optimization of type 2 fuzzy systems based on bio inspired methods a concise review a review of the optimization methods used in the design of type 2 fuzzy systems which are relatively novel models of imprecision has been considered in this work the fundamental focus of the work has been based on the basic reasons of the need for optimizing type 2 fuzzy systems for different areas of application recently bio inspired methods have emerged as powerful optimization algorithms for solving complex problems in the case of designing type 2 fuzzy systems for particular applications the use of bio inspired optimization methods have helped in the complex task of finding the appropriate parameter values and structure of the fuzzy systems in this review we consider the application of genetic algorithms particle swarm optimization and ant colony optimization as three different paradigms that help in the design of optimal type 2 fuzzy systems we also provide a comparison of the different optimization methods for the case of designing type 2 fuzzy systems

comprehensive analysis of a new fuzzy rule interpolation method the first published result in fuzzy rule interpolation was the spl alpha cut based fuzzy rule interpolation termed as kh fuzzy rule interpolation originally devoted for complexity reduction a modified version of the kh approach has been presented by yam et al 1999 which eliminates the subnormality problem while at the same time intending to maintain the advantageous computational properties of the original method this paper presents a comprehensive analysis of the new method which includes detailed comparison with the original kh fuzzy rule interpolation method concerning the explicit functions of the methods preservation of piecewise linearity and stability the fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques all these comparisons shows that the new method preserves the advantageous properties of the kh method and alleviates its most significant disadvantage the problem of subnormality

methods for comparison of coalition influence on games in characteristic function form and their interrelationships abstract this paper extends two existent methods called the blockability relation and the viability relation for simple games to compare influence of coalitions to those for games in characteristic function form and shows that the newly defined relations satisfy transitivity and completeness it is shown in this paper that for every game in characteristic function form the blockability relation and the viability relation have a complementary interrelationship

complementary cooperation minimal winning coalitions and power indices we introduce a new simple game which is referred to as the complementary weighted multiple majority game c wmmg for short c wmmg models a basic cooperation rule the complementary cooperation rule and can be taken as a sister model of the famous weighted majority game wmg for short in c wmmg each player is characterized by a nonnegative vector with a fixed dimension and players in the same coalition cooperate by producing a characteristic vector for this coalition each dimension of this vector equals the maximum of the corresponding dimensions of its members the value of a coalition is 1 if and only if the sum of its characteristic vector is larger than that of its complementary coalition in which case the coalition is called winning otherwise the coalitional value is 0 in this paper we concentrate on the two dimensional c wmmg an interesting property of this case is that there are at most n 1 minimal winning coalitions mwcs for short and they can be enumerated in time o nlogn where n is the number of players this property guarantees that the two dimensional c wmmg is more handleable than wmg in particular we prove that the main power indices i e the shapley shubik index the penrose banzhaf index the holler packel index and the deegan packel index are all polynomially computable to make a comparison with wmg we know that it may have exponentially many mwcs and none of the four power indices is polynomially computable unless p np still for the two dimensional case we show that local monotonicity holds for all of the four power indices in wmg this property is possessed by the shapley shubik index and the penrose banzhaf index but not by the holler packel index or the deegan packel index since our model fits very well the cooperation and competition in team sports we hope that it can be potentially applied in measuring the values of players in team sports say help people give more objective ranking of nba players and select mvps and consequently bring new insights into contest theory and the more general field of sports economics it may also provide some interesting enlightenments into the design of non additive voting mechanisms last but not least the threshold version of c wmmg is a generalization of wmg and natural variants of it are closely related with the famous airport game and the stable marriage roommates problem

fuzzy interpolative reasoning via scale and move transformations interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule based systems possible this paper presents an interpolative reasoning method by means of scale and move transformations it can be used to interpolate fuzzy rules involving complex polygon gaussian or other bell shaped fuzzy membership functions the method works by first constructing a new inference rule via manipulating two given adjacent rules and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions this method has three advantages thanks to the proposed transformations 1 it can handle interpolation of multiple antecedent variables with simple computation 2 it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets and 3 it suggests a variety of definitions for representative values providing a degree of freedom to meet different requirements comparative experimental studies are provided to demonstrate the potential of this method

np completeness for calculating power indices of weighted majority games in this paper we prove that both problems for calculating the banzhaf power index and the shapley shubik power index for weighted majority games are np complete

