showed that the problem was in conp the existence of this algorithm implies that the covering and equivalence problems for uninitiated probabilistic automata are also polynomial time solvable the algorithm used to determine the equivalence of probabilistic automata can also solve the path equivalence problem for nondeterministic finite automata without lambda transitions and the equivalence problem for unambiguous finite automata in polynomial time this paper studies the approximate equivalence or delta equivalence problem for probabilistic automata an algorithm for the approximate equivalence problem for positive p

redefined fuzzy hv submodules and many valued implications this paper considers a relationship between fuzzy sets and algebraic hyperstructures a generalization of ideas presented by davvaz b davvaz fuzzy h v submodules fuzzy sets syst 117 2001 477 484 and bhakat and das s k bhakat p das email protected q fuzzy subgroup fuzzy sets syst 80 1996 359 368 is presented in fact the main purpose of this paper is to introduce and study a new sort of fuzzy h v submodule of an h v module called email protected q fuzzy h v submodules these fuzzy h v submodules are characterized by their level h v submodules the concept of a fuzzy h v submodule with thresholds is introduced and some interesting properties are investigated

rings characterized by their fuzzy submodules the notions of pure ideals and pure submodules play an important role in the study of rings and their module categories in this paper we introduce right t pure fuzzy ideals and pure fuzzy submodules of an r module we establish their basic properties and use them to obtain fuzzy theoretic characterizations of right weakly regular rings among other results we prove that a ring r is right weakly regular if and only if each fuzzy submodule of a cyclic r module is pure fuzzy

the fuzzy normal subgroup using the concept of fuzzy spaces we define the fuzzy normal subgroup in a fuzzy group its relation with the classical fuzzy normal subgroup is studied

on fuzzy semiprimary ideals in this paper semiprimary ideals are redefined in terms of fuzzy points and it is proved that this definition is equivalent to that of kumar 1991 several results regarding semiprimary and fuzzy semiprimary ideals are derived it is shown by examples that the characterization of semiprimary ideals by prime radicals does not hold for this definition of fuzzy semiprimary ideals

fuzzy pogroupoids in this paper we show that for given a pogroupoid x the associated poset x is c2 1 free if and only if the relation is transitive for any fuzzy subset of x also we determine the set c x of fuzzy subsets such that x y y x for all x y x furthermore with a given finite poset x or the associated pogroupoid x we may then associate a polynomial whose coefficients count the number of congruence classes mod x of fuzzy subsets of x along with another polynomial invariant of interest

low rank exploitation in semidefinite programming for control many control related problems can be cast as semidefinite programs even though there exist polynomial time algorithms and excellent publicly available solvers the time it takes to solve these problems can be excessive what many of these problems have in common in particular in control is that some of the variables enter as matrix valued variables this leads to a low rank structure in the basis matrices which can be exploited when forming the newton equations in this article we describe how this can be done and show how our code called strul can be used in conjunction with the semidefinite programming solver sdpt3 the idea behind the structure exploitation is classical and is implemented in lmi lab but we show that when using a modern semidefinite programming framework such as sdpt3 the computational time can be significantly reduced finally we describe how the modelling language yalmip has been changed in such a way that our code which can be freely downloaded can be interfaced using sta

the lower and upper approximations in a quotient hypermodule with respect to fuzzy sets this paper provides a continuation of ideas presented by davvaz and mahdavipour b davvaz m mahdavipour roughness in modules inform sci 176 2006 3658 3674 the notion of hypermodule is a generalization of the notion of module in this paper we consider the quotient hypermodule m a and interpret the lower and upper approximations as subsets of the quotient hypermodule m a then we introduce the concept of quotient rough sub hypermodule also using the concept of fuzzy sets we introduce and discuss the concept of fuzzy rough hypermodules and then we obtain the relation between fuzzy rough sub hypermodules and level rough sets this relation is characterized as a necessary and sufficient condition

