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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25 May 2003
TL;DR: By using Karl Popper's Falsificationism, the present approach to fuzzy sets (FSs) for words is scientifically incorrect and a new theory of fuzzy sets for words that is based on collecting data from people that reflect intra- and inter-levels of uncertainties about a word is presented.
Abstract: This paper begins with a delineation of two approaches to fuzzy sets, abstract mathematics and models for words. It demonstrates, by using Karl Popper's Falsificationism, the present approach to fuzzy sets (FSs) for words is scientifically incorrect. A new theory of fuzzy sets is then presented for words that is based on collecting data from people -person MFs-that reflect intra- and inter-levels of uncertainties about a word, and defines a word FS as the union of all such person fuzzy sets. It also demonstrates that intra-uncertainty about a word can be modeled using type-2 person fuzzy sets, and that inter-uncertainty about a word can be modeled by means of an equally weighted union of each person's type-2 fuzzy set. Finally, it proposes a methodology for obtaining a parsimonious parametric type-2 fuzzy set approximation to the aggregated type-2 person FSs. This new theory of fuzzy sets for words is testable and is therefore subject to refutation.
179 citations
TL;DR: A fuzzy augmented Lagrangian genetic algorithm (GA) is presented for optimization of steel structures subjected to the constraints of the AISC allowable stress design specifications taking into account the fuzziness in the constraints.
Abstract: In the traditional optimization algorithms, constraints are satisfied within a tolerance defined by a crisp number. In actual engineering practice, constraint evaluation involves many sources of imprecision and approximation. When an optimization algorithm is forced to satisfy the design constraints exactly, it can miss the global optimum solution within the confine of commonly acceptable approximations. Extending the augmented Lagrangian genetic algorithm (GA) of Adeli and Cheng, a fuzzy augmented Lagrangian GA is presented for optimization of steel structures subjected to the constraints of the AISC allowable stress design specifications taking into account the fuzziness in the constraints. The membership function for the fuzzy domain is found by the intersection of the fuzzy membership function for the objective function and the constraints using the max-min procedure of Bellman and Zadeh. Nonlinear quadratic fuzzy membership functions are used for objective function and constraints. The algorithm is applied to two space axial-load structures including a large 37-story structure with 1,310 members. The features and advantages of the new fuzzy GA include acknowledging the imprecision and fuzziness in the code-based design constraints, increased likelihood of obtaining the global optimum solution, improved convergence, and reduced total computer processing time.
179 citations
TL;DR: This paper presents what it believes to be a straightforward and computationally efficient procedure for dealing with the FLP problem with any general class of nonlinear membership functions.
179 citations
TL;DR: An approach to multiple attributes decision making is given based on the proposed aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of the proposed approach.
178 citations
TL;DR: A new arithmetical principle is proposed and a new method is proposed that is easy to interpret the multiplication operation with the membership functions of fuzzy numbers and the canonical representation of multiplication operation on fuzzy numbers is computed.
Abstract: The representation of multiplication operation on fuzzy numbers is very useful and important in the fuzzy system such as the fuzzy decision making. In this paper, we propose a new arithmetical principle and a new arithmetical method for the arithmetical operations on fuzzy numbers. The new arithmetical principle is the L−1-R−1 inverse function arithmetic principle. Based on the L−1-R−1 inverse function arithmetic principle, it is easy to interpret the multiplication operation with the membership functions of fuzzy numbers. The new arithmetical method is the graded multiple integrals representation method. Based on the graded multiple integrals representation method, it is easy to compute the canonical representation of multiplication operation on fuzzy numbers. Finally, the canonical representation is applied to a numerical example of fuzzy decision.
178 citations