induced i l fuzzy topological spaces abstract in this paper we introduce the notion of induced i l fuzzy topological spaces by using the i l valued lower semicontinuous mappings and investigate some of their basic properties in particular we give a necessary and sufficient condition for an i l fuzzy topological space to be induced and prove that this kind of induced space preserves the cartesian product and the n compactness as well

adaptive estimation of fuzzy cognitive maps with proven stability and parameter convergence fuzzy cognitive maps fcms have been introduced by kosko to model complex behavioral systems in various scientific areas one issue that has not been adequately studied so far is the conditions under which they reach a certain equilibrium point after an initial perturbation this is equivalent to studying the existence and uniqueness of solutions for their concept values in this paper we study the existence of solutions of fcms equipped with continuous differentiable sigmoid functions having contractive or at least non expansive properties this is done by using an appropriately defined contraction mapping theorem and the non expansive mapping theorem it is proved that when the weight interconnections fulfill certain conditions the concept values will converge to a unique solution regardless of the exact values of the initial concept values perturbations or in some cases a solution exists that may not necessarily be unique otherwise the existence or the uniqueness of equilibrium cannot be assured based on these results an adaptive weight estimation algorithm is proposed that employs appropriate weight projection criteria to assure that the uniqueness of fcm solution is not compromised in view of these results recently proposed extensions of fcm which are the fuzzy cognitive networks fcn are invoked

a novel risk decision making based on decision theoretic rough sets under hesitant fuzzy information decision theoretic rough sets dtrss play a crucial role in risk decision making problems with respect to the minimum expected risk dtrss deduce the rules of three way decisions considering the new expression of evaluation information with hesitant fuzzy sets hfss we introduce hfss into dtrss and explore their decision mechanisms more specifically we take into account the losses of dtrss with hesitant fuzzy elements and propose a new model of hesitant fuzzy decision theoretic rough sets hfdtrss some properties of the expected losses and their corresponding scores are carefully investigated under the hesitant fuzzy information three way decisions and the associated cost of each object are further derived with the above analysis a novel risk decision making method with the aid of hfdtrss is developed besides the three way decisions with dtrss the method investigates the ranking and resource allocation by utilizing the associated costs of alternatives and multiobjective 0 1 integer programming our study also offers a solution in the aspect of determining losses of dtrs and extends the range of applications

some characterization theorems on induced i l topological spaces in this paper we give some necessary and sufficient conditions for an i l topological space to be a stratified space a weakly induced space or an induced space by interior and closure operators and by the convergence of molecular nets

joint unitary triangularization for gaussian multi user mimo networks the problem of transmitting a common message to multiple users over the gaussian multiple input multiple output broadcast channel is considered where each user is equipped with an arbitrary number of antennas a closed loop scenario is assumed for which a practical capacity approaching scheme is developed by applying judiciously chosen unitary operations at the transmit and receive nodes the channel matrices are triangularized so that the resulting matrices have equal diagonals up to a possible multiplicative scalar factor this along with the utilization of successive interference cancellation reduces the coding and decoding tasks to those of coding and decoding over the single antenna additive white gaussian noise channel over the resulting effective channel any off the shelf code may be used for the two user case it was recently shown that such joint unitary triangularization is always possible in this paper it is shown that for more than two users it is necessary to carry out the unitary linear processing jointly over multiple channel uses i e space time processing is employed it is further shown that exact triangularization where all resulting diagonals are equal is still not always possible and appropriate conditions for the existence of such are established for certain cases when exact triangularization is not possible an asymptotic construction is proposed that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small at the price of processing a sufficiently large number of channel uses together

linguistic summarization using if then rules and interval type 2 fuzzy sets linguistic summarization ls is a data mining or knowledge discovery approach to extract patterns from databases many authors have used this technique to generate summaries like most senior workers have high salary which can be used to better understand and communicate about data however few of them have used it to generate if then rules like if x is large and y is medium then z is small which not only facilitate understanding and communication of data but can also be used in decision making in this paper an ls approach to generate if then rules for causal databases is proposed both type 1 and interval type 2 fuzzy sets are considered five quality measures the degrees of truth sufficient coverage reliability outlier and simplicity are defined among them the degree of reliability is especially valuable for finding the most reliable and representative rules and the degree of outlier can be used to identify outlier rules and data for close up investigation an improved parallel coordinates approach for visualizing the if then rules is also proposed experiments on two datasets demonstrate our ls and rule visualization approaches finally the relationships between our ls approach and the wang mendel wm method perceptual reasoning and granular computing are pointed out

