characterizations of discrete sugeno integrals as polynomial functions over distributive lattices we give several characterizations of discrete sugeno integrals over bounded distributive lattices as particular cases of lattice polynomial functions that is functions which can be represented in the language of bounded lattices using variables and constants we also consider the subclass of term functions as well as the classes of symmetric polynomial functions and weighted infimum and supremum functions and present their characterizations accordingly moreover we discuss normal form representations of these functions

weighted minimum and maximun operations in fuzzy sets theory abstract this short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper as medians and corrects a misleading statement about it

on sugeno integral as an aggregation function the sugeno integral for a given fuzzy measure is studied under the viewpoint of aggregation in particular we give some equivalent expressions of it we also give an axiomatic characterization of the class of all the sugeno integrals some particular subclasses such as the weighted maximum and minimum functions are investigated as well

benchmarking in linguistic importance weighted aggregations in this work we concentrate on the issue of weighted aggregations and provide a possibilistic approach to the process of importance weighted transformation when both the importances interpreted as benchmarks and the ratings are given by symmetric triangular fuzzy numbers we will show that using the possibilistic approach i small changes in the membership function of the importances can cause only small variations in the weighted aggregate ii the weighted aggregate of fuzzy ratings remains stable under small changes in the nonfuzzy importances iii the weighted aggregate of crisp ratings still remains stable under small changes in the crisp importances whenever we use a continuous implication operator for the importance weighted transformation we illustrate the proposed method by some simple examples

on four noncommutative fuzzy connectives and their axiomatization in most of the query languages conjunctive and disjunctive combinations of conditions remain the usual way for aggregation fuzzy query languages also offer trade off operators such as means in order to compensate between elementary conditions in this paper we would like to introduce a new type of condition basically founded on the interaction between two predicates thus enriching the panoply of tools the user is provided with and the power of query languages

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

temporal scenario modelling and recognition based on possibilistic logic we propose in this paper a new approach for the modelling and recognition of temporal scenarios a scenario is represented by three different structures the first one models the logical dependency between the elements of the scenario using possibilistic logic while the second one is the minimal temporal graph representing all temporal constraints between the events the third structure explains the way the matching between observations and scenarios has to be done the consistency between the three structures is ensured

continuous preference logic for system evaluation in this paper we investigate mathematical models that are suitable for modeling decisions in the area of system evaluation comparison and selection our interest is focused on soft computing models that can be directly related to observable properties of human reasoning and have a record of use in system evaluation practice we analyze various approaches to defining andness and orness and use a generalized conjunction disjunction gcd to build compound preference logic functions and logic models for system evaluation we also present applications of the continuous preference logic in decision models based on the lsp method

on conditions under which some generalized sugeno integrals coincide a solution to dubois problem abstract in the paper we characterize the class of all pairs of fuzzy implications and dual fuzzy implications such that the q integral and q cointegral coincide this gives a solution to the problem posed by didier dubois during the conference fsta 2016 the 13th international conference on fuzzy set theory and applications as a corollary we obtain the necessary and sufficient conditions under which the seminormed fuzzy integral and the semiconormed fuzzy integral are equal for all measurable functions

fuzzy sets and decision analysis abstract this survey points out recent advances in multiple attribute decision making methods dealing with fuzzy or ill defined information fuzzy maut as well as fuzzy outranking methods are reviewed aggregation procedures choice problems and treatment of interactive attributes are covered trends in research and open problems are indicated

choice processes for non homogeneous group decision making in linguistic setting several choice processes of alternatives for non homogeneous group decision making problems assuming linguistic preference relations for expressing the opinions of individuals and linguistic values for expressing their respective power or importance degrees are presented these processes are designed using two choice degrees of alternatives based on the concept of fuzzy majority quantifier guided linguistic dominance degree and quantifier guided linguistic non dominance degree being the last one a generalization of orlovski s non dominated alternative concept in order to deal with non weighted linguistic information the linguistic ordered weighted averaging lowa operator is applied to deal with weighted linguistic information three operators of linguistic weighted information aggregation are used the linguistic weighted disjunction lwd operator the linguistic weighted conjunction lwc operator and the linguistic weighted averaging lwa operator

