representation of multivalued functions using the direct cover method an efficient method for representing multivalued functions is described the method employs an algorithm which generates an efficient cover for a given function directly i e without resorting to the intermediate step of creating a table of prime implicants data are presented to show that the covers generated are as efficient in terms of cover size as prime implicant based methods more importantly however the direct cover method is shown to require much less computation time than prime implicant based methods thus making it practical for functions with a large number of input variables and or as the radix of implementation increases the algorithm is introduced by applying it to functional representations employing the traditional max and min operation next a modified form of the algorithm is presented for use with the sum and product operators more appropriate to i2l and other current summation technologies

synthesis of operational transconductance amplifier based analog fuzzy functional blocks and its application a synthesis of analog fuzzy functional blocks a complementary membership function circuit a maximum circuit a complementary maximum circuit and a defuzzifier circuit based on operational transconductance amplifiers ota s is presented the complementary membership function circuit and the maximum circuit are synthesized from the formulations using bounded difference operations the defuzzifier circuit is synthesized as the follower aggregation circuit composed of multiplier type ota s spice simulations showed that the proposed fuzzy functional blocks feature high speed operations and low power consumption the complementary membership function circuit the maximum circuit and the complementary maximum circuit were built with discrete components and commercially available ota s and the performances of these circuits were confirmed by experiments as an application a singleton fuzzy controller with 3 spl times 3 rules is synthesized using the proposed circuits the simulation of this controller showed that the inference speed of the order of 15 mrps rules per second is easily realizable

neuro fuzzy system with high speed low power analog blocks this paper proposes several improved cmos analog circuits for neuro fuzzy system including gaussian like membership function circuit minimization circuit and a centroid algorithm defuzzification circuit not using division a two input one output neuro fuzzy system composed of these circuits is implemented and testified for non linear function approximating all the circuits have been fabricated in smic 0 18 m mixed signal cmos technology experiment results show that all the proposed circuits provide characteristics of high operation capacity high speed and simple structures they are very suitable for rapid implementation of high speed complex neuro fuzzy system

designing sequential systems with fuzzy j k flip flops abstract we develop a designing framework for dealing with fuzzy computation using fuzzy j k flip flops in situations where some hardware implementation of integrated circuits utilizing ideas of fuzzy sets have already been introduced relevant design procedures become strongly required it should be stressed that they do not arise as a straightforward generalization of methods suitable for two valued digital systems but have to be formulated in a different way however they reduce to well known methods when boolean expressions are put into account the general structure of the j k flip flop described by set and reset equations is provided next a resulting excitation table is summarized different methods of designing the associated combinational part of the sequential system are studied

formulation of mindlin engesser model for stiffened plate vibration in this paper a mindlin engesser model is developed for the vibration analysis of moderately thick plates with arbitrarily oriented stiffeners the theoretical derivation incorporates the mindlin theory to account for the effects of transverse shear deformation and rotary inertia of plates and the engesser theory to account for the shear deformation of stiffeners with the inclusion of torsion effect in the method of solution the resulting energy functionals are minimized using the ritz procedure with a set of admissible two dimensional functions expressed in the form of simple polynomials the key kinematic feature of these shape functions is that they are boundary oriented and no boundary losses are introduced as in discretization methods with the aim of demonstrating the applicability and versatility of the method numerical examples including plates of various shapes with arbitrarily oriented stiffeners are presented several findings and conclusions regarding the method have been highlighted and discussed

effect of elastic foundation on asymmetric vibration of polar orthotropic linearly tapered circular plates asymmetric vibrations of polar orthotropic circular plates of linearly varying thickness resting on an elastic foundation of winkler type are discussed on the basis of the classical plate theory ritz method has been employed to obtain the natural frequencies of vibration using the functions based upon the static deflection of polar orthotropic plates which has faster rate of convergence as compared to the polynomial co ordinate functions frequency parameter of the plate with elastically restrained edge conditions are presented for various values of taper parameter rigidity ratio and foundation parameter a comparison of the results with those available in the literature obtained by finite element method receptance method and polynomial co ordinate functions shows an excellent agreement