fuzzy causal networks general model inference and convergence in this paper we first propose a general framework for fuzzy causal networks fcns then we study the dynamics and convergence of such general fcns we prove that any general fcn with constant weight matrix converges to a limit cycle or a static state or the trajectory of the fcn is not repetitive we also prove that under certain conditions a discrete state general fcn converges to its limit cycle or static state in o n steps where n is the number of vertices of the fcn this is in striking contrast with the exponential running time 2 sup n which is accepted widely for classic fcns

some characterization theorems on lattice valued induced spaces abstract in this paper we systematically discuss topological and algebraic characteristics on induced spaces and the related weakly induced spaces and fully stratified spaces

on the temporal granularity in fuzzy cognitive maps the theory of fuzzy cognitive maps fcms is a powerful approach to modeling human knowledge that is based on causal reasoning taking advantage of fuzzy logic and cognitive map theories fcms enable system designers to model complex frameworks by defining degrees of causality between causal objects they can be used to model and represent the behavior of simple and complex systems by capturing and emulating the human being to describe and present systems in terms of tolerance imprecision and granulation of information however fcms lack the temporal concept that is crucial in many real world applications and they do not offer formal mechanisms to verify the behavior of systems being represented which limit conventional fcms in knowledge representation in this paper we present an extension to fcms by exploiting a theory from formal languages namely the timed automata which bridges the aforementioned inadequacies indeed the theory of timed automata enables fcms to effectively deal with a double layered temporal granularity extending the standard idea of b time that characterizes the iterative nature of a cognitive inference engine and offering model checking techniques to test the cognitive and dynamic comportment of the framework being designed

separation properties of induced i l topological spaces the concept of induced i l topological spaces has been introduced by kubiak ph d thesis uam poznan 1985 and independently by wang kexue tongbao 34 5 1989 333 in this paper the separation properties in the sense of hutton reilly of induced i l topological spaces are investigated the main result of the paper is a characterization of l topological spaces by means of the appropriate hutton reilly separation properties of its induced i l topological space

paracompactness on l fuzzy topological spaces abstract in this paper we introduce a new kind of paracompactness called paracompactness on l fuzzy topological spaces and obtain some of its properties such as that it is a good extension hereditary with respect to closed subsets and that the cartesian product of an n compaact space and a paracompact space is a paracompact space as well as that a paracompact hausdorff space is both a regular and normal space

similarity based inverse approximate reasoning this paper investigates the inverse problem of ap proximate reasoning to conclude a from b and a b from different angles we develop a method to and a solution to the inverse problem by the use of the law of contrapositive symme try in the process generalized modus ponens generalized modus tollens and their generating functions are studied extensively an attempt is made here to establish that the concept of similarity plays an important role in inverse approximate reasoning we apply the concept of similarity to model inverse approximate reasoning and develop a new methodology that is named similarity based inverse approximate reasoning for a solution to the problem algorithms are presented and illustrated with simple yet concrete examples we then use zadeh s compositional rule of inference cri as a combi nation of cylindrical extension and projection and thereby model generalized modus tollens in a different way we thus develop a third way to find a solution to the inverse problem of approximate reasoning a comparison between the result of application of our technique and the real static characteristic of a dc shunt motor is presented

an extension to fuzzy cognitive maps for classification and prediction fuzzy cognitive maps fcms as an illustrative causative representation of modeling and manipulation of complex systems can be used to model the dynamic behavior of the investigated systems however due to defects in expression and architecture the traditional fcms and most of their relevant extensions are not applicable to classification problems to solve this problem this paper presents an approach that directly extends the model by translating the reasoning mechanism of traditional fcms to a set of fuzzy if then rules moreover the proposed approach fully considers the contribution of the inputs to the activation of the fuzzy rules and quantifies the causalities using mutual subsethood which works in conjunction with volume defuzziflcation in a gradient descent learning framework in this manner our approach enhances the capability of the conventional fcms to automatically identify membership functions and quantify causalities despite the increase in the number of tunable parameters experimental results show that the proposed approach efficiently extends the application of the traditional fcms into classification problems while keeping the ability for prediction and approximation

