Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Fuzzy dynamic programming: an application to unit commitment

Abstract: A new approach using fuzzy dynamic programming is proposed for the unit commitment of a power system. A characteristic feature of the approach is that the errors in the forecast hourly loads can be taken into account by using fuzzy set notations, making the approach superior to the conventional dynamic programming method which assumes that the hourly loads are exactly known and there exist no errors in the forecast loads. To reach an optimal commitment strategy under the fuzzy environment, a fuzzy dynamic programming model in which the hourly loads, the cost, and system security are all expressed in fuzzy set notations is developed. The effectiveness of the approach is demonstrated by the unit commitment of the Taiwan power system, which contains six nuclear units, 48 thermal units, and 44 hydro units. >

Reduction of fuzzy rule base via singular value decomposition

Abstract: Introduces a singular value-based method for reducing a given fuzzy rule set. The method conducts singular value decomposition of the rule consequents and generates certain linear combinations of the original membership functions to form new ones for the reduced set. The present work characterizes membership functions by the conditions of sum normalization (SN), nonnegativeness (NN), and normality (NO). Algorithms to preserve the SN and NN conditions in the new membership functions are presented. Preservation of the NO condition relates to a high-dimensional convex hull problem and is not always feasible in which case a closed-to-NO solution may be sought. The proposed method is applicable regardless of the adopted inference paradigms. With product-sum-gravity inference and singleton support fuzzy rule base, output errors between the full and reduced fuzzy set are bounded by the sum of the discarded singular values. The work discusses three specific applications of fuzzy reduction: fuzzy rule base with singleton support, fuzzy rule base with nonsingleton support (which includes the case of missing rules), and the Takagi-Sugeno-Kang (TSK) model. Numerical examples are presented to illustrate the reduction process.

Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets

Abstract: Out of several generalizations of fuzzy set theory for various objectives, the notions introduced by Atanassov (1983) and Atanassov and Gargov (1989) in defining intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are interesting and very useful in modeling real life problems. Ranking of interval-valued intuitionistic fuzzy sets plays a vital role in decision-making, data analysis, artificial intelligence and socioeconomic system and it was studied in Xu (2007c), Xu and Chen (2007a) and Ye (2009). In this paper a new method for ranking interval-valued intuitionistic fuzzy sets has been introduced and studied. The method is illustrated by numerical examples and compared with other methods. And then a new method for handling multi-criteria fuzzy decision-making problems based on interval-valued intuitionistic fuzzy sets is presented in which criterion values for alternatives are interval-valued intuitionistic fuzzy sets. The method proposed here can provide a useful way to efficiently help the decision-maker to make his decision. An illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Projection models for intuitionistic fuzzy multiple attribute decision making

Abstract: The aim of this paper is to investigate the intuitionistic fuzzy multiple attribute decision-making problems where the attribute values are expressed in intuitionistic fuzzy numbers or interval-val...