an approximation scheme for stochastic integer programs arising in capacity expansion planning for capacity expansion forms a crucial part of the strategic level decision making in many applications consequently quantitative models for economic capacity expansion planning have been the subject of intense research however much of the work in this area has been restricted to linear cost models and or limited degree of uncertainty to make the problems analytically tractable this paper addresses a stochastic capacity expansion problem where the economies of scale in expansion costs are handled via fixed charge cost functions and forecast uncertainties in the problem parameters are explicitly considered by specifying a set of scenarios the resulting formulation is a multistage stochastic integer program we develop a fast linear programming based approximation scheme that exploits the decomposable structure and is guaranteed to produce feasible solutions for this problem through a probabilistic analysis we prove that the optimality gap of the heuristic solution almost surely vanishes asymptotically as the problem size increases

heuristic minimization of mvl functions a direct cover approach a heuristic method to obtain near minimal covers of p valued switching functions is introduced first we describe transform tools useful in the processing of mvl functions they are p adic shifting weighting and implicant detecting transformations based on these tools a direct cover algorithm is presented that uses local information for heuristic decision making the heuristics are taken from weight coefficients calculated for canonical terms and implicants the method allows to assign cost factors to implicants further the algorithms can be modified easily so as to correspond to various connectives e g max plus

lower bounding procedures for multiperiod telecommunications network expansion problems this paper suggests an improved formulation for the multiperiod network topology and capacity expansion problem and proposes new lower bounding schemes based on it it differs from earlier formulations and solution methods in that entirely new and different subproblems are solved and a number of lower bound tightening schemes are added within the framework of a lagrangian relaxation dual ascent and multiplier adjustment procedures are suggested for the lagrange multiplier updating procedure computational results are reported to demonstrate the tightness of the bounds generated by the suggested procedures heuristics based on converting the dual information obtained from the lagrangian procedure into primal feasible solutions are tested the tests show that the lagrangian based heuristics generate solutions superior to solutions generated by other heuristics proposed in the literature

ultra efficient fuzzy min max circuits based on carbon nanotube fets to implement a fuzzy system the first and the most essential step is to design basic fuzzy modules such as analog min and max circuits this paper presents efficient minimum and maximum circuits using carbon nanotube fets cntfets for nanotechnology based fuzzy circuits and systems the proposed approach considerably reduces the design complexity in the fuzzy space in the proposed design the chirality of carbon nanotubes is utilized for threshold voltage determination extensive simulations conducted using hspice and the stanford cntfet model at 16 nm feature size demonstrate that the proposed fuzzy logic blocks considerably improve the performance parameters and function much more robustly even in the presence of process variations as compared to their cntfet based counterparts

a dynamic programming algorithm for the local access telecommunication network expansion problem abstract in this paper we consider the local access telecommunication network expansion problem in which growing demand can be satisfied by expanding cable capacities and or installing concentrators in the network the problem is known to be np hard we prove that the problem is weakly np hard and present a pseudo polynomial dynamic programming algorithm for the problem with time complexity o nb 2 and storage requirements o nb where n refers to the size of the network and b to an upper bound on concentrator capacity the cost structure in the network is assumed to be decomposable but may be non convex non concave and node and edge dependent otherwise this allows for incorporation of many aspects occurring in practical planning problems computational results indicate that the algorithm is very efficient and can solve medium to large scale problems to optimality within fractions of seconds to minutes

quantization and roundoff noises in fixed point fir digital filters the errors in a fixed point finite impulse response fir filter due to quantization analog to digital conversion and roundoff are considered expressions for the exact moments of the filter output noise are derived it is well known that when the input signal satisfies certain conditions the popular additive white noise model can be valid in describing the quantization noise the characteristics of multiplicative roundoff noises however differ from what this model predicts even under conditions where the roundoff noises are white hence the additive white noise model does not provide accurate results on the characteristics of the output error in an fir filter using the exact formulas for the moments the author computes the exact power spectrum of the filter output error these results agree well with those obtained from simulation