production control of manufacturing systems with production rate dependent failure rates it is known that for single part type production systems with homogeneous markovian machine failure rates special single threshold feedback policies called hedging point policies are optimal and the stationary probability distribution of the part type surplus for given tentative hedging point values can be obtained analytically this approach is extended to multiple threshold policies with production rate dependent machine failure rates it is shown that the stationary distribution of the part type surplus can be obtained under the extended policy and in the presence of production rate dependent failure rates the advantage of multiple threshold policies is that they can provide a piecewise constant step function approximation of any feedback policy it is observed that hedging point policies are not always optimal and in fact feedback policies are not always optimal either

production control of a pull system with production and demand uncertainty we consider a continuous material flow manufacturing system with an unreliable production system and a variable demand source which switches randomly between zero and a maximum level the failure and repair times of the production system and the switching times of the demand source are assumed to be exponentially distributed random variables the optimal production flow control policy that minimizes the expected average inventory carrying and backlog costs is characterized as a double hedging policy the optimal hedging levels are determined analytically by minimizing the closed form expression of the cost function we investigate two approximate single hedging policies it is empirically shown that an approximate policy that uses a single hedging level which is the sum of a production uncertainty term and a demand uncertainty term gives accurate results for the expected average cost

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

multi step ranking of alternatives in a multi criteria and multi expert decision making environment in this work we introduce a decision model in the form of a recursive aggregation algorithm that attempts to mimic a multi step ranking process of a set of alternatives in a multi criteria and multi expert decision making environment the main idea is rather intuitive each alternative is initially assigned a list of values representing the group experts opinion about the extent to which the alternative satisfies a set of given criteria then the values for each alternative are combined with the weighted mean operator according to vectors of weights one for each decision maker in the group these weights express the personal judgement of the decision makers about the relative importance of the individual criteria consequently a new vector of values is obtained for each alternative these new values are combined again with the weighted mean operator taking into account the different degrees of influence each decision maker accepts from the rest of the group the latter aggregation step is repeated again and again for each alternative until a consensus is attained

a general framework for explaining the results of a multi attribute preference model the automatic generation of an explanation of the prescription made by a multi attribute decision model is crucial in many applications such as recommender systems this task is complex since the quantitative models are not designed to be easily explainable the major limitation of the previous research is that there is no formal justification of the arguments that are selected in the explanation the goal of this paper is to define a general framework to justify which arguments shall be selected in the case where the decision model is based on weights assigned to the attributes due to the complexity of explaining a preference model based on utility theory several explanation reasonings are necessary to cover all cases ranging from situations where the prescription is trivial to situations where the prescription is much more tight the set of selected arguments is in this framework a non dominated element of a combinatorial structure in the sense of an order relation our general approach is instantiated precisely on three models the probabilistic expected utility model the qualitative pessimistic minmax model and the concordance rule which are all constructed from a weight vector

variance of the throughput of an n station production line with no intermediate buffers and time dependent failures in this study the variance of the throughput of an n station production line with no intermediate buffers and time dependent failures is analytically determined time to failure and time to repair distributions are assumed to be exponential the analytical method yields a closed form expression for the variance of the throughput the method is based on determining the limiting variance of the total residence sojourn time in a specific state of an irreducible recurrent markov process from the probability of visiting that state at time t given an initial state this probability function is the instantaneous availability of a production system in the reliability context a production line with no interstation buffers and time dependent failures is basically a series system with hot standby the same procedure can be applied to determine the variance of the throughputs of various arrangements of workstations including series parallel series parallel systems provided that the instantaneous availabilities of these systems can be written explicitly numerical experiments show that although the expected throughput decreases monotonically the variance of the throughput may increase and then decrease as the number of stations in the line increases depending on the system parameters numerical experiments that investigate this phenomenon and also the dependence of the coefficient of variation on the number of stations are also presented in this study

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

including importances in owa aggregations using fuzzy systems modeling ordered weighted averaging owa operators are described and are shown to provide a general class of parameterized aggregation operators that include the max min and average we suggest an approach to the inclusion of importances in the owa operator aggregation technique the methodology suggested involves a transformation of the scores to be aggregated by their respective importances we show how we can construct transformation functions with the aid of the fuzzy modeling technology

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

a prolongation restriction operator for whitney elements on simplicial meshes the paper is mainly focused on the construction of two transfer operators between nested grids in the case of whitney finite elements node edge face or volume based these transfer operators instances of what is called chain map in homology have duals acting on cochains that is to say arrays of degrees of freedom in the context of the finite element discretization of variational problems we show how these duals can act as restriction prolongation operators in a multigrid approach to such problems especially those involving vector fields e g electromagnetism the duality between the operation of mesh refinement of a simplicial complex and that of restriction prolongation of degrees of freedom from one mesh to a nested one is thus analyzed and explained we use the language of p forms with frequent explanatory references to the more traditional vector fields formalism