generalized fuzzy hyperideals of hyperrings the concept of quasi coincidence of a fuzzy interval value with an interval valued fuzzy set is considered in fact this is a generalized concept of the quasi coincidence of a fuzzy point with a fuzzy set by using this new idea the notion of interval valued a b fuzzy hyperideals in a hyperring is introduced and consequently a generalization of a fuzzy hyperideal is defined in this paper we study the related properties of the fuzzy hyperideals and in particular the interval valued q fuzzy hyperideals in a hyperring will be investigated moreover we also consider the concept of implication based interval valued fuzzy hyperideals in a hyperring some recent results obtained by b davvaz and j m zhan on hyperstructures are extended and consolidated

structure of fuzzy subrings abstract conditions are given for a fuzzy subring of a commutative ring with identity to have a fuzzy coefficient field the results obtained are then used to determine structural properties of fuzzy subrings e g to determine when a fuzzy subring is a fuzzy polynomial subring or a fuzzy power series subring

θ t fuzzy rough approximation operators and the tl fuzzy rough ideals on a ring in this paper we consider a ring as a universal set and study t fuzzy rough approximation operators with respect to a tl fuzzy ideal of a ring first some new properties of generalized t fuzzy rough approximation operators are obtained then a new fuzzy algebraic structure tl fuzzy rough ideal is defined and its properties investigated and finally the homomorphism of t fuzzy rough approximation operators is studied

globally convergent algorithms for robust pole assignment by state feedback it is observed that an algorithm proposed in 1985 by kautsky nichols and van dooren knv amounts to maximizing at each iteration the determinant of the candidate closed loop eigenvector matrix x with respect to one of its columns with unit length constraint subject to the constraint that it remains an achievable closed loop eigenvector matrix this interpretation is used to prove convergence of the knv algorithm it is then shown that a more efficient algorithm is obtained if det x is concurrently maximized with respect to two columns of x and such a scheme is easily extended to the case where the eigenvalues to be assigned include complex conjugate pairs variations exploiting the availability of multiple processors are suggested convergence properties of the proposed algorithms are established their superiority is demonstrated numerically

specialized fast algorithms for iqc feasibility and optimization problems the conventional way to treat integral quadratic constraint iqc problems is to transform them into semi definite programs sdps sdps can then be solved using interior point methods which have been proven efficient this approach however is not always the most efficient since it introduces additional decision variables to the sdp and the additional decision variables sometimes largely increase the complexity of the problem in this paper we demonstrate how to solve iqc problems by other alternatives more specifically we consider two cutting plane algorithms we will show that in certain cases these cutting plane algorithms can solve iqc problems much faster than the conventional approach numerical examples as well as some explanations from the point of view of computational complexity are provided to support our point

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

roughness in n ary hypergroups this paper is aimed at studying the rough sets within the context of the commutative n ary hypergroups for this approach the presentation of a detailed study of the various types of n ary subhypergroups is of the greatest importance this study was initiated in v leoreanu fotea several types of n ary subhypergroups italian journal of pure and applied mathematics in press subsequently we shall use the findings in this study to define the upper and lower approximation of a subset with respect to an invertible n ary subhypergroup of a commutative n ary hypergroup in the final part the concept of n ary rough subhypergroup is introduced

fuzzy group decision making for facility location selection the selection of a facility location among alternative locations is a multicriteria decision making problem including both quantitative and qualitative criteria the conventional approaches to facility location problem tend to be less effective in dealing with the imprecise or vagueness nature of the linguistic assessment under many situations the values of the qualitative criteria are often imprecisely defined for the decision makers the aim of the paper is to solve facility location problems using different solution approaches of fuzzy multi attribute group decision making the paper includes four different fuzzy multi attribute group decision making approaches the first one is a fuzzy model of group decision proposed by blin the second is the fuzzy synthetic evaluation the third is yager s weighted goals method and the last one is fuzzy analytic hierarchy process although four approaches have the same objective of selecting the best facility location alternative they come from different theoretic backgrounds and relate differently to the discipline of multi attribute group decision making these approaches are extended to select the best facility location alternative by taking into account quantitative and qualitative criteria a short comparative analysis among the approaches and a numeric example to each approach are given