automated synthesis of combinational logic using theorem proving techniques recent findings indicate that logic design still constitutes 50 percent of the total design effort and yet few automated tools are being used in industry the use of an automated theorem proving system in the logic design process presents an intriguing addition to traditional design automation tools this paper deals with the automated synthesis of combinational logic the method consists of a theorem proving implementation of a systematic uniform procedure for the synthesis of an arbitrary switching function any multiple valued including binary function can be synthesized in a top down fashion using the functional blocks of the designer s choice the method is general enough to allow for the choice of an arbitrary logic system and radix additional constraints of modularity technology dependence fault tolerance and others may be imposed upon the design it may also be possible to accommodate into this approach formal design verification design for testability functional level modeling and formal analysis of race and hazard conditions

multiple valued logic its status and its future multiple valued logic in which the number of discrete logic levels is not confined to two has been the subject of much research over many years the practical objective of this work has been to increase the information content of the digital signals in a system to a higher value than that provided by binary operation in this tutorial survey paper we will review the historical developments in this field both in circuit realizations and in methods of handling multiple valued design data and consider the present state of the art and future expectations

modular decomposition of combinatorial multiple values circuits a decomposition approach to the modular design of multiple valued logic functions is discussed systematic procedures to utilize a fixed set of building blocks from which an arbitrary function can be designed are illustrated the building blocks are composed of t gates multiplexers the first step is the partitioning of all logic functions into classes representative building blocks for each class are then developed finally optimization techniques are described that reduce the number of building blocks required in the design this approach is in principle applicable to functions in any radix and will always yield a design for the target function examples are presented to illustrate the approach for ternary functions

simplified method for solving problems of vibrating plates of doubly connected arbitrary shape part ii applications and experiments abstract the eigenfrequencies of ring shaped polygonal plates ring shaped elliptical plates rectangular plates with elliptical inner boundaries and circular plates with elliptical inner boundaries are obtained the method developed by the author in the companion paper part i is applied for finding the eigenfrequencies to verify the present results experimental tests have also been carried out for some important cases

on the design of 4 valued digital systems the availability of 4 valued i2l circuits presents a new perspective for digital systems designers this correspondence explores several aspects of digital system design using 4 valued logic elements an approach to designing the ith stage of an alu employing these elements is presented the realization of rudimentary alu operations is shown using the t gate as a universal building block system design based on both post and boolean 4 valued logics is discussed

a dual ascent procedure for large scale uncapacitated network design the fixed charge network design problem arises in a variety of problem contexts including transportation communication and production scheduling we develop a family of dual ascent algorithms for this problem this approach generalizes known ascent procedures for solving shortest path plant location steiner network and directed spanning tree problems our computational results for several classes of test problems with up to 500 integer and 1 98 million continuous variables and constraints show that the dual ascent procedure and an associated drop add heuristic generate solutions that in almost all cases are guaranteed to be within 1 to 4 of optimality moreover the procedure requires no more than 150 seconds on an ibm 3083 computer the test problems correspond to dense and sparse networks including some models that arise in freight transport

processors for generalized stack filters new processor structures for generalized stack filters are proposed they can be implemented using different numbers of boolean function units the class of pipeline parallel structures for generalized stack filters is simple and modular in structure and suitable for vlsi implementation coder and decoder networks are developed for the mutual transform of binary weighted and unary weighted codes as the thresholding and addition units of the processors the area time complexity a spl middot t of the proposed filters is o k sup 3 due to the feedback instead of o 2 sup k for the threshold decomposition structure where k is the number of bits for sample representation

high level design space exploration of locally linear neuro fuzzy models for embedded systems recently artificial neural networks and neuro fuzzy systems are being introduced in embedded systems due to often used solution for classification and nonlinear system identification in this paper we present a parametric neuro fuzzy hardware and a framework for exploring design space for an efficient hardware realization of neuro fuzzy models for embedded systems the proposed hardware can be used as a stand alone core or be coupled with a central processing unit for the purpose of online training we also present a framework to explore the design space for optimal design parameters hardware core parameters so that an efficient neuro fuzzy hardware in terms of area power consumption and performance delay can be selected it examines whole design space to find pareto efficient hardware without increasing time to market and non recurring engineering cost with the aid of high level design space exploration also the performance of the proposed hardware is compared against a soft core embedded processor named nios ii s the results obtained show that the selected core is able to perform actions faster than nios ii while it dissipates less power moreover the proposed framework is put into action through three different scenarios to show off the capabilities of framework for generating pareto optimal points upon different application demands