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

semantics of quotient operators in fuzzy relational databases abstract the quotient operator plays an important role for query evaluation in relational databases its extension to fuzzy databases raises the question of the intended interpretation of the intermediary degrees attached to the items in the fuzzy relations this note points out that the fuzzy quotient operator should be defined in slightly different ways depending on the possible interpretations of the degrees levels of satisfaction of a gradual property levels of importance of a required property uncertainty pertaining to the membership of an element to a subset

production control of a manufacturing system with multiple machine states the production control of a single product manufacturing system with arbitrary number of machine states failure modes is discussed the objective is to find a production policy that would meet the demand for the product with minimum average inventory or backlog cost the optimal production policy has a special structure and is called a hedging point policy if the hedging points are known the optimal production rate is readily specified assuming a set of tentative hedging points the simple structure of the optimal policy is utilized to find the steady state probability distribution of the surplus inventory or backlog once this function is determined the average surplus cost is easily calculated in terms of the values of the hedging points the average cost is then minimized to find the optimum hedging points

social choice axioms for fuzzy set aggregation the problem of aggregating n fuzzy sets f1 f2 fn on a set is viewed as one of merging the opinions of n individuals e g experts that rate objects belonging to this approach contrasts with the pure set theoretic point of view and leads to interpreting already known axioms underlying fuzzy connectives in a way different from that of multiple criteria aggregation various natural properties of a voting procedure including the ones proposed by arrow are expressed in the fuzzy set setting a number of conditions limiting the choice of fuzzy set operations are proposed and classified according to whether they are imperative mainly technical or facultative families of solutions are obtained that include those proposed in earlier works the case of non homogeneous groups is briefly examined lastly the application of the voting paradigm to the management of antagonistic local decision rules in knowledge based systems is outlined

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

fuzzy set based methods in instance based reasoning a formal framework of instance based prediction is presented in which the generalization beyond experience is founded on the concepts of similarity and possibility the underlying extrapolation principle is formalized within the framework of fuzzy rules thus instance based reasoning can be realized as fuzzy set based approximate reasoning more precisely our model makes use of so called possibility rules these rules establish a relation between the concepts of similarity and possibility which takes the uncertain character of similarity based inference into account inductive inference is possibilistic in the sense that predictions take the form of possibility distributions on the set of outcomes rather than precise deterministic estimations the basic model is extended by means of fuzzy set based modeling techniques this extension provides the basis for incorporating domain specific expert knowledge thus our approach favors a view of instance based reasoning according to which the user interacts closely with the system

a weighted max min model for fuzzy goal programming abstract after narasimhan s pioneering study of applying fuzzy set theory to goal programming in 1980 many achievements in the field have been recorded most of them followed the max min approach however when objectives have different levels of importance only the weighted additive model of tiwari et al seems to be applicable however the shortcoming of the additive model is that the summation of quasiconcave functions may not be quasiconcave this study proposes a novel weighted max min model for fuzzy goal programming fgp and for fuzzy multiple objective decision making the proposed model adapts well to even the most complicated membership functions numerical examples demonstrate that the proposed model can be effectively incorporated with other approaches to fgp and is superior to the weighted additive approach

penalizing strategic preference manipulation in multi agent decision making we consider the problem of group decision making where the selection process is based upon a group preference function obtained by an aggregation of the participating agents individual preference functions we describe some methods for formulating the group preference from the individual preference functions we note the possibility of the individual agents strategically manipulating the information they provide so as to further their own goal of getting their most preferred alternative selected by the group with this in mind we suggest ways of modifying the formulation of the group decision functions to discourage strategic manipulation by the participating agents

towards a general theory of action and time abstract a formalism for reasoning about actions is proposed that is based on a temporal logic it allows a much wider range of actions to be described than with previous approaches such as the situation calculus this formalism is then used to characterize the different types of events processes actions and properties that can be described in simple english sentences in addressing this problem we consider actions that involve non activity as well as actions that can only be defined in terms of the beliefs and intentions of the actors finally a framework for planning in a dynamic world with external events and multiple agents is suggested