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

a structure exploiting preprocessor for semidefinite programs derived from the kalman yakubovich popov lemma semidefinite programs derived from the kalman yakubovich popov kyp lemma are quite common in control and signal processing applications the programs are often of high dimension which makes them hard or impossible to solve with general purpose solvers here we present a customized preprocessor kypd that utilizes the inherent structure of this particular optimization problem the key to an efficient implementation is to transform the optimization problem into an equivalent semidefinite program this equivalent problem has much fewer variables and the matrices in the linear matrix inequality constraints are of low rank kypd can use any primal dual solver for semidefinite programs as an underlying solver

a cutting plane method for solving kyp sdps semidefinite programs originating from the kalman yakubovich popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them however the number of variables is often very large making the computational time extremely long algorithms more efficient than general purpose solvers are thus needed to this end structure exploiting algorithms have been proposed based on the dual formulation in this paper a cutting plane algorithm is proposed in a comparison with a general purpose solver and a structure exploiting solver it is shown that the cutting plane based solver can handle optimization problems of much higher dimension

efficient computation of a guaranteed lower bound on the robust stability margin for a class of uncertain systems sufficient conditions for the robust stability of a class of uncertain systems with several different assumptions on the structure and nature of the uncertainties can be derived in a unified manner in the framework of integral quadratic constraints these sufficient conditions in turn can be used to derive lower bounds on the robust stability margin for such systems the lower bound is typically computed with a bisection scheme with each iteration requiring the solution of a linear matrix inequality feasibility problem we show how this bisection can be avoided altogether by reformulating the lower bound computation problem as a single generalized eigenvalue minimization problem which can be solved very efficiently using standard algorithms we illustrate this with several important commonly encountered special cases diagonal nonlinear uncertainties diagonal memoryless time invariant sector bounded popov uncertainties structured dynamic uncertainties and structured parametric uncertainties we also present a numerical example that demonstrates the computational savings that can be obtained with our approach

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

some remarks on congruences obtained from the l fuzzy nakano hyperoperation in this paper we study relations which are congruences with respect to and p where p is the p cut of the l fuzzy hyperoperation the main idea is to start from an equivalence relation r 1 which is a congruence with respect to and 1 and for each email protected x construct an equivalence relation r p which is a congruence with respect to and p furthermore for each email protected r p we construct a quotient hyperoperation p and we show that the hyperalgebra x r p p is a join space and the hyperalgebra x r p p p is a hyperlattice

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

generalized rough sets over fuzzy lattices this paper studies generalized rough sets over fuzzy lattices through both the constructive and axiomatic approaches from the viewpoint of the constructive approach the basic properties of generalized rough sets over fuzzy lattices are obtained the matrix representation of the lower and upper approximations is given according to this matrix view a simple algorithm is obtained for computing the lower and upper approximations as for the axiomatic approach a set of axioms is constructed to characterize the upper approximation of generalized rough sets over fuzzy lattices

f polygroups ii first a product between two f subpolygroups of a given f polygroup is defined and then a necessary and sufficient condition is given in order that the product be an f subpolygroup then by considering the notion of homomorphism of f polygroups some related results are obtained finally the concept of quotient f polygroup is defined and then some theorems are proved

positive polynomials and robust stabilization with fixed order controllers recent results on positive polynomials are used to obtain a convex inner approximation of the stability domain in the space of coefficients of a polynomial an application to the design of fixed order controllers robustly stabilizing a linear system subject to polytopic uncertainty is then proposed based on linear matrix inequality optimization the key ingredient in the design procedure resides in the choice of the central polynomial several numerical examples illustrate the relevance of the approach

sampling method for semidefinite programmes with non negative popov function constraints an important class of optimisation problems in control and signal processing involves the constraint that a popov function is non negative on the unit circle or the imaginary axis such a constrain

distributed semidefinite programming with application to large scale system analysis distributed algorithms for solving coupled semidefinite programs commonly require many iterations to converge they also put high computational demand on the computational agents in this paper we show that in case the coupled problem has an inherent tree structure it is possible to devise an efficient distributed algorithm for solving such problems the proposed algorithm relies on predictor corrector primal dual interior point methods where we use a message passing algorithm to compute the search directions distributedly message passing here is closely related to dynamic programming over trees this allows us to compute the exact search directions in a finite number of steps this is because computing the search directions requires a recursion over the tree structure and hence terminates after an upward and downward pass through the tree furthermore this number can be computed a priori and only depends on the coupling structure of the problem we use the proposed algorithm for analyzing robustness of large scale uncertain systems distributedly we test the performance of this algorithm using numerical examples