simplified method for solving problems of vibrating plates of doubly connected arbitrary shape part i derivation of the frequency equation abstract a simplified approximate method for solving problems of vibrating plates of doubly connected arbitrary shapes is presented in the analysis an arbitrarily shaped boundary is divided into small segments and general transformed expressions for the bending slope the bending moment and the shearing force of a segment are given under the assumption that the angle between the normal to the segment and the reference axis is constant the boundary conditions along the outer and the inner edges are satisfied by means of the fourier expansion collocation method the equation for finding the eigenfrequencies and mode shapes is obtained for arbitrarily shaped boundaries

discrete interval truth values logic and its application in this paper we focus on functions defined on a special subset of the power set of 0 1 r 1 the elements in the subset will be called discrete interval truth values and operations on the truth values the operations discussed in this paper will be called regular because they are one of the extensions of the regularity which was first introduced by kleene in his ternary logic mukaidono investigated some properties of ternary functions which can be represented by the regular operations he called such ternary functions regular ternary logic functions regular ternary logic functions are useful for representing and analyzing ambiguities such as transient states and or initial states in binary logic circuits that boolean functions cannot cope with furthermore they are also applied to studies of fail safe systems for binary logic circuits in this paper we will discuss an extension of regular ternary logic functions to functions on the discrete interval truth values first we will suggest an extension of the regularity in the sense of kleene into operations on the discrete interval truth values we will then present some mathematical properties of functions on the discrete interval truth values consisting of regular operations and one application of these functions

bi decomposition of multi valued logical functions and its applications abstract the bi decomposition of multi valued logical mvl functions including disjoint and non disjoint cases is considered using a semi tensor product an mvl function can be expressed in its algebraic form based on this form straightforward verifiable necessary and sufficient conditions are provided for each case respectively the constructive proofs also lead to constructing corresponding decompositions using these results the implicit function theorem ift of k valued functions as a special bi decomposition is obtained finally as an application the normalization of dynamic algebraic d a boolean networks is investigated using ift of k valued functions

a learning multiple valued logic network algebra algorithm and applications we propose a multiple valued logic mvl network with functional completeness and develop its learning capability the mvl network consists of layered arithmetic piecewise linear processors since the arithmetic operations of the network are basically a wired sum and a piecewise linear operation their implementations should be rather simple and straightforward furthermore the mvl network can be trained by the traditional backpropagation algorithm directly the algorithm trains the networks using examples and appears to be available for most mvl problems of interest

multiple valued logic charge coupled devices a new method to implement multiple valued logic in large scale integrated circuits is introduced the data are represented by discrete amounts of charge in a charge coupled device in this paper the design principles and realizations in four valued logic of a minimum and maximum circuit a complement circuit a literal a successor and an adder are presented also the designs of a binary to quaternary converter and vice versa are discussed charge coupled devices offer low power consumption high packing density and the possibility to perform most ic compatible multiple valued logic in any arbitrary radix

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

elasticity solutions for free vibrations of annular plates from three dimensional analysis abstract this article examines the vibrational characteristics of annular plates by using the three dimensional elasticity theory it aims to raise the quality of the investigation beyond that provided by the two dimensional plate theories by resorting to a full three dimensional analysis a polynomials ritz model based on sets of orthogonally generated polynomial functions to approximate the spatial displacements of the plates in cylindrical polar coordinates is presented the model is then used to extract the full vibration spectrum of natural frequencies and mode shapes the vibration responses due to the variations of boundary conditions and thickness are investigated frequency parameters and three dimensional deformed mode shapes are presented in vivid graphical forms the accuracy of the method is validated through appropriate convergence and comparison studies

measures of general fuzzy rough sets on a probabilistic space fuzzy rough set is a generalization of crisp rough set which deals with both fuzziness and vagueness in data the measures of fuzzy rough sets aim to dig its numeral characters in order to analyze data effectively in this paper we first develop a method to compute the cardinality of fuzzy set on a probabilistic space and then propose a real number valued function for each approximation operator of the general fuzzy rough sets on a probabilistic space to measure its approximate accuracy the functions of lower and upper approximation operators are natural generalizations of the belief function and plausibility function in dempster shafer theory of evidence respectively by using these functions accuracy measure roughness degree dependency function entropy and conditional entropy of general fuzzy rough set are proposed and the relative reduction of fuzzy decision system is also developed by using the dependency function and characterized by the conditional entropy at last these measure functions for approximation operators are characterized by axiomatic approaches

