Topic
Membership function
About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.
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TL;DR: Simulation studies reported in this paper indicate that the proposed adaptive fuzzy vector filters are computationally attractive, yield excellent performance and are able to preserve structural information while efficiently suppressing noise in cDNA microarray data.
98 citations
TL;DR: A new fuzzy linear programming method for solving fuzzy heterogeneous multiattribute decision making (MADM) problems with fuzzy truth degrees and incomplete weight information is developed.
Abstract: One of the critical activities for outsourcing success is outsourcing provider selection, which may be regarded as a type of fuzzy heterogeneous multiattribute decision making (MADM) problems with fuzzy truth degrees and incomplete weight information. The aim of this paper is to develop a new fuzzy linear programming method for solving such MADM problems. In this method, the decision maker's preferences are given through pair-wise alternatives' comparisons with fuzzy truth degrees, which are expressed with trapezoidal fuzzy numbers (TrFNs). Real numbers, intervals, and TrFNs are used to express heterogeneous decision information. Giving the fuzzy positive and negative ideal solutions, we define TrFN-type fuzzy consistency and inconsistency indices based on the concept of the relative closeness degrees. The attribute weights are estimated through constructing a new fuzzy linear programming model, which is solved by using the developed fuzzy linear programming method with TrFNs. The relative closeness degrees of alternatives can be calculated to generate their ranking order. An example of the IT outsourcing provider selection problem is analyzed to demonstrate the implementation process and applicability of the method proposed in this paper.
98 citations
TL;DR: This paper deals with problems which arise if for well justified statistical models like linear regression only fuzzy data are available, and an application of Zadeh's extension principle to optimal classical estimators finds that they do not keep their optimality properties.
98 citations
TL;DR: This paper introduces an optimization-based framework for constructing three-way approximations of fuzzy sets and proposes a least-cost model based on a semantic distance function between membership grades in [0, 1] and values in { n, m, p }.
98 citations
TL;DR: This paper sets forth in detail point-set lattice-theoretic or poslat foundations of all mathematical and fuzzy set disciplines in which the operations of taking the image and pre-image of (fuzzy) subsets play a fundamental role; such disciplines include algebra, measure and probability theory, and topology.
Abstract: This paper sets forth in detail point-set lattice-theoretic or poslat foundations of all mathematical and fuzzy set disciplines in which the operations of taking the image and pre-image of (fuzzy) subsets play a fundamental role; such disciplines include algebra, measure and probability theory, and topology. In particular, those aspects of fuzzy sets, hinging around (crisp) powersets of fuzzy subsets and around powerset operators between such powersets lifted from ordinary functions between the underlying base sets, are examined and characterized using point-set and lattice-theoretic methods. The basic goal is to uniquely derive the powerset operators and not simply stipulate them, and in doing this we explicitly distinguish between the “fixed-basis” case (where the underlying lattice of membership values is fixed for the sets in question) and the “variable-basis” case (where the underlying lattice of membership values is allowed to change). Applications to fuzzy sets/logic include: development a...
98 citations