a clustering procedure for reducing the number of representative solutions in the pareto front of multiobjective optimization problems abstract in many multiobjective optimization problems the pareto fronts and sets contain a large number of solutions and this makes it difficult for the decision maker to identify the preferred ones a possible way to alleviate this difficulty is to present to the decision maker a subset of a small number of solutions representatives of the pareto front characteristics in this paper a two steps procedure is presented aimed at identifying a limited number of representative solutions to be presented to the decision maker pareto front solutions are first clustered into families which are then synthetically represented by a head of the family solution level diagrams are then used to represent analyse and interpret the pareto front reduced to its head of the family solutions the procedure is applied to a reliability allocation case study of literature in decision making contexts both without or with explicit preferences by the decision maker on the objectives to be optimized

computation of several power indices by generating functions abstract in this paper we propose methods to compute the deegan packel the public good and the shift power indices by generating functions for the particular case of weighted voting games furthermore we define a new power index which combines the ideas of the shift and the deegan packel power indices and also propose a method to compute it with generating functions we conclude by some comments about the complexity to compute these power indices

the construction of the sh lie algebra of closed bosonic strings we present a construction of the closed string algebra in terms of gaussian processes and crossed products also we give a purely functional analytical prove of the sh lie structure

the golden number and fibonacci sequences in the design of voting structures abstract some distinguished types of voters as vetoes passers or nulls as well as some others play a significant role in voting systems because they are either the most powerful or the least powerful voters in the game independently of the measure used to evaluate power in this paper we are concerned with the design of voting systems with at least one type of these extreme voters and with few types of equivalent voters with this purpose in mind we enumerate these special classes of games and find out that its number always follows a fibonacci sequence with smooth polynomial variations as a consequence we find several families of games with the same asymptotic exponential behavior except for a multiplicative factor which is the golden number or its square from a more general point of view our studies are related with the design of voting structures with a predetermined importance ranking

pragmatical adaptive synchronization new fuzzy model of two different and complex chaotic systems by new adaptive control abstract in this paper 1 a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and 2 a new adaptive approach and a new control lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors by using this new model the numbers of fuzzy rules of chaotic systems can be reduced from 2 n to 2 n and only 2 subsystems are needed where n is the number of nonlinear terms the fuzzy systems become much simpler in addition through the new fuzzy model the new fuzzy systems are much simpler than t s fuzzy systems when nonlinear systems are complicated and can be used to any other kind of application in fuzzy logic control or fuzzy modeling mathieu van der pol system which is called m v system in this paper and quantum cellular neural networks nanosystem which is called q cnn system in this paper are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control lyapunov function the t s fuzzy modeling and traditional adaptive control are also given in appendix b t s fuzzy model of chaotic systems appendix c traditional adaptive method for comparison

size of obdd representation of 2 level redundancies functions abstract we consider an explicit boolean function depending on n i 1 j variables encoding 2 level cascade redundancies in critical systems we establish lower and upper bounds on the size of its obdd representation the exact lower bound of this function is comprised between 2 min i 2 1ptj 2 and o 2 min i 1ptj the upper bound is 2 i 1ptj 2 log 2 i we further show that when one of the parameters i or j is constant this function admits obdds whose size is polynomial in other parameter the latter result is constructive and we show variable orderings that witness this polynomial size

properties of ladder tournaments abstract ladder tournaments use work trials to screen workers for positions in organizations despite being common in many industries their properties remain poorly understood especially in organizations characterized by complex complementarities and externalities in their production process in this study we formalize the ranking rule generated by a ladder tournament and derive measures of relative performance that can be used to compare workers when their true inputs cannot be observed we show that this rule is reflexive but not generally transitive unless the organization has fewer than three layers of hierarchy or is complete it follows that complete organizations have an embedded merit based hierarchical structure we also study the relationship between a worker s tournament rank and his utility or usefulness as measured by the frequency with which he plays a pivotal role we show that a worker s likelihood of being pivotal is a weakly increasing function of his rank this finding implies that in complete organizations ladder tournaments discriminate more effectively between workers than do mechanisms based on pivotability or marginal productivity

approximate reasoning algorithm of interval valued fuzzy sets based on least square method in this paper we develop a new method for bidirectional approximate reasoning of interval valued fuzzy sets by employing least squares method and investigate some properties for our proposed approximate reasoning method furthermore we use four numerical examples to illustrate our proposed method reasonable

fuzzy interpolative reasoning for sparse fuzzy rule based systems based on bm alpha cuts and transformations techniques in sparse fuzzy rule based systems the fuzzy rule bases are usually incomplete in this situation the system may not properly perform fuzzy reasoning to get reasonable consequences in order to overcome the drawback of sparse fuzzy rule based systems there is an increasing demand to develop fuzzy interpolative reasoning techniques in sparse fuzzy rule based systems in this paper we present a new fuzzy interpolative reasoning method via cutting and transformation techniques for sparse fuzzy rule based systems it can produce more reasonable results than the existing methods the proposed method provides a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule based systems