algebraic fuzzy flip flop circuits abstract algebraic fuzzy flip flop circuits in discrete and continuous mode are presented the algebraic fuzzy flip flop is one example of the general fuzzy flip flop concept which has been defined as an extension of the binary j k flip flop two types of the algebraic fuzzy flip flop which are reset type and set type are defined using complementation algebraic product and algebraic sum operations for fuzzy negation t norm and s norm respectively a unified equation of the reset type and set type of an algebraic fuzzy flip flop is derived for the purpose of realization of hardware circuits based on the equation two types of hardware circuits in discrete mode and continuous mode are constructed moreover the characteristics of various fuzzy flip flops presented previously are investigated such as min max fuzzy flip flop in both discrete and continuous mode and the algebraic fuzzy flip flop presented in this paper

attribute reduction based on generalized fuzzy evidence theory in fuzzy decision systems attribute reduction is viewed as an important issue in data mining and knowledge representation this paper studies attribute reduction in fuzzy decision systems based on generalized fuzzy evidence theory the definitions of several kinds of attribute reducts are introduced the relationships among these reducts are then investigated in a fuzzy decision system it is proved that the concepts of fuzzy positive region reduct lower approximation reduct and generalized fuzzy belief reduct are all equivalent the concepts of fuzzy upper approximation reduct and generalized fuzzy plausibility reduct are equivalent and a generalized fuzzy plausibility consistent set must be a generalized fuzzy belief consistent set in a consistent fuzzy decision system an attribute set is a generalized fuzzy belief reduct if and only if it is a generalized fuzzy plausibility reduct but in an inconsistent fuzzy decision system a generalized fuzzy belief reduct is not a generalized fuzzy plausibility reduct in general

design of an analog cmos fuzzy logic controller chip we propose an analog fuzzy logic controller chip structure in 1 2 m cmos technology it employs a new architecture for fuzzifier circuit that generates membership functions with a very suitable range and precision these membership functions are simply tunable by setting some voltages on ic pins input has three membership functions and output is five singleton membership functions also a novel defuzzifier circuit is used which occupies a small chip area the controller is tested for two inputs one output and nine tunable fuzzy rules the proposed architecture has an operation speed of 6 25 mflips 6 25 106 fuzzy logic inference per second and power consumption of 16 3 mw the whole chip area is less than 0 7 mm2 which is very small simulation tests show a good functionality of controller in response to some inputs to confirm the success of the design the application of the system to the synthesis of a second order system in a feedback loop is also considered

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

the prospects for multivalued logic a technology and applications view advances in multiple valued logic mvl have been inspired in large part by advances in integrated circuit technology multiple valued logic has matured to the point where four valued logic is now part of commercially available vlsi ic s besides reduction in chip area mvl offers other benefits such as the potential for circuit test this paper describes the historical and technical background of mvl and areas of present and future application it is intended as well to serve as a tutorial for the nonspecialist

examples of fuzzy metrics and applications in this paper we present new examples of fuzzy metrics in the sense of george and veeramani the examples have been classified attending to their construction and most of the well known fuzzy metrics are particular cases of those given here in particular novel fuzzy metrics by means of fuzzy and classical metrics and certain special types of functions are introduced we also give an extension theorem for two fuzzy metrics that agree in its nonempty intersection finally we give an application of this type of fuzzy metrics to color image processing we propose a fuzzy metric that simultaneously takes into account two different distance criteria between color image pixels and we use this fuzzy metric to filter noisy images obtaining promising results this application is also illustrative of how fuzzy metrics can be used in other engineering problems

