two dimensional velocity distribution in open channels using renyi entropy in this work the concept of entropy based on probability is applied in modeling the vertical distribution of velocity in open channel turbulent flow using the principle of maximum entropy one dimensional velocity distribution is derived by maximizing the renyi entropy subject to some constraints by assuming dimensionless velocity as a random variable the renyi entropy based equation is capable of modeling the velocity distribution from the channel bed to the water surface the derived velocity distribution is tested with field and laboratory observations and is also compared with existing entropy based velocity distributions the present model has shown good agreement with observed data and its prediction accuracy is superior than the other existing models

on the structure of generalized rough sets in this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that 1 any reflexive binary relation determines a topology 2 if q is a reflexive and symmetric relation on a set x then o email protected x q a a is a topology such that a is open if and only if it is closed 3 conversely for every topological space x o satisfying the condition that a is open if and only if it is closed there exists a reflexive and symmetric relation r such that o email protected x r a a 4 let q be an equivalence relation on x for any pseudo w closed subset a of x q a is an w closed set if and only if w x x x email protected a for any email protected x moreover we consider properties of generalized rough sets

rough set theory applied to fuzzy ideal theory we use covers of the universal set to define approximation operators on the power set of the given set in section 1 we determine basic properties of the upper approximation operator and show how it can be used to give algebraic structural properties of certain subsets we define a particular cover on the set of ideals of a commutative ring with identity in such a way that both the concepts of the fuzzy prime spectrum of a ring and rough set theory can simultaneously be brought to bear on the study of fuzzy ideals of a ring

schwarz waveform relaxation methods for parabolic equations in space frequency domain some schwarz waveform relaxation algorithms based on frequency domain analysis for parabolic equations are proposed and analyzed in this paper we mainly study an overlapping process with dirichlet transmission conditions and a non overlapping process with robin transmission conditions the convergence conditions for these algorithms are also obtained by our frequency domain analysis numerical experiments are given to illustrate effectiveness of the algorithms

a short note on algebraic t rough sets our aim in this paper is to introduce the concept of a set valued homomorphism for groups which is a generalization of ordinary homomorphism then using the definitions of lower inverse and upper inverse we introduce the definition of uniform set valued homomorphism and prove that every set valued homomorphism is uniform finally the concept of probabilistic t rough set is defined

relative reducts in consistent and inconsistent decision tables of the pawlak rough set model a relative reduct can be considered as a minimum set of attributes that preserves a certain classification property this paper investigates three different classification properties and suggests three distinct definitions accordingly in the pawlak rough set model while the three definitions yield the same set of relative reducts in consistent decision tables they may result in different sets in inconsistent tables relative reduct construction can be carried out based on a discernibility matrix the study explicitly stresses a fact that the definition of a discernibility matrix should be tied to a certain property regarding the three classification properties we can define three distinct definitions accordingly based on the common structure of the specific definitions of relative reducts and discernibility matrices general definitions of relative reducts and discernibility matrices are suggested

derivation of rouse equation for sediment concentration using shannon entropy abstract sediment concentration is fundamental for determining sediment transport in open channels the rouse equation one of several methods for computing sediment concentration has been derived using deterministic hydraulic principles this study derives the rouse equation using the shannon entropy theory the derivation requires a hypothesis on the cumulative probability distribution function of sediment concentration in terms of flow depth which is formulated in a general form and can specialize in several specific forms reported in the literature the advantage of using the entropy theory is that it permits quantification of uncertainty associated with concentration and determination of parameters in terms of specified information such as mean concentration

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

generalized fuzzy rough sets this paper presents a general framework for the study of fuzzy rough sets in which both constructive and axiomatic approaches are used in constructive approach a pair of lower and upper generalized approximation operators is defined the connections between fuzzy relations and fuzzy rough approximation operators are examined in axiomatic approach various classes of fuzzy rough approximation operators are characterized by different sets of axioms axioms of fuzzy approximation operators guarantee the existence of certain types of fuzzy relations producing the same operators

derivation of hunt equation for suspension distribution using shannon entropy theory abstract in this study the hunt equation for computing suspension concentration in sediment laden flows is derived using shannon entropy theory considering the inverse of the void ratio as a random variable and using principle of maximum entropy probability density function and cumulative distribution function of suspension concentration is derived a new and more general cumulative distribution function for the flow domain is proposed which includes several specific other models of cdf reported in literature this general form of cumulative distribution function also helps to derive the rouse equation the entropy based approach helps to estimate model parameters using suspension data of sediment concentration which shows the advantage of using entropy theory finally model parameters in the entropy based model are also expressed as functions of the rouse number to establish a link between the parameters of the deterministic and probabilistic approaches

on fuzzy rough sets based on tolerance relations dubois and prade 1990 1 introduced the notion of fuzzy rough sets as a fuzzy generalization of rough sets which was originally proposed by pawlak 1982 8 later radzikowska and kerre introduced the so called i t fuzzy rough sets where i is an implication and t is a triangular norm in the present paper by using a pair of implications i j we define the so called i j fuzzy rough sets which generalize the concept of fuzzy rough sets in the sense of radzikowska and kerre and that of mi and zhang basic properties of i j fuzzy rough sets are investigated in detail

