Topic
Membership function
About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors reviewed three basic views of the representation of membership functions, together with fundamental measurement of linguistic terms of linguistic variables, and concluded that such measurements are either on an "ordinal" or an "interval" scale based on whether the appropriate axioms are validated by the empirical data, with an allowance for stochastic variation.
264 citations
TL;DR: An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy geometric aggregation operator, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account.
Abstract: An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy decision making technique, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account. To get a broad view of the techniques used, first, some operational laws on interval-valued intuitionistic fuzzy values are introduced. Based on these operational laws, a generalized interval-valued intuitionistic fuzzy geometric aggregation operator is proposed which is used to aggregate decision makers' opinions in group decision making process. In addition, some of its properties are discussed. Then Choquet integral-based Hamming distance between interval-valued intuitionistic fuzzy values is defined. Combining the interval-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria interval-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is used to illustrate the developed procedures.
264 citations
01 Jun 2008
TL;DR: Results from a simulated coupled tank experiment demonstrated that IT2 FLCs that employ the proposed type reduction algorithm share similar robustness properties as FLC's based on the Karnik-Mendel type reducer.
Abstract: This paper introduces an alternative type-reduction method for interval type-2 (IT2) fuzzy logic systems (FLSs), with either continuous or discrete secondary membership function. Unlike the Karnik-Mendel type reducer which is based on the wavy-slice representation of a type-2 fuzzy set, the proposed type reduction algorithm is developed using the vertical-slice representation. One advantage of the approach is the output of the type reducer can be expressed in closed form, thereby providing a tool for the theoretical analysis of IT2 FLSs. The computational complexity of the proposed method is also lower than the uncertainty bounds method and the enhanced Karnik-Mendel method. To assess the feasibility of the proposed type-reducer, it is used to calculate the output of an IT2 fuzzy logic controller (FLCs). Results from a simulated coupled tank experiment demonstrated that IT2 FLCs that employ the proposed type reduction algorithm share similar robustness properties as FLCs based on the Karnik-Mendel type reducer.
264 citations
TL;DR: The results of the experiments indicate that neither the product nor the minimum fit the data sufficiently well, but the latter seems to be preferable.
263 citations
TL;DR: A tentative assessment of the role of fuzzy sets in decision analysis is provided and a critical standpoint on the state-of-the-art is taken, in order to highlight the actual achievements and question what is often considered debatable by decision scientists observing the fuzzy decision analysis literature.
262 citations