fuzzy interpolation and extrapolation a practical approach fuzzy interpolation does not only help to reduce the complexity of fuzzy models but also makes inference in sparse rule based systems possible it has been successfully applied to systems control but limited work exists for its applications to tasks like prediction and classification almost all fuzzy interpolation techniques in the literature make strong assumptions that there are two closest adjacent rules available to the observation and that such rules must flank the observation for each attribute also some interpolation approaches cannot handle fuzzy sets whose membership functions involve vertical slopes to avoid such limitations and develop a more practical approach this paper extends the work of huang and shen the result enables both interpolation and extrapolation which involve multiple fuzzy rules with each rule consisting of multiple antecedents two realistic applications namely truck backer upper control and computer activity prediction are provided in this paper to demonstrate the utility of the extended approach experiment based comparisons to the most commonly used mamdani fuzzy reasoning mechanism and to other existing fuzzy interpolation techniques are given to show the significance and potential of this research

a generalized concept for fuzzy rule interpolation the concept of fuzzy rule interpolation in sparse rule bases was introduced in 1993 it has become a widely researched topic in recent years because of its unique merits in the topic of fuzzy rule base complexity reduction the first implemented technique of fuzzy rule interpolation was termed as spl alpha cut distance based fuzzy rule base interpolation despite its advantageous properties in various approximation aspects and in complexity reduction it was shown that it has some essential deficiencies for instance it does not always result in immediately interpretable fuzzy membership functions this fact inspired researchers to develop various kinds of fuzzy rule interpolation techniques in order to alleviate these deficiencies this paper is an attempt into this direction it proposes an interpolation methodology whose key idea is based on the interpolation of relations instead of interpolating spl alpha cut distances and which offers a way to derive a family of interpolation methods capable of eliminating some typical deficiencies of fuzzy rule interpolation techniques the proposed concept of interpolating relations is elaborated here using fuzzy and semantic relations this paper presents numerical examples in comparison with former approaches to show the effectiveness of the proposed interpolation methodology

fuzzy interpolative reasoning for sparse fuzzy rule based systems based on the areas of fuzzy sets fuzzy interpolative reasoning is an inference technique for dealing with the sparse rules problem in sparse fuzzy rule based systems in this paper we present a new fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on the areas of fuzzy sets the proposed method uses the weighted average method to infer the fuzzy interpolative reasoning results and has the following advantages 1 it holds the normality and the convexity of the fuzzy interpolative reasoning result 2 it can deal with fuzzy interpolative reasoning with complicated membership functions 3 it can deal with fuzzy interpolative reasoning when the fuzzy sets of the antecedents and the consequents of the fuzzy rules have different kinds of membership functions 4 it can handle fuzzy interpolative reasoning with multiple antecedent variables 5 it can handle fuzzy interpolative reasoning with multiple fuzzy rules and 6 it can handle fuzzy interpolative reasoning with logically consistent properties with respect to the ratios of fuzziness we use some examples to compare the fuzzy interpolative reasoning results of the proposed method with those of the existing fuzzy interpolative reasoning methods in terms of the six evaluation indices the experimental results show that the proposed method performs more reasonably than the existing methods the proposed method provides us a useful way to deal with fuzzy interpolative reasoning in sparse fuzzy rule based systems

measures on infinite dimensional grassmann manifolds abstract a 1 parameter family of quasi invariant measures is presented these measures are cylinder measures in graph coordinates their characteristic functions are represented as integrals relative to an infinite product measure this is applied to the problem of determining the support properties of the measures one of the measures can be used to define the unitary structure for the basic representation of the affine extension of the restricted unitary group

achievable hierarchies in voting games with abstention abstract it is well known that he influence relation orders the voters the same way as the classical banzhaf and shapley shubik indices do when they are extended to the voting games with abstention vga in the class of complete games moreover all hierarchies for the influence relation are achievable in the class of complete vga the aim of this paper is twofold firstly we show that all hierarchies are achievable in a subclass of weighted vga the class of weighted games for which a single weight is assigned to voters secondly we conduct a partial study of achievable hierarchies within the subclass of h complete games that is complete games under stronger versions of influence relation

weighted multiple majority games with unions generating functions and applications to the european union abstract an a priori system of unions or coalition structure is a partition of a finite set of players into disjoint coalitions which have made a prior commitment to cooperate in playing a game this paper provides ready to apply procedures based on generating functions that are easily implementable to compute coalitional power indices in weighted multiple majority games as an application of the proposed procedures we calculate and compare coalitional power indices under the decision rules prescribed by the treaty of nice and the new rules proposed by the council of the european union

