Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to Zadeh, which considers both the mean and dispersion of alternatives and gives two groups of indicesbased on the uniform and the proportional probability distributions.
Abstract: Most approaches for ranking fuzzy numbers proposed in the literature are based on fuzzy sets theory only, and suffer from lack of discrimination and occasionally conflict with intuition. It is true that fuzzy numbers are frequently partial order and cannot be compared. However,this does not alleviate the need for comparison in practical applications. In this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to Zadeh. It considers both the mean and dispersion of alternatives and gives two groups of indices based on the uniform and the proportional probability distributions. The approach is also extended to the comparison of random fuzzy numbers by means of a mean fuzzy number. It is shown that several comparison indices in the literature can be obtained based on the probability present measure approach. Finally some typical examples are used to compare the various different approaches. The different interpretations of the dispersion index under different physical situations are emphasized.
465 citations
TL;DR: It is shown that fuzzy set approach produces more consistent models (in terms of their performance), and how the power law of granularity helps construct mappings between system's variables in rule-based models.
465 citations
TL;DR: The expected interval is defined as the expectedvalue of an interval random set generated by the fuzzy number and the expected value of this number isdefined as the centre of the expected interval.
462 citations
TL;DR: The theory of fuzzy power sets is shown very naturally to require the use of a fuzzy implication operator and emphasis is placed on the dependence of the choice of operators upon the purposes the user has in hand.
462 citations
TL;DR: This paper proposes a new approach to fuzzy modeling that can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985) because it has the same structure as that of Takagi & Sugeno (1985), because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model.
Abstract: This paper proposes a new approach to fuzzy modeling. The suggested fuzzy model can express a given unknown system with a few fuzzy rules as well as Takagi and Sugeno's model (1985), because it has the same structure as that of Takagi and Sugeno's model. It is also as easy to implement as Sugeno and Yasukawa's model (1993) because its identification mimics the simple identification procedure of Sugeno and Yasukawa's model. The suggested algorithm is composed of two steps: coarse tuning and fine tuning. In coarse tuning, fuzzy C-regression model (FCRM) clustering is used, which is a modified version of fuzzy C-means (FCM). In fine tuning, gradient descent algorithm is used to precisely adjust parameters of the fuzzy model instead of nonlinear optimization methods used in other models. Finally, some examples are given to demonstrate the validity of this algorithm.
461 citations