multiple valued decomposition of generalized boolean functions and the complexity of programmable logic arrays generalized boolean functions are shown to be useful for the design of programmable logic arrays pla s and the complexity of three types of pla s is obtained by the theory of multiple valued decomposition a two level pla consists of an and array and an or array and they are cascaded to perform a two level and or circuit a pla with decoders consists of decoders an and array and an or array a three level pla consists of a d array an and array and an or array and they are cascaded to perform a three level or and or circuit it is shown that a generalized boolean function f x1 x2 xr x bni b where b 0 1 is represented by a generalized boolean expression of 2ni valued variables x i and f can be directly realized by a pla with decoders or a three level pla to realize a function of n variables n 2r the following sizes are shown to be sufficient for a two level pla n 2n for a pla with two bit decoders 4 n 4 2n for a three level pla 2n 3n l 2n 2n2especially in the case of pla with two bit decoders the following sizes are shown to be necessary and sufficient for an arbitrary symmetric function 3 2 n 3n and for a parity function n 2n

treatments of over restrained boundaries for doubly connected plates of arbitrary shape in vibration analysis abstract the problem of the free flexural vibrations of plates of doubly connected arbitrary shape is investigated a hybrid energy approach which combines both the advantages of the rayleigh ritz method and the lagrange multiplier method is developed for analysing the aforementioned plate problems the rayleigh ritz method with a set of pb 2 shape functions is used to formulate the plates with classical boundary conditions as a single continuum element while the lagrange multipliers are imposed at discrete points in the inner plate boundaries for instance when the overrestrained boundary has occurred the admissible pb 2 shape function consists of the product of a two dimensional polynomial and a basic function the basic function is defined by the product of the equations of the prescribed piecewise continuous boundary shape each raised to the power of 0 1 or 2 corresponding respectively to a free simply supported or clamped edge this set of functions automatically satisfies all the kinematic boundary conditions of the plate at the outset numerical results for several examples of doubly connected plates of arbitrary shape are presented to demonstrate the applicability and accuracy of the present method

meaningful special classes of ternary logic functions regular ternary logic functions and ternary majority functions special ternary logic functions namely regular functions suitable for treating ambiguity and majority functions based on an extended majority principle are considered the one to one correspondence between n ary monotone regular ternary logic functions and n 1 ary monotone boolean functions is investigated as well as the one to one correspondence between n ary monotone ternary majority functions and n 1 ary monotone binary threshold functions the ternary majority functions are enumerated

generating the group of reversible logic gates reversible logic plays a fundamental role both in ultra low power electronics and in quantum computing it is therefore important to have an insight into the structure of the group formed by the reversible logic gates and their cascading into reversible circuits such insight is gained from constructing chains of maximal subgroups the subgroup of control gates plays a prominent role as it is a sylow 2 subgroup

a low power fully programmable membership function generator using both transconductance and current modes abstract in this paper a membership function generator mfg is presented which can produce triangular trapezoidal s shaped or z shaped membership functions the presented structure can operate in both trans conductance voltage current and current mode current current with high programmability the slope keeping the height or width of the membership function constant height keeping the width constant and width keeping the height constant of the membership function are independently programmable moreover the width of the trapezoid can be varied without changing slope or height and all the generated shapes can be positioned horizontally the topology primarily is presented in transconductance mode which can be converted to current mode with a little change in the input section of the circuit simulation results for the proposed circuit are presented in two operation modes the most remarkable feature of the proposed mfg is its capability of generating outputs while consumes a very low amount of power the analytical analysis of the proposed circuits is also given in hspice using tsmc 0 18 m cmos technology

synthesis of discrete functions using i 2 l technology algebraic methods for designing multiple valued i2l circuits are presented a new operation namely the truncated difference is introduced and proved to be an efficient tool for both analyzing and synthesizing circuits

the element free kp ritz method for free vibration analysis of conical shell panels in this paper the free vibration of conical panels is analyzed by the mesh free kp ritz method both 1 d and 2 d versions of the kp ritz approach are formulated for conical panels for conical panels with two simply supported straight edges the 1 d kp ritz version is used where the kernel particle estimation is employed in hybridized form with harmonic functions to approximate the 2 d displacement field for conical panels having arbitrary boundary conditions the displacement field is approximated by the 2 d kp ritz version with 2 d form of kernel particle functions employed the classical thin shell theory based on love s hypothesis is employed in the present analyses and based on the kernel particle concept and ritz technique the eigenequations of the frequencies of the conical panels are obtained to validate the accuracy of stability of the present method convergence studies were carried out based on the influences of the support size and the number of nodes comparisons were also made with existing results available in the open literature this study also examines in detail the effects of variation in the semi vertex angle and boundary conditions on the frequency characteristics of conical panels