cooperation through social influence abstract we consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents we model this scenario by an influence game a cooperative simple game in which a team or coalition of players succeeds if it is able to convince enough agents to participate in the task to vote in favor of a decision we take the linear threshold model as the influence model we show first the expressiveness of influence games showing that they capture the class of simple games then we characterize the computational complexity of various problems on influence games including measures length and width values shapley shubik and banzhaf and properties of teams and players finally we analyze those problems for some particular extremal cases with respect to the propagation of influence showing tighter complexity characterizations

binary decision diagrams for generating and storing non dominated project portfolios with interval valued project scores abstract when selecting a portfolio i e set of projects the projects are often evaluated by additive scores with respect to multiple attributes uncertainty or incomplete information about projects scores can be modeled with plausible lower and upper bounds on the projects scores it is recommended to select a non dominated nd portfolio that is a portfolio such that it is not possible to select another portfolio which has i at least as high value with respect to every attribute for all plausible scores ii and has strictly higher value with respect to at least one attribute for some plausible scores in this paper we lay a foundation on computing nd project portfolios we also present an algorithm based on binary decision diagrams bdds for generating the nd portfolios we show that our algorithms can provide significant computational advantages over previous algorithms we also explore how bdds can be used for storing large numbers of nd portfolios and how such bdds can be efficiently generated

interpolative reasoning with insufficient evidence in sparse fuzzy rule bases abstract rule based fuzzy approximate reasoning uses various techniques of modified modus ponens the observation is in most cases not identical with any of the antecedents in the rules however a conclusion still can be computed by using some combination of all consequents where an overlapping of observation and antecedent is present if the rule base is sparse i e it contains insufficient information on the total state space it might occur that an observation has absolutely no overlapping with any of the antecedents and so not even a single rule is fired i e no conclusion can be computed on the basis of modus ponens in such a case interpolative reasoning in the strict sense can be applied some kind of weighted average of the flanking rules is calculated this technique can be extended to a form of extrapolation when the observation is not flanked from both sides linear interpolation and extrapolation is presented and then the idea is extended to arbitrary approximation

weighted fuzzy interpolative reasoning for sparse fuzzy rule based systems based on piecewise fuzzy entropies of fuzzy sets in this paper we propose a new method for weighted fuzzy interpolative reasoning in sparse fuzzy rule based systems based on piecewise fuzzy entropies of fuzzy sets first the proposed method uses the representative values of antecedent fuzzy sets the representative values of observation fuzzy sets and the representative values of consequence fuzzy sets of fuzzy rules to get the characteristic points of the fuzzy interpolative result represented by a fuzzy set then it calculates the piecewise fuzzy entropies between any two characteristic points of the antecedent fuzzy sets the piecewise fuzzy entropies between any two characteristic points of the observation fuzzy sets and the piecewise fuzzy entropies between any two characteristic points of the consequence fuzzy sets of the fuzzy rules respectively then it calculates the weights of the antecedent fuzzy sets of each fuzzy rule respectively and calculates the weight of each fuzzy rule then it calculates the piecewise fuzzy entropies between any two characteristic points of the fuzzy interpolative result finally it uses the secant method to calculate the degree of membership of each obtained characteristic point of the fuzzy interpolative result the experimental results show that the proposed method outperforms the existing methods for dealing with the multivariate regression problems the mackey glass chaotic time series prediction problem and the time series prediction problems

the c algebra of bosonic strings we give a rigorous definition of witten sc string algebra to this end we present a new construction ofc algebras associated to special geometric situations kahler foliations and generalize this later construction to the string case through this we get a natural geometrical interpretation of the string of semi infinite forms as well as the fermionic algebra structure using the non commutative geometric concepts for investigating the string algebra we get a natural fredholm module representation of dimension 26

an interval type 2 fuzzy model of computing with words as a methodology computing with words allows the use of words instead of numbers or symbols in the process of computing and reasoning and thus conforms more to humans inference when it is used to describe real world problems motivated by zadeh s paradigm of computing with words the literature has proposed a kind of type 1 fuzzy automata as a formal model of computing with words which takes type 1 fuzzy subsets of symbols as input however type 1 fuzzy representation provides a limited platform for approximating the meaning of words since it is not able to capture linguistic uncertainty in this paper we develop a formal interval type 2 fuzzy model of computing with words by generalizing the existing type 1 fuzzy sets based model to an interval type 2 fuzzy environment concretely we take interval type 2 fuzzy automata i e interval type 2 fuzzy finite automata and interval type 2 fuzzy pushdown automata which combine interval type 2 fuzzy set theory and automaton theory as a computational model of computing with words furthermore we develop the extension principles to extend from computing with values to computing with words and show that computing with words can be implemented with computing with values in the interval type 2 fuzzy setting at an extra computational cost

