Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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TL;DR: A linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is presented ensuring the accuracy and consistency of the model.
180 citations
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: The proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm and its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals.
178 citations
TL;DR: A set of properties that must be fulfilled by any method of evaluation of quantified statements is proposed, and a general approach for the evaluation ofquantified statements based on the fuzzy cardinality and fuzzy relative cardinality of fuzzy sets is described.
178 citations