periodic forced response of structures having three dimensional frictional constraints abstract many mechanical systems have moving components that are mutually constrained through frictional contacts when subjected to cyclic excitations a contact interface may undergo constant changes among sticks slips and separations which leads to very complex contact kinematics in this paper a 3 d friction contact model is employed to predict the periodic forced response of structures having 3 d frictional constraints analytical criteria based on this friction contact model are used to determine the transitions among sticks slips and separations of the friction contact and subsequently the constrained force which consists of the induced stick slip friction force on the contact plane and the contact normal load the resulting constrained force is often a periodic function and can be considered as a feedback force that influences the response of the constrained structures by using the multi harmonic balance method along with fast fourier transform the constrained force can be integrated with the receptance of the structures so as to calculate the forced response of the constrained structures it results in a set of non linear algebraic equations that can be solved iteratively to yield the relative motion as well as the constrained force at the friction contact this method is used to predict the periodic response of a frictionally constrained 3 d o f oscillator the predicted results are compared with those of the direct time integration method so as to validate the proposed method in addition the effect of super harmonic components on the resonant response and jump phenomenon is examined

fuzzy measures on metric spaces abstract the aim of the present paper is to study the regularity and tightness properties of fuzzy measures on metric spaces among other results we shall give lusin s theorem and egoroff s theorem we shall also prove the singleton characterization of atom of fuzzy measure and an algorithm to evaluate the fuzzy integrals of non negative measurable functions over an atom and a union of finite disjoint atoms

the fuzzy set theory approach to the vehicle routing problem when demand at nodes is uncertain abstract the problem of vehicle routing when demand at the nodes is uncertain is considered the quantities to be picked up at the nodes are assumed to be only approximately known a network with one depot from which vehicles depart and to which they return after completing their service is considered the paper develops a model to design vehicle routing when demand at the nodes is uncertain the model is based on the heuristic sweeping algorithm the rules of fuzzy arithmetic and fuzzy logic

a possibility measure is not a fuzzy measure abstract in this note we show that a possibility measure is not a particular type of fuzzy measure except in trivial cases

weakly tight functions their jordan type decomposition and total variation in effect algebras in the present paper we have studied envelopes of a function m defined on a subfamily e containing 0 and 1 of an effect algebra l the notion of a weakly tight function is introduced and its relation to tight functions is investigated examples and counterexamples are constructed for illustration a jordan type decomposition theorem for a locally bounded real valued weakly tight function m defined on e is established the notions of total variation m on the subfamily e and m atoms on a sub effect algebra e along with a few examples of m atoms for null additive as well as non null additive functions are introduced and studied finally it is proved for a real valued additive function m on a sub effect algebra e that m is non atomic if and only if its total variation m is non atomic

a fuzzy set theory approach to the aircrew rostering problem abstract the paper develops a model to solve the aircrew rostering problem consisting of the assignment of crew members to planned rotations the crew rostering problem includes the construction of personalized monthly schedules rosters the basic algorithm to solve the aircrew rostering problem developed in this paper is a modification of the day by day heuristic method an approximate reasoning algorithm is used to determine the strength of the decision maker s preference to assign a specific rotation to a specific pilot the developed model is tested on a numerical example whose dimensions are characteristic of small and medium sized air carriers

a fuzzy logic approach to dynamic dial a ride problem different versions of the dynamic dial a ride problem are found in every day practice transportation of people in low density areas transportation of the handicapped and elderly persons and parcel pick up and delivery service in urban areas carrier which is providing the transportation service receives calls for transportation the problem is to assign every new passenger request to one of the vehicles and to design a new route and schedule for this vehicle this assignment must be done in real time two approximate reasoning algorithms are developed in this paper using the first approximate reasoning algorithm we make the decision about which vehicle will accept the new request the second developed approximate reasoning algorithm was used to design the new route and schedule for the vehicle chosen to serve the new request the model developed has been tested on a greater number of different numerical examples the results obtained are very promising

the receptance based perturbative multi harmonic balance method for the calculation of the aperiodic steady state response of non linear systems abstract a receptance based perturbative multi harmonic balance rpmhb method has been developed recently 1 the method can be applied to systems containing almost any type of non linear element it is computationally efficient particularly when the number of the non linear elements is small this method has been successfully applied to calculate the periodic steady state response of localized non linear systems in this paper the rpmhb method is generalized to calculate the aperiodic steady state response of systems containing localized non linear elements when the response is not periodic the commonly used fft algorithm is not applicable to overcome this problem a direct fit algorithm is suggested to calculate the coefficients of the frequency components numerical examples are presented to illustrate the features of this method