string quantization on group manifolds and the holomorphic geometry of diffs1 s1 the recent results by bowick and rajeev on the relation of the geometry of diffs1 s1 and string quantization in d are extended to a string moving on a group manifold a new derivation of the curvature formula 26 12m3 1 6m n m for the canonical holomorphic line bundle over diffs1 s1 is given which clarifies the relation of that bundle with the complex line bundles over infinite dimensional grassmannians studied by pressley and segal

reasoning conditions on ko czy s interpolative reasoning method in sparse fuzzy rule bases abstract in our pre work the two sufficient and necessary conditions have been given on koczy s interpolative reasoning method in sparse fuzzy rule bases to guarantee that the reasoning consequence is of triangular type if the fuzzy rules and an observation are defined by triangular type membership functions however the two conditions are too strong to use the reasoning method on practical applications in this paper we analyze the properties of the reasoning method in detail and give several applicable sufficient conditions on it in order to make the reasoning consequence always a normal and convex fuzzy set

note the complexity of power index comparison abstract we study the complexity of the following problem given two weighted voting games g and g that each contain a player p in which of these games is p s power index value higher we study this problem with respect to both the shapley shubik power index and the banzhaf power index our main result is that for both of these power indices the problem is complete for probabilistic polynomial time i e is pp complete we apply our results to partially resolve some recently proposed problems regarding the complexity of weighted voting games we also study the complexity of the raw shapley shubik power index deng and papadimitriou showed that the raw shapley shubik power index is p metric complete we strengthen this by showing that the raw shapley shubik power index is many one complete for p and our strengthening cannot possibly be further improved to parsimonious completeness since we observe that in contrast with the raw banzhaf power index the raw shapley shubik power index is not p parsimonious complete

size of ordered binary decision diagrams representing threshold functions an ordered binary decision diagram obdd is a graph representation of a boolean function in this paper the size of ordered binary decision diagrams representing threshold functions is discussed we consider two cases the case when a variable ordering is given and the case when it is adaptively chosen we show 1 o 2n2 upper bound for both cases 2 2n2 lower bound for the former case and 3 n2 n2 lower bound for the latter case we also show some relations between the variable ordering and the size of obdds representing threshold functions

on the complexity of cooperative solution concepts we study from a complexity theoretic standpoint the various solution concepts arising in cooperative game theory we use as a vehicle for this study a game in which the players are nodes of a graph with weights on the edges and the value of a coalition is determined by the total weight of the edges contained in it the shapley value is always easy to compute the core is easy to characterize when the game is convex and is intractable np complete otherwise similar results are shown for the kernel the nucleolus the e core and the bargaining set as for the von neumann morgenstern solution we point out that its existence may not even be decidable many of these results generalize to the case in which the game is presented by a hypergraph with edges of size k 2

compact representation of near optimal integer programming solutions it is often useful in practice to explore near optimal solutions of an integer programming problem we show how all solutions within a given tolerance of the optimal value can be efficiently and compactly represented in a weighted decision diagram the structure of the diagram facilitates rapid processing of a wide range of queries about the near optimal solution space as well as reoptimization after changes in the objective function we also exploit the paradoxical fact that the diagram can be reduced in size if it is allowed to represent additional solutions we show that a sound reduction operation applied repeatedly yields the smallest such diagram that is suitable for postoptimality analysis and one that is typically far smaller than a tree that represents the same set of near optimal solutions we conclude that postoptimality analysis based on sound reduced diagrams has the potential to extract significantly more useful information from an integer programming model than was previously feasible

interpolation with function space representation of membership functions this paper generalizes a previous cartesian approach for interpolating fuzzy rules comprised of membership functions with finite number of characteristic points instead of representing membership functions as points in cartesian spaces they now become elements in the space of square integrable function interpolation is thus conducted between the antecedent and consequent function spaces the generalized representation allows an extended class of membership functions satisfying two monotonicity conditions to be accommodated in the interpolation process they include the popular bell shaped membership functions which were not possible before with the cartesian representation the work also extends the similarity triangle based interpolation technique from the previous cartesian representation to the new representation ensuing issues on computational complexity and nonunique conclusion are discussed other concepts such as spanning set and extensibility functions are also presented under the generalized framework examples to illustrate the extended approach and to compare with the cartesian approach are given