an optimization technique for the design of multiple valued pla s an optimization technique for the design of two types of multiple valued plas is described in a type i pla the multiple valued function is realized directly whereas in a type ii pla output encoding is used to encode the binary output of the pla in both types multiple function literal circuits are used for the purpose of minimization it is shown that the proposed technique leads to a considerably reduced size of pla when compared to the earlier techniques

free vibrations of doubly curved in plane non homogeneous shells a method for investigating free vibrations rectangular non homogeneous shells is proposed by non homogeneity we define a chage of stiffness of shell bending caused by an introduction of another material or change of a shell thickness is defined it is assumed that a shell possesses an arbitrary value of rectangular parts with different bending stiffness

relationship between p valued majority functions and p valued threshold functions in a previous paper trans iece japan vol j63 d p 493 500 1980 vol j64 d p 172 3 1981 and vol e 67 p 47 8 1984 the authors defined a new class of multiple valued logic functions called multiple valued majority functions the authors clarifies the distinction of multiple valued majority functions from multiple valued threshold functions through the difference between a number function and an inner product of an input vector and a weight vector

knowledge reduction in random information systems via dempster shafer theory of evidence knowledge reduction is one of the main problems in the study of rough set theory this paper deals with knowledge reduction in random information systems based on dempster shafer theory of evidence the concepts of belief and plausibility reducts in random information systems are first introduced it is proved that both of belief reduct and plausibility reduct are equivalent to classical reduct in random information systems the relative belief and plausibility reducts in consistent and inconsistent random decision systems are then proposed and compared to the relative reduct and relationships between the new reducts and some existing ones are examined

fuzzy rough data reduction with ant colony optimization feature selection refers to the problem of selecting those input features that are most predictive of a given outcome a problem encountered in many areas such as machine learning pattern recognition and signal processing in particular solution to this has found successful application in tasks that involve datasets containing huge numbers of features in the order of tens of thousands which would be impossible to process further recent examples include text processing and web content classification rough set theory has been used as such a dataset pre processor with much success but current methods are inadequate at finding minimal reductions the smallest sets of features possible to alleviate this difficulty a feature selection technique that employs a hybrid variant of rough sets fuzzy rough sets has been developed recently and has been shown to be effective however this method is still not able to find the optimal subsets regularly this paper proposes a new feature selection mechanism based on ant colony optimization in an attempt to combat this the method is then applied to the problem of finding optimal feature subsets in the fuzzy rough data reduction process the present work is applied to complex systems monitoring and experimentally compared with the original fuzzy rough method an entropy based feature selector and a transformation based reduction method pca comparisons with the use of a support vector classifier are also included

generic lr fuzzy cells for fuzzy hardware synthesis a novel primitive cell structure for high performance hardware realization of fuzzy computations is proposed in this paper such a cell structure is called generic lr fuzzy cell because it is an integral unit that encapsulates an lr fuzzy set and a basic fuzzy operation such as implication or arithmetic operation based on the proposed cell structure we can develop two major kinds of fuzzy cell lr fuzzy implication cell and lr fuzzy arithmetic cell for the systematic synthesis of fuzzy application specific integrated circuits asics or general purposed fuzzy processors the fuzzy systems synthesized with lr fuzzy cells possess the characteristics of decentralized knowledge manipulations and massively parallel inference the system expandability and reconfigurability are also warrantable this paper emphasizes on the design and application of fuzzy implication cell the lr fuzzy implication cell is implemented with analog current mode technology by this technology an implication cell has the characteristics including small circuit area high performance low power dissipation etc moreover the implication cell manipulates continuous data so that the realization of a pure fuzzy system is possible in this paper the key circuit characteristics of fuzzy implication cell are evaluated in details and there are two cases fuzzy knowledge system and fuzzy mean filter implemented to confirm the effectiveness and efficiency of fuzzy hardware synthesis by the lr fuzzy cells