a new fuzzy logic approach to capacitated dynamic dial a ride problem abstract almost all dial a ride problems darp described in the literature pertain to the design of optimal routes and schedules for n customers who specify pick up and drop off times in this article we assume that the customer is mainly concerned with the drop off time because it is the most important to the customer based on the drop off time specified by the customer and the customer s location a pick up time is calculated and given to the customer by the dispatching office we base our formulation on a dynamic fuzzy logic approach in which a new request is assigned to a vehicle the fuzzy logic algorithm chooses the vehicle to transport the customer by seeking to satisfy two objectives the first reflects the customer s preference and minimizes the time a customer spends in the vehicle and the second reflects the company s preference and minimizes the distance a vehicle needs to travel to transport the customer the proposed heuristic algorithm is relatively simple and computationally efficient in comparison with most deterministic algorithms for solving both small and large sized problems

graph theoretic relaxations of set covering and set partitioning problems in this paper we review the graph theoretic relaxations of the set covering problem scp and the set partitioning problem ssp these are a network relaxation which can be solved by the greedy method a matching relaxation and a graph covering relaxation other relaxations such as assignment shortest route and minimum spanning tree are also presented

lebesgue and saks decompositions of σ finite fuzzy measures two kinds of absolute continuity of fuzzy measures are distinguished and relations between them are established the scope of fuzzy measures under our consideration is limited in a family of those that are finite and absolute continuous with respect to a finite autocontinuous fuzzy measure under this restriction lebesgue decomposition and saks decomposition are proved

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

an extension of set partitioning with application to scheduling problems abstract the well known problems of set covering set partitioning and set packing are defined and their interrelationship is considered a natural generalisation called the extended set partitioning model is presented and the three standard models are shown to be special cases of this generalisation in addition the extended model includes another type of set problem which can be of greater use in certain applications the model forms the basis of a computer assisted bus crew scheduling system developed by the authors the system is in regular use by dublin city services in the republic of ireland finally the equivalence between a special case of the set partitioning problem and the shortest route problem is considered and it is shown that this equivalence also applies to the extended model

the autocontinuity of set function and the fuzzy integral abstract the autocontinuity and some other concepts of a set function are introduced and sugeno s fuzzy measure with some annexed conditions is studied on a fuzzy measure space egoroffs theorem is proved it is also proved that f mean convergence is equivalent to convergence in measure for a sequence of measurable functions finally some convergence theorems of sequence of fuzzy integrals are proved especially using the concept of autocontinuity a necessary and sufficient condition for the convergence in measure theorem is given

sugeno integral based on absolutely monotone real set functions the class of all absolutely monotone and sign stable set functions with m a 0 denoted by amss is introduced necessary and sufficient conditions are obtained for a set function m m a 0 to be a member of amss a sugeno type integral of an a measurable real valued function is defined with respect to an absolutely monotone and sign stable set function and some of its properties are shown a representation of a comonotone cosigned additive functional by sugeno integral based on m amss is obtained

fuzzy control of model car this paper discusses fuzzy control of a model car fuzzy control rules are derived by modelling an expert s driving actions experiments are performed using a model car with a sensing unit and a micro computer

the completion of a fuzzy measure and its applications this paper discusses first the completion of a fuzzy measure which is defined on a ring then as an application of the complete fuzzy measure both convergence almost everywhere and convergence in fuzzy measure egoroff s theorems are provided

autocontinuity convergence in measure and convergence in distribution abstract it is shown that the autocontinuity is equivalent to the property that the convergence in measure implies the convergence in distribution this result is applied to denneberg s dominated convergence theorem for the choquet integral

asymptotic structural characteristics of fuzzy measure and their applications abstract in fuzzy measure theory as sugeno s fuzzy measures lose additivity in general the concept almost which is well known in classical measure theory splits into two different concepts almost and pseudo almost in order to replace the additivity it is quite necessary to investigate some asymptotic behaviors of a fuzzy measure at sequences of sets which are called waxing and waning and to introduce some new concepts such as autocontinuity converse autocontinuity and pseudo autocontinuity these concepts describe some asymptotic structural characteristics of a fuzzy measure in this paper by means of the asymptotic structural characteristics of fuzzy measure we also give four forms of generalization for both egoroff s theorem riesz s theorem and lebesgue s theorem respectively and prove the almost everywhere pseudo almost everywhere convergence theorem the convergence in measure pseudo in measure theorem of the sequence of fuzzy integrals in the last two theorems the employed conditions are not only sufficient but also necessary