on the use of binary decision diagrams for solving problems on simple games abstract simple games are yes no cooperative games which arise in many practical applications recently we have used reduced ordered binary decision diagrams and quasi reduced ordered binary decision diagrams abbreviated as robdd s and qobdd s respectively for the representation of simple games and for the computation of some power indices in the present paper we continue this work we show how further important computational problems on simple games can be solved using qobdd s viz the identification of some key players the computation of the desirability relation on individuals the test whether a simple game is proper and strong respectively and the computation of qobdd representations for the sets of all minimal winning coalitions all shift minimal winning coalitions and all blocking coalitions respectively applications of these solutions include the computation of recent power indices based on shift minimal winning coalitions and the test for linear separability of a directed simple game

the neighborhood role in the linear threshold rank on social networks abstract centrality and influence spread are two of the most studied concepts in social network analysis several centrality measures most of them based on topological criteria have been proposed and studied in recent years new centrality measures have been defined inspired by the two main influence spread models namely the independent cascade model ic model and the linear threshold model lt model the linear threshold rank ltr is defined as the total number of influenced nodes when the initial activation set is formed by a node and its immediate neighbors it has been shown that ltr allows to rank influential actors in a more distinguishable way than other measures like the pagerank the katz centrality or the independent cascade rank in this paper we propose a generalized ltr measure that explore the sensitivity of the original ltr with respect to the distance of the neighbors included in the initial activation set we appraise the viability of the approach through different case studies our results show that by using neighbors at larger distance we obtain rankings that distinguish better the influential actors however the best differentiating ranks correspond to medium distances our experiments also show that the rankings obtained for the different levels of neighborhood are not highly correlated which validates the measure generalization

finding the optimal variable ordering for binary decision diagrams the ordered binary decision diagram is a canonical representation for boolean functions presented by r e bryant 1985 as a compact representation for a broad class of interesting functions derived from circuits however the size of the diagram is very sensitive to the choice of ordering on the variables hence for some applications such as differential cascode voltage switch dcvs trees it becomes extremely important to find the ordering leading to the most compact representation an algorithm for this problem with time complexity o n sup 2 3 sup n is presented this represents an improvement over the previous best algorithm

adaptive fuzzy interpolation based on general representative values of polygonal fuzzy sets and the shift and modification techniques abstract adaptive fuzzy interpolative reasoning afir can overcome the limitation of the conventional fuzzy interpolation techniques because it can find and solve the contradictions of the fuzzy interpolative reasoning fir results in order to ensure that the derived fir results are consistent in this paper we propose a new afir method to solve the inconsistencies occurring after the fir process the proposed afir method is based on the general representative values of polygonal fuzzy sets and the proposed shift and modification techniques the proposed afir method includes a new contradictions solving method to get a higher similarity degree between the afir results in order to demonstrate the higher consistency of the afir results obtained by the proposed afir method we apply the proposed afir method to deal with the diarrheal disease prediction problem the experimental results show that the proposed afir method outperforms yang and shen s afir method 2011 and cheng et al s afir method 2016 in terms of the degree of similarity between the afir results

weighted fuzzy interpolative reasoning systems based on interval type 2 fuzzy sets abstract in this paper we present a weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on interval type 2 fuzzy sets we also apply the proposed weighted fuzzy interpolative reasoning method to deal with the truck backer upper control problem the proposed method satisfies the seven evaluation indices for fuzzy interpolative reasoning the experimental results show that the proposed method outperforms the existing methods it provides us with a useful way for dealing with fuzzy interpolative reasoning in sparse fuzzy rule based systems

on the complexity of vlsi implementations and graph representations of boolean functions with application to integer multiplication lower bound results on boolean function complexity under two different models are discussed the first is an abstraction of tradeoffs between chip area and speed in very large scale integrated vlsi circuits the second is the ordered binary decision diagram obdd representation used as a data structure for symbolically representing and manipulating boolean functions the lower bounds demonstrate the fundamental limitations of vlsi as an implementation medium and that of the obdd as a data structure it is shown that the same technique used to prove that any vlsi implementation of a single output boolean function has area time complexity at sup 2 omega n sup 2 also proves that any obdd representation of the function has omega c sup n vertices for some c 1 but that the converse is not true an integer multiplier for word size n with outputs numbered 0 least significant through 2n 1 most significant is described for the boolean function representing either output i 1 or output 2n i 1 where 1