on causal inference in fuzzy cognitive maps fuzzy cognitive maps fcm is a powerful paradigm for representing human knowledge and causal inference this paper formally analyzes the causal inference mechanism of fcm we focus on binary concept states it is known that given initial conditions fcm is able to reach only certain states in its state space we prove that the problem of finding whether a state is reachable in the fcm is nondeterministic polynomial np hard that we can divide fuzzy cognitive maps containing circles into basic fcm modules the inference patterns in these basic modules can be studied individually in a hierarchical fashion this paper also presents a recursive formula for computing fcm s inference patterns in terms of key vertices the theoretical results presented in this paper provide a feasible and effective framework for the analysis and design of fuzzy cognitive maps in real world large scale applications

intuitionistic fuzzy cognitive maps uncertainty and imprecision characterize human cognitive and reasoning processes fuzzy cognitive maps fcms are computationally simple yet effective structures to approximately model and simulate such processes a limitation of current fcms is that they are unable to model the hesitancy introduced into a complex system due to imperfect facts missing information and indecision to cope with this issue we propose a novel extension of the fcm model which is based on the theory of intuitionistic fuzzy sets this intuitionistic fcm ifcm model which is denoted as ifcm ii inherently exploits the mathematical framework of intuitionistic fuzzy sets for the definition of the concepts constituting the cognitive map and their interrelations as well as for reasoning furthermore unlike the previous ifcm model which is denoted as ifcm i it enables an intuitionistic estimation of hesitancy at the output concepts thus offering a natural mechanism to assess the quality of its output the advantages of the proposed ifcm model over the current fcm and ifcm models are demonstrated with reproducible numeric examples for process control and decision support applications

l fuzzy normal spaces and tietze extension theorem abstract in this paper we prove a characterization theorem for normal l fuzzy topological spaces l is an infinitely distributive lattice with an order reversing involution in the particular case l 0 1 this theorem reduces to a known result of kat tov fund math 38 1951 85 91 and tong duke math j 19 1952 289 292 as an important application we obtain a fuzzy version of tietze extension theorem this yields an affirmative answer to a question raised in a series of papers by rodabaugh fuzzy sets and systems 11 1983 163 183

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

from fuzzy cognitive maps to granular cognitive maps fuzzy cognitive maps fcms form a class of graph oriented fuzzy models describing causal relationships among concepts in this study we augment these models by introducing their generalization coming in the form of granular fcms in contrast with fcms in the granular fcms the connections between the nodes states are described in the form of information granules especially intervals and fuzzy sets key scenarios in which granular models and granular fcms arise are presented in order to offer a compelling rationale behind the formation of such models in the context of system modeling we show that information granularity emerges as an important design asset we discuss detailed schemes of allocation of information granularity and quantify a performance of the resulting granular fcm in terms of a coverage criterion for illustrative purposes the detailed studies are completed for granular fcms with interval valued connections

on compactness of induced i l fuzzy topological spaces abstract the induced i l fuzzy topological spaces for l fuzzy topological spaces introduced by wang geping is a kind of important fuzzy topological space in this paper the author studies the fuzzy compactness of induced i l fuzzy topological spaces some available relations between molecular nets of an l fuzzy topological space and that of its induced i l fuzzy topological space are firstly presented by using these relations the author obtains that the induced i l fuzzy topological space is strong fuzzy compact resp fuzzy compact n compact if and only if the l fuzzy topological space is strong fuzzy compact resp fuzzy compact n compact the author also proves that the induced i l fuzzy topological space is paracompact if and only if the l fuzzy topological space is paracompact

a new fuzzy cognitive map structure based on the weighted power mean we introduce a new structure for fuzzy cognitive maps fcm where the traditional fan in structure involving an inner product followed by a squashing function to describe the causal influences of antecedent nodes to a particular consequent node is replaced with a weighted mean type operator in this paper we employ the weighted power mean wpm through appropriate selection of the weights and exponents in the wpm operators we can both account for the relative importance of different antecedent nodes in the dynamics of a particular node as well as take a perspective ranging continuously from the most pessimistic minimum to the most optimistic maximum on the normalized aggregation of antecedents for each node we consider this fcm structure to be more intuitive than the traditional one as the nonlinearity involved in the wpm is more scrutable with regard to the aggregation of its inputs we provide examples of this new fcm structure to illustrate its behavior including its convergence and compare it with a traditional fcm architecture on a scenario presented in previous works