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

the probability monopoly probability is a very special case of fuzziness it always faces two limits first it works with bivalent sets a second probability measures need small infinities a probability measure maps the sets in a sigma algebra to the unit interval spl lsqb o 1 spl rsqb fuzzy theory challenges the probability monopoly probabilists have attacked it with gusto to keep their monopoly status to have the only uncertainty theory in the unit interval spl lsqb o 1 spl rsqb but the fuzzy math is sound its world view of shades of gray has a deep intuitive ring and the new fuzzy products have come into their own in the marketplace

further discussion on the hahn decomposition theorem for signed fuzzy measure abstract this paper gives a counterexample that the union of two negative sets is not a negative set for signed fuzzy measure showing that the proof of theorem 2 in liu 1993 is not valid furthermore we provide a proof for the hahn decomposition theorem when the space x is countable or the signed fuzzy measure possess the property d

use of a fuzzy theory technique for grouping of trips in the vehicle routing and scheduling problem abstract a technique of grouping trips on the basis of their similarity is presented it is to be used in conjunction with any of the existing routing and scheduling models of demand responsive transportation drt vehicles the proposed approach treats the similarity of two trips as a fuzzy relation for a given trip pair the level of similarity is defined by the membership grade of the fuzzy relation for different attributes of the trips the composite similarity of the trip pair is then computed by a fuzzy integral based on the matrix of the composite similarity trip groups are identified by connecting trip pairs whose membership grade is greater than a given value the technique allows grouping of trips when the total number of trips is very large without losing the flexibility of the manual grouping process it permits the selection of different similarity criteria different values of weights among the criteria and the cut off point of similarity grade depending on the requirements of the day this is possible by expressing the similarity as a fuzzy relation the technique can be used as part of pre screening of the original set of trips before any of the existing scheduling algorithms is applied

convergence in measure theorems of nonlinear integrals of functions integrable to the pth power abstract one can find a subadditive measure and a sequence f n n n of nonnegative measurable functions converging in measure to such a function f with the property that for any p 1 f n p no longer converges in measure to f p therefore in nonadditive measure theory an additional and intrinsic discussion is needed to prove integral convergence theorems for functions integrable to the pth power the purpose of the paper is to propose a method for automatically deriving pth power versions of convergence in measure theorems of nonlinear integrals from already established ones the proposed method is based on the robustness of some properties of integral functional under the operation f f p raising a nonnegative function f to the pth power

lebesgue decomposition theorem for σ finite signed fuzzy measures further research on signed fuzzy measures is made lebesgue decomposition theorems for finite signed fuzzy measures and fuzzy measures are proved under the null null additive condition thus the relative result in classical measure theory is generalized

fuzzy sets theory applications in traffic and transportation abstract an entire array of different traffic and transportation parameters are clearly characterized by uncertainty subjectivity imprecision and ambiguity thus in the mathematical modeling phase of traffic and transportation processes whose individual parameters are uncertain ambiguous or subjectively estimated mathematical methods must be used that are able to satisfactorily deal with uncertainty ambiguity and subjectivity fuzzy set theory is a very convenient mathematical device for treating uncertainty subjectivity ambiguity and indetermination the purpose of this paper is to point out the possibility of using fuzzy set theory in solving complex traffic and transportation problems classification and analysis of up to date results in applying fuzzy set theory in modeling complex traffic and transportation processes are given in this paper

fuzzy valued fuzzy measures and generalized fuzzy integrals in this paper the concept of fuzzy valued fuzzy measures is introduced at first and then based on the generalized fuzzy integral given by wu et al fuzzy sets and systems 57 1993 219 the generalized fuzzy integral of fuzzy valued functions with respect to fuzzy valued fuzzy measures is defined and the properties and convergence theorems are given all these are extensions of the sugeno theory of fuzzy integrals and its applications ph d thesis tokyo institute of technology 1974 and wu et al 1993 theory

an analytical solution for periodic response of elastic friction damped systems abstract this paper presents an analytical method for determining the steady state response of an elastic friction damped single degree of freedom system the method is based on a procedure that uses solution forms for the response within the intervals where the system possesses constant damping characteristic and combines these solutions to form an exact periodic motion of the system stability of the steady state response is directly determined by using floquet s theory the method is applied to a number of examples of practical significance in vibration control demonstrating its validity and effectiveness

traffic control process of expressway by fuzzy logic abstract there are many complicated and fuzzy situations in the case of controlling the traffic flow on an urban expressway data obtained by traffic detectors and information about other roads all should be considered to determine the best operation the control of an urban expressway therefore has been dependent upon skilled operators judgement and decision the objective of the study reported here is to describe the judgement process of the operator by fuzzy logic and to suggest a traffic control system that could determine the pattern of on ramp control of the expressway automatically establishing a fuzzy logic traffic controller according to a real operation process would be valuable to decrease the work load of the skilled operators who make decisions every time and helpful to develop a more effective operation procedure in this study a simple fuzzy reasoning model for on ramp control is constructed the actual operating data were gathered on hanshin expressway the osaka sakai route is the example route on which the performance of the model is examined as a result of the study it becomes clear that the fuzzy logic traffic controller system is effective to describe and take the place of human operators in addition improvement of the model and a total system of fuzzy traffic control is suggested