fuzzy interpolative reasoning based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules in this paper we propose a new fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules first the proposed method gets the characteristic points of the observation polygonal fuzzy sets and the characteristic points of the antecedent polygonal fuzzy sets of the fuzzy rules respectively by using the cut operations respectively where 0 1 then it calculates the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set respectively then it calculates the difference between the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set then it calculates the weight of each fuzzy rule based on the obtained differences between the ranking values of the observation polygonal fuzzy sets and the ranking values of the antecedent polygonal fuzzy sets then based on the obtained characteristic points of the observation polygonal fuzzy sets the obtained characteristic points of the antecedent polygonal fuzzy sets and the obtained weights of the fuzzy rules it gets the characteristic points of the fuzzy interpolative reasoning result represented by a polygonal fuzzy set the experimental results show that the proposed method can overcome the drawbacks of the existing methods for fuzzy interpolative reasoning in sparse fuzzy rule based systems

fuzzy interpolative reasoning based on the ratio of fuzziness of rough fuzzy sets in this paper we propose a method to construct a polygonal rough fuzzy set from a set of polygonal fuzzy sets representing the aggregation of multiple experts opinions and propose a new fuzzy interpolative reasoning method for sparse fuzzy rule based systems based on the ratio of fuzziness of the constructed polygonal rough fuzzy sets where the values of the antecedent variables and the consequence variable appearing in the fuzzy rules are represented by the constructed polygonal rough fuzzy sets the proposed fuzzy interpolative reasoning method can overcome the drawbacks of the existing method due to the fact that it can deal with fuzzy interpolative reasoning using polygonal rough fuzzy sets and it gets more reasonable fuzzy interpolative reasoning results than the existing method

on the dimension of simple monotonic games we show that the following problem is np hard and hence computationally intractable given d weighted majority games decide whether the dimension of their intersection exactly equals d our result indicates that the dimension of simple monotonic games is a combinatorially complicated concept

power indices of simple games and vector weighted majority games by means of binary decision diagrams abstract a simple game is a pair consisting of a finite set n of players and a set w 2 n of winning coalitions vector weighted majority games v wmg are a special case of simple games in which an integer vector weight can be assigned to each player and there is a quota which a coalition has to achieve in order to win binary decision diagrams bdds are used as compact representations for boolean functions and sets of subsets this paper shows how a quasi reduced and ordered bdd qobdd of the winning coalitions of a v wmg can be build how one can compute the minimal winning coalitions and how one can easily compute the banzhaf shapley shubik holler packel and deegan packel indices of the players e g in case of weighted majority games it is shown that the banzhaf and holler packel indices of all players can be computed in expected time o nq and in general the banzhaf indices can be computed in time linear in the size of the qobdd representation of the winning coalitions other running times are proven as well the algorithms were tested on some real world games e g the international monetary fund and the eu treaty of nice

weighted fuzzy interpolative reasoning based on weighted increment transformation and weighted ratio transformation techniques in this paper we present a new weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems the proposed method uses weighted increment transformation and weighted ratio transformation techniques to handle weighted fuzzy interpolative reasoning in sparse fuzzy rule based systems it allows each variable that appears in the antecedent parts of fuzzy rules to associate with a weight between zero and one moreover we also propose an algorithm that automatically tunes the optimal weights of the antecedent variables appearing in the antecedent parts of fuzzy rules we also apply the proposed weighted fuzzy interpolative reasoning method to handle the truck backer upper control problem the proposed weighted fuzzy interpolative reasoning method performs better than the ones obtained by the traditional fuzzy inference system 2000 huang and shen s method 2008 and chen and ko s method 2008 the proposed method provides us with a useful way to deal with weighted fuzzy interpolative reasoning in sparse fuzzy rule based systems

on the obdd representation of general boolean functions the behavior of ordered binary decision diagrams obdd for general boolean functions is studied a tight upper bound of 2 sup n n 2 epsilon for the worst case obdd size is derived although the size of an obdd is dependent on the ordering of decision variables it is shown that almost all functions are not sensitive to variable ordering

fuzzy rule interpolation for multidimensional input spaces with applications a case study fuzzy rule based systems have been very popular in many engineering applications however when generating fuzzy rules from the available information this may result in a sparse fuzzy rule base fuzzy rule interpolation techniques have been established to solve the problems encountered in processing sparse fuzzy rule bases in most engineering applications the use of more than one input variable is common however the majority of the fuzzy rule interpolation techniques only present detailed analysis to one input variable case this paper investigates characteristics of two selected fuzzy rule interpolation techniques for multidimensional input spaces and proposes an improved fuzzy rule interpolation technique to handle multidimensional input spaces the three methods are compared by means of application examples in the field of petroleum engineering and mineral processing the results show that the proposed fuzzy rule interpolation technique for multidimensional input spaces can be used in engineering applications