generalized lower and upper approximations in a ring in this paper the concepts of set valued homomorphism and strong set valued homomorphism of a ring are introduced and related properties are investigated the notions of generalized lower and upper approximation operators constructed by means of a set valued mapping which is a generalization of the notion of lower and upper approximation of a ring are provided we also propose the notion of generalized lower and upper approximations with respect to an ideal of a ring which is an extended notation of rough ideal introduced lately by davvaz b davvaz roughness in rings information science 164 2004 147 163 in a ring and discuss some significant properties of them

fuzzy filters and fuzzy prime filters of bounded r l monoids and pseudo bl algebras the logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics the sets of provable formulas in corresponding inference systems from the point of view of uncertain information can be described by fuzzy filters of those algebraic semantics bounded residuated lattice ordered monoids email protected monoids are a common generalization of pseudo bl algebras and consequently of pseudo mv algebras and heyting algebras i e algebras behind fuzzy and intuitionistic reasoning in the paper we introduce and investigate fuzzy filters of bounded email protected monoids and fuzzy prime filters of pseudo bl algebras

fuzzy hv submodules abstract in this paper we define the concept of fuzzy h v submodule of an h v module and study a few results in this respect we also consider the fundamental relation e defined on an h v module m and prove a fundamental theorem concerning the module m e

robust stability analysis of sparsely interconnected uncertain systems in this paper we consider robust stability analysis of large scale sparsely interconnected uncertain systems by modeling the interconnections among the subsystems with integral quadratic constraints we show that robust stability analysis of such systems can be performed by solving a set of sparse linear matrix inequalities we also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness the sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques and our numerical results illustrate the effectiveness of this approach compared to methods that are based on the standard formulation of the analysis problem

fuzzy hyperlattices in this paper we introduce the notion of fuzzy hyperlattices and establish connections between fuzzy hyperlattices and hyperlattices then we discuss the relations between the weak homomorphism of fuzzy hyperlattices and the weak homomorphism of corresponding hyperlattices moreover we define and analyze the hypercongruence on hyperlattices and the fuzzy strong hypercongruence on fuzzy hyperlattices and we study the interrelation between the fuzzy hypercongruence on fuzzy hyperlattices and the homomorphism of fuzzy hyperlattices also a relation between the fuzzy hypercongruence on fuzzy hyperlattices and the hypercongruence on corresponding hyperlattices is obtained finally we apply the hypercongruence and the fuzzy strong hypercongruence to construct quotient structures of hyperlattices and fuzzy hyperlattices respectively

characterizations of regular ordered semigroups in terms of α β fuzzy generalized bi ideals in this paper the concept of an a b fuzzy generalized bi ideal in an ordered semigroup is introduced which is a generalization of the concept of a fuzzy generalized bi ideal in an ordered semigroup using this concept some characterization theorems are provided the upper lower parts of an q fuzzy generalized bi ideal are introduced and some characterizations of regular ordered semigroups are given also we consider the concept of implication based fuzzy generalized bi ideals in an ordered semigroup in particular the implication operators in lukasiewicz system of continuous valued logic are discussed

a new type of fuzzy n ary hyperstructures the aim of this paper is to consider and study a new kind of fuzzy n ary hyperstructures such as fuzzy n ary hypergroups and fuzzy m n ary hyperrings

the l fuzzy nakano hypergroup in this paper we start with a lattice x and define in terms of a family of crisp hyperoperations p one hyperoperation for each p x we show that for every p the hyperalgebra x p is a join space and the hyperalgebra x p is very similar to a hyperlattice then we use the hyperoperations p as p cuts to introduce an l fuzzy hyperoperation and show that x is an l fuzzy join space and the hyperalgebra x p is very similar to an l fuzzy hyperlattice