# Showing papers in "Fuzzy Sets and Systems in 2002"

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TL;DR: This paper defines a broad family of fuzzy rough sets, each one of which, called an (I, J)-fuzzy rough set, is determined by an implicator I and a triangular norm J.

911 citations

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TL;DR: Fixed-point theorems are given for complete fuzzy metric spaces in the sense of George and Veeramani and also for Kramosil and Michalek's fuzzy metric Spaces which are complete in Grabiec's sense.

387 citations

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TL;DR: A new class of distance measures for interval numbers that takes into account all the points in both intervals is developed first, and then it is used to formulate the distance measure for fuzzy numbers.

383 citations

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TL;DR: The transformation method is introduced as a powerful approach for both the simulation and the analysis of systems with uncertain model parameters based on the concept of α-cuts, a special implementation of fuzzy arithmetic that avoids the well-known effect of overestimation.

327 citations

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TL;DR: This paper presents an algorithm of complexity o(n3) for finding an exact optimal solution (in the sense of utility scores) to the n-asset portfolio selection problem under possibility distributions.

271 citations

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TL;DR: The problem of the interval approximation of fuzzy numbers is discussed and a new interval approximation operator, which is the best one with respect to a certain measure of distance between fuzzy numbers, is suggested.

267 citations

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TL;DR: In the new millennium more and more researchers will attempt to capture Type 2 representation and develop reasoning with Type 2 formulas that reveal the rich information content available in information granules, as well as expose the risk associated with the graded representation of words and computing with words.

219 citations

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TL;DR: A new approach is presented to make use of both the decision makers' social fuzzy preference relation on alternatives and decision matrix to form an optimization model that can be used to determine the attribute weights and rank the alternatives.

215 citations

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TL;DR: Sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities (LMIs).

211 citations

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TL;DR: An iterative procedure for approximating the optimal consensus of expert opinions is proposed and the importance of each expert is taken into consideration in the process of aggregation.

203 citations

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TL;DR: The intention of this paper is to provide business which are affected by diversified management with a new method to conduct short-term forecasting with a fuzzy seasonal ARIMA (FSARIMA) forecasting model, which includes both interval models with interval parameters and the possible distribution of future value.

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TL;DR: An equivalent multi objective linear programming form of the problem has been formulated in the proposed methodology using fuzzy set theory approach and the proposed solution procedure has been used to solve numerical examples.

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TL;DR: A new approach to database summarization is introduced through a model based on a hierarchical conceptual clustering algorithm, SAINTETIQ, which incrementally builds a summary hierarchy from database records using a fuzzy set-based representation of data.

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TL;DR: These main results extend, generalize and fuzzify some known results in fuzzy metric spaces, probabilistic metric spaces and uniform spaces.

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TL;DR: It is demonstrated that the Kalman filter can be an effective tool for improving the performance of a fuzzy system and is compared with gradient descent and adaptive neuro-fuzzy inference system (ANFIS) based optimization of fuzzy membership functions.

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TL;DR: This work characterize all the solutions in the four possible cases of the functional equation given by the distributivity condition: F(x, G(y,z) = G(F(X, y),F( x,z)) for all x,y,Z, where the unknown functions F,G are uninorms and/or t-operators.

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TL;DR: It is proved that every standard fuzzy metric space has an (up to isometry) unique fuzzy metric completion and that for each fuzzy metrics space there is an ( up to uniform isomorphism) unique complete fuzzy metricspace that contains a dense subspace uniformly isomorphic to it.

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TL;DR: This note gives a theory of state transition matrices for linear systems of fuzzy differential equations used to give a fuzzy version of the classical variation of constants formula.

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TL;DR: It is proved that the category of intuitionistic fuzzy topological spaces and gradation preserving mappings is a topological category and an analogue of Tychonoff's theorem is proved.

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TL;DR: A taxonomy of fuzzy graphs is presented that treats fuzziness in vertex existence, edgeexistence, edge connectivity, and edge weight, and provides algorithmic solutions to some standard graph-theoretic problems for fuzzy graphs.

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TL;DR: The correlation coefficient calculated in this paper is a fuzzy number, rather than a crisp value, based on Zadeh's extension principle, and a pair of nonlinear programs are formulated to find the α-cut of the fuzzy correlation coefficient.

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TL;DR: The results from two examples indicate that the two-stage method proposed in this paper has better performance than the previous studies.

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TL;DR: Two estimation methods along with a fuzzy least-squares approach are proposed that can be effectively used for the parameter estimation of fuzzy regression models.

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TL;DR: It is shown that the first model reduces to the classical newsboy problem, and therefore an optimal solution is easily available, and the second model shows that the objective function is concave and hence present a characterization of the optimal solution.

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TL;DR: The main result of this paper shows that the KH controller approximating function, being a simple fractional function, fulfils the stability condition and can be interpreted as KH controllers are universal approximators in the space of continuous functions.

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TL;DR: The applied grade of membership (GoM) model, suitable for dealing with large datasets, is presented for classification of individual tree crowns into species groups, in high spatial resolution colour infrared aerial photographs.

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TL;DR: Simulation results show that the proposed fuzzy controller can stabilize completely a parallel-type double inverted pendulum system within 10.0 s for a wide range of the initial angles of the two pendulums.

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TL;DR: A unified algebraic approach to the natural structure of domains of linguistic variables, which was proposed by Ho and Wechler, is given and it is shown that a class of finite symmetrical RH_algebras has a rich enough algebraic structure.

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TL;DR: This paper deals with limit theorems for fuzzy-valued measurable mappings which provide, as a whole, a foundation of statistical analysis with fuzzy data, and isomorphic isometric embeddings of the fuzzy sample spaces, endowed with Lp-metrics, into respective LP-spaces, which are Banach spaces of type 2.

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TL;DR: A fuzzy multipurpose decision making model integrating different preference representations: preference orderings, utility functions and fuzzy preference relations is presented and its internal consistency is studied.