weighted fuzzy rule interpolation based on ga based weight learning techniques in this paper we propose a weighted fuzzy interpolative reasoning method for sparse fuzzy rule based systems it is based on a genetic algorithm ga based weight learning technique the proposed method can deal with fuzzy rule interpolation with weighted antecedent variables it also can deal with fuzzy rule interpolation based on polygonal membership functions and bell shaped membership functions we also propose a ga based weight learning algorithm to automatically learn the optimal weights of the antecedent variables of the fuzzy rules furthermore we apply the proposed weighted fuzzy interpolative reasoning method and the proposed ga based weight learning algorithm to deal with the truck backer upper control problem the computer activity prediction problem multivariate regression problems and time series prediction problems based on statistical analysis techniques the experimental results show that the proposed weighted fuzzy interpolative reasoning method by the use of the optimally learned weights that were obtained by the proposed ga based weight learning algorithm has statistically significantly smaller error rates than the existing methods

on the computational complexity of coalitional resource games we study coalitional resource games crgs a variation of qualitative coalitional games qcgs in which each agent is endowed with a set of resources and the ability of a coalition to bring about a set of goals depends on whether they are collectively endowed with the necessary resources we investigate and classify the computational complexity of a number of natural decision problems for crgs over and above those previously investigated for qcgs in general for example we show that the complexity of determining whether conflict is inevitable between two coalitions with respect to some stated resource bound i e a limit value for every resource is co np complete we then investigate the relationship between crgs and qcgs and in particular the extent to which it is possible to translate between the two models we first characterise the complexity of determining equivalence between crgs and qcgs we then show that it is always possible to translate any given crg into a succinct equivalent qcg and that it is not always possible to translate a qcg into an equivalent crg we establish some necessary and some sufficient conditions for a translation from qcgs to crgs to be possible and show that even where an equivalent crg exists it may have size exponential in the number of goals and agents of its source qcg

a note on the construction of the c algebra of bosonic strings this work continues investigations on the c algebra of bosonic strings started in comm math phys 136 369 1991 there a canonical section of a bundle was used implicitly in order to pass to an algebra of functions in this article an algebra of sections is worked with directly this clarifies the discussion on associativity of the algebra

on the ordinal equivalence of the johnston banzhaf and shapley power indices abstract in this paper we characterize the games in which johnston shapley shubik and penrose banzhaf coleman indices are ordinally equivalent meaning that they rank players in the same way we prove that these three indices are ordinally equivalent in semicomplete simple games which is a newly defined class that contains complete games and includes most of the real world examples of binary voting systems this result constitutes a twofold extension of diffo lambo and moulen s result diffo lambo and moulen 2002 in the sense that ordinal equivalence emerges for three power indices not just for the shapley shubik and penrose banzhaf coleman indices and it holds for a class of games strictly larger than the class of complete games

answering an open problem on t norms for type 2 fuzzy sets abstract this paper proves that a binary operation on 0 1 ensuring that the binary operation is a t norm or is a t conorm is a t norm where and are special convolution operations defined by f g x sup f y g z y z x f g x sup f y g z y z x for any f g map 0 1 0 1 where and are a continuous t norm and a continuous t conorm on 0 1 answering negatively an open problem posed in 8 besides some characteristics of t norm and t conorm are obtained in terms of the binary operations and

adaptive fuzzy interpolation based on ranking values of polygonal fuzzy sets and similarity measures between polygonal fuzzy sets after the fuzzy interpolative reasoning processes if two unequal fuzzy interpolative reasoning results are derived or one derived and another observed for a consequence variable of a fuzzy rule then it is called a contradiction in the fuzzy interpolative reasoning process in recent years some adaptive fuzzy interpolation methods for sparse fuzzy rule based systems have been presented to solve contradictions after fuzzy interpolative reasoning processes in this paper a new adaptive fuzzy interpolation method is proposed for sparse fuzzy rule based systems based on ranking values and similarity measures of polygonal fuzzy sets which can solve contradictions occurred in fuzzy interpolative reasoning processes we also apply the proposed adaptive fuzzy interpolation method to predict the diarrheal disease rates in roadless villages the diarrheal disease prediction problem focuses on the issue to measure how the construction of a new road or railway in a previously roadless area may affect the epidemiology of infectious diseases in northern coastal ecuador the experimental results show that the proposed adaptive fuzzy interpolation method can overcome the drawbacks of the existing methods

fundamentals of simple games from a viewpoint of blockability relations this paper shows some elementary facts on simple games with respect to blockability relations it is verified in this paper that fundamental concepts on simple games as null players dictators veto players and so on can be expressed in terms of blockability relations more some new concepts as conflict free and so on are introduced from the viewpoint of blockability relations into the framework of simple games