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

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

generalized rough sets based on relations rough set theory has been proposed by pawlak as a tool for dealing with the vagueness and granularity in information systems the core concepts of classical rough sets are lower and upper approximations based on equivalence relations this paper studies arbitrary binary relation based generalized rough sets in this setting a binary relation can generate a lower approximation operation and an upper approximation operation but some of common properties of classical lower and upper approximation operations are no longer satisfied we investigate conditions for a relation under which these properties hold for the relation based lower and upper approximation operations

estimation of two dimensional velocity distribution profile using general index entropy in open channels abstract estimation of velocity distribution profile is a challenging subject of open channel hydraulics in this study an entropy based method is used to derive two dimensional velocity distribution profile the general index entropy gie can be considered as the generalized form of shannon entropy which is suitable to combine with the different form of cumulative distribution function cdf using the principle of maximum entropy pome the velocity distribution is defined by maximizing the gie by treating the velocity as a random variable the combination of gie and a cdf proposed by marini et al 2011 was utilized to introduce an efficient entropy model whose results are comparable with several well known experimental and field data consequently in spite of less sensitivity of the related parameters of the model to flow conditions and less complexity in application of the model compared with other entropy based methods more accuracy is obtained in estimating velocity distribution profile either near the boundaries or the free surface of the flow

on characterizations of i t fuzzy rough approximation operators in rough set theory the lower and upper approximation operators defined by a fixed binary relation satisfy many interesting properties various fuzzy generalizations of rough approximations have been made in the literature this paper proposes a general framework for the study of i t fuzzy rough approximation operators within which both constructive and axiomatic approaches are used in the constructive approach a pair of lower and upper generalized fuzzy rough approximation operators determined by an implicator i and a triangular norm t is first defined basic properties of i t fuzzy rough approximation operators are investigated the connections between fuzzy relations and fuzzy rough approximation operators are further established in the axiomatic approach an operator oriented characterization of rough sets is proposed that is i t fuzzy approximation operators are defined by axioms different axiom sets of t upper and i lower fuzzy set theoretic operators guarantee the existence of different types of fuzzy relations which produce the same operators finally an open problem proposed by radzikowska and kerre in fuzzy sets and systems 126 2002 137 is solved

uncertainty analysis of shear stress estimation in circular channels by tsallis entropy abstract accurate prediction of the shear stress distribution is essential for the successful design of stable erodible bed channels and for the sediment transport studies considerable attention in recent years has been given to the estimation of velocity distribution using entropy concept in open channels despite the importance of knowledge about shear stress distribution there are very few studies on the application of the entropy methods for prediction of the shear stress distribution in open channels the tsallis entropy has been employed in this study for estimating the shear stress in open channels in this approach a pair of mean and maximum shear stresses are used to evaluate the shear stress distribution on the entire channel cross section we then calculated the prediction uncertainty of the shear stress obtained from the tsallis entropy in a circular open channel moreover the distribution of prediction error for the tsallis approach is examined in two cases both before and after data normalization the quantitative results from this uncertainty analysis showed satisfactory results for the tsallis entropy model for estimating shear stress in the entire section the 95 confidence bounds cb are obtained for the shear stress distribution predicted by the model closely match the observed values

neighborhood operator systems and approximations this paper presents a framework for the study of generalizing the standard notion of equivalence relation in rough set approximation space with various categories of k step neighborhood systems based on a binary relation on a finite universe six families of binary relations are obtained and the corresponding six classes of k step neighborhood systems are derived extensions of pawlak s rough set approximation operators based on such neighborhood systems are proposed properties of neighborhood operator systems and rough set approximation operators are investigated and their connections are examined

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

generalized fuzzy rough sets determined by a triangular norm the theory of rough sets has become well established as an approach for uncertainty management in a wide variety of applications various fuzzy generalizations of rough approximations have been made over the years this paper presents a general framework for the study of t fuzzy rough approximation operators in which both the constructive and axiomatic approaches are used by using a pair of dual triangular norms in the constructive approach some definitions of the upper and lower approximation operators of fuzzy sets are proposed and analyzed by means of arbitrary fuzzy relations the connections between special fuzzy relations and the t upper and t lower approximation operators of fuzzy sets are also examined in the axiomatic approach an operator oriented characterization of rough sets is proposed that is t fuzzy approximation operators are defined by axioms different axiom sets of t upper and t lower fuzzy set theoretic operators guarantee the existence of different types of fuzzy relations producing the same operators the independence of axioms characterizing the t fuzzy rough approximation operators is examined then the minimal sets of axioms for the characterization of the t fuzzy approximation operators are presented based on information theory the entropy of the generalized fuzzy approximation space which is similar to shannon s entropy is formulated to measure uncertainty in t generalized fuzzy rough sets a notion of fuzziness is introduced some basic properties of this measure are examined for a special triangular norm t min it is proved that the measure of fuzziness of the generalized fuzzy rough set is equal to zero if and only if the set is crisp and definable

formulating the shear stress distribution in circular open channels based on the renyi entropy the principle of maximum entropy is employed to derive the shear stress distribution by maximizing the renyi entropy subject to some constraints and by assuming that dimensionless shear stress is a random variable a renyi entropy based equation can be used to model the shear stress distribution along the entire wetted perimeter of circular channels and circular channels with flat beds and deposited sediments a wide range of experimental results for 12 hydraulic conditions with different froude numbers 0 375 to 1 71 and flow depths 20 3 to 201 5 mm were used to validate the derived shear stress distribution for circular channels model performance enhanced with increasing flow depth mean relative error re of 0 0414 and only deteriorated slightly at the greatest flow depth re of 0 0573 for circular channels with flat beds the renyi entropy model predicted the shear stress distribution well at lower sediment depth the renyi entropy model results were also compared with shannon entropy model results both models performed well for circular channels but for circular channels with flat beds the renyi entropy model displayed superior performance in estimating the shear stress distribution the renyi entropy model was highly precise and predicted the shear stress distribution in a circular channel with re of 0 0480 and in a circular channel with a flat bed with re of 0 0488