on the optimal design of multiple valued plas a description is given of the design and analysis of three types of multivalued plas programmable logic arrays type 1 plas realize functions directly in the form of the max of min of literal functions and constants in type 2 plas the body of the pla is binary and the output is encoded as a multiple valued logic value type 3 plas are the same as type 2 plas except for the use of 2 bit decoders and a permutation network on the input using the number of columns required to realize a given function as a measure to compare plas it is shown that type 3 plas are superior to type 2 which in turn are superior to type 1

vibration of eccentric ring and line supported circular plates carrying concentrated masses abstract the vibration of circular plates supported by combinations of ring and line supports and which are carrying concentrated masses is investigated for the first time to the author s knowledge by using the newly developed pb 2 rayleigh ritz method a set of ritz functions consisting of the product of the boundary expressions is used as the admissible displacement function this set of pb 2 ritz functions can accurately approximate the mode shapes of these circular plates with any prescribed boundary conditions and interior supports such as eccentric annular and or line supports to validate the present method numerical calculations have been carried out for several simplified plate problems and these are compared with those results available in the literature excellent agreement is achieved in all cases

a hardware friendly arithmetic method and efficient implementations for designing digital fuzzy adders a new hardware friendly mathematical method for realizing low complexity universal adder cells as well as its efficient hardware implementations is proposed in this paper this method can be used in binary logic multiple valued logic mvl and specifically digital fuzzy systems the proposed mathematical method can be implemented in both voltage and current modes the voltage mode hardware implementation is very simple and is based on input capacitors and mvl or analog inverters and buffers in addition the current mode hardware implementation leads to simple and efficient structures for digital fuzzy systems simulations are carried out for ternary logic as well as for digital fuzzy logic with high precision by using 180nm standard cmos technology and at 1 8v supply voltage simulation results demonstrate that the proposed designs have excellent functionality and are very suitable for implementing mvl and fuzzy arithmetic circuits

free vibration analysis of arbitrarily shaped plates with clamped edges using wave type functions the basic idea related to the non dimensional dynamic influence green s function defined in an infinite membrane has been applied to the free vibration analysis of arbitrarily shaped plates with clamped edges another non dimensional dynamic influence function newly defined in the paper exactly satisfies the governing homogeneous differential equations of plates and is regular in the entire domain the proposed method uses the boundary discretization scheme similar to that of the boundary element method but does not require any interpolation function between the nodes distributed along the boundary as a result the method has a significant advantage in its simplicity and accuracy although the method uses no interpolation function it gives very accurate eigenvalues and mode shapes compared with the exact solutions or fem results it should be also noted that particular attention is given to reduce the size of the system matrix whose determinant equation yields eigenvalues and to overcome the functional dependence problem of the non dimensional dynamic influence functions

knowledge acquisition in incomplete information systems a rough set approach abstract this paper deals with knowledge acquisition in incomplete information systems using rough set theory the concept of similarity classes in incomplete information systems is first proposed two kinds of partitions lower and upper approximations are then formed for the mining of certain and association rules in incomplete decision tables one type of optimal certain and two types of optimal association decision rules are generated two new quantitative measures random certainty factor and random coverage factor associated with each decision rule are further proposed to explain relationships between the condition and decision parts of a rule in incomplete decision tables the reduction of descriptors and induction of optimal rules in such tables are also examined

free vibration of symmetrically laminated thick perforated plates abstract this paper investigates the free vibration of symmetrically laminated thick doubly connected plates of arbitray plate perimeter for the outer boundary and a hole defined by a super elliptical equation which is able to describe a rectangle ellipse or quasi rectangle the laminated perforated plates can be subject to free simply supported or clamped edge conditions convergence and comparisons with established work have been studied to ensure accuracy of results efforts are made to interpret the frequency results to provide physical insight to the problem

substitution systems and nonextensive statistics abstract substitution systems evolve in time by generating sequences of symbols from a finite alphabet at a certain iteration step the existing symbols are systematically replaced by blocks of n k symbols also within the alphabet with n k a natural number being the length of the k th block of the substitution the dynamics of these systems leads naturally to fractals and self similarity by using b calculus garcia morales 2012 universal maps for deterministic substitution systems both of constant and non constant length are formulated in 1d it is then shown how these systems can be put in direct correspondence with tsallis entropy a second law of thermodynamics is also proved for these systems in the asymptotic limit of large words