characterization of weighted maximum and some related operations abstract the complete characterization of weighted maximum and minimum operations as well as the ordered weighted maximum and minimum is established the results are obtained via stability properties of the operations these properties are expressed by functional equations solutions of these equations correspond to the studied operations

importance weighting and andness control in de morgan dual power means and owa operators abstract importance weighted aggregation plays a central role in utilization of information resources for information retrieval and fusion pattern and object recognition decision making etc a class of aggregation operators of particular interest is formed by the aggregation operators between the min minimum and the max maximum the so called averaging operators two key issues in the choice of such an operator for a given application are the kind of importance weighting and the andness minness of the operator two main kinds of importance weighting for such operators namely multiplicative and implicative are proposed and discussed the purpose of this paper is to facilitate the choice and application of such operators through providing a systematization of their classes according to their behavior and equipping some classical averaging operators namely the power means and the owa operators with importance weighting schemes and direct parametric andness control for both kinds of importance weighting for increased efficacy and for symmetric behavior by andness and orness 1 andness at the same degree of both measures the two classes of averaging operators are applied in a de morgan dual form the main issue in the choice of underlying the classical averaging operator appears to be the computational cost of its application

flexible queries in relational databases the example of the division operator abstract allowing for flexible queries enables database users to express preferences inside minimal requirements and if necessary priorities inside compound queries in other words clear cut properties can be refined by ordering the interpretations compatible with them according to user s preferences often the representation of these preferences can be viewed as modelling linguistic like terms in requests in this paper the theoretical issues raised by the introduction of flexible queries are studied in the case of the division operator in the framework of fuzzy sets and possibility theory the notion of division is well known in the context of regular relations and the extension of this operation to fuzzy relations induced by the flexible queries is investigated several types of extended divisions can be envisaged depending on the meaning of the grades attached to the tuples of the fuzzy relations degree of fulfillment of gradual properties level of importance of components in a query or uncertainty pervading data we focus on the first two meanings which are associated with different multiple valued logic implications and we examine their properties and their expression in the framework of an extended sql like language where no specific construct for the division is available

an application of aggregation procedures to the definition of measures of similarity between fuzzy sets abstract in this paper we examine four classes of procedures of aggregation of local valued relations with weights these procedures are based on the use of a valued implication or coimplication we highlight the existence of a hierarchy among those procedures and show that some of them preserve the transitivity of local relations these results are applied for the definition of a measure of similarity between fuzzy sets

an improved algebraic multigrid method for solving maxwell s equations we propose two improvements to the reitzinger and schoberl algebraic multigrid amg method for solving the eddy current approximations to maxwell s equations the main focus in the reitzinger schoberl method is to maintain null space properties of the weak nabla times nabla times operator on coarse grids while these null space properties are critical they are not enough to guarantee h independent convergence of the overall multigrid method we illustrate how the reitzinger schoberl amg method loses h independence due to the somewhat limited approximation property of the grid transfer operators we present two improvements to these operators that not only maintain the important null space properties on coarse grids but also yield significantly improved multigrid convergence rates the first improvement is based on smoothing the reitzinger schoberl grid transfer operators the second improvement is obtained by using higher order nodal interpolation to derive the corresponding amg interpolation operators while not completely h independent the resulting amg cg method demonstrates improved convergence behavior while maintaining low operator complexity

upper and lower images of a fuzzy set induced by a fuzzy relation applications to fuzzy inference and diagnosis in fuzzy set theory the image of a fuzzy set induced by a fuzzy relation is usually obtained by a sup t norm composition this corresponds to the upper image which gathers the elements in relation with at least one element of the fuzzy set however the dual point of view leading to the definition of the lower image as the fuzzy set of elements in relation with all the elements of the fuzzy set whose image is computed is not often considered fuzzy sets and fuzzy relations depending on the situations can be interpreted either in a conjunctive manner or as subsets of mutually exclusive possible values for variables whose precise values are ill known disjunctive view the applications of upper and lower images are investigated in both interpretations the generalized modus ponens used in fuzzy rule based systems corresponds to the disjunctive view the interest of upper and lower images is also emphasized for diagnosis problems where the conjunctive interpretation is encountered

on β precision aggregation in this paper we propose an extension of the current fuzzy connectives to precision aggregators which include a certain tolerance towards noise and measurement errors in the values of the aggregated criteria when their cardinality is large to do this we have set our extension proposal in the framework of yager s mam mom and mica operators and study the properties of the new extended operators a simple example illustrates the practical use of the extended aggregators