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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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TL;DR: In this article, a complex neutrosophic set is introduced to handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature, which is an extension of the complex intuitionistic fuzzy sets.
Abstract: Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false amplitude term with phase term, respectively. Complex neutrosophic set is an extension of the neutrosophic set. Further set theoretic operations such as complement, union, intersection, complex neutrosophic product, Cartesian product, distance measure, and ź-equalities of complex neutrosophic sets are studied here. A possible application of complex neutrosophic set is presented in this paper. Drawbacks and failure of the current methods are shown, and we also give a comparison of complex neutrosophic set to all such methods in this paper. We also showed in this paper the dominancy of complex neutrosophic set to all current methods through the graph.
136 citations
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TL;DR: In this paper, interval-valued fuzzy relations between sets X and Y are introduced as fuzzy subsets of the cartesian product X×Y, and t-norms andt-conorms are chosen in such a way that as many properties of relations in 2-valued logic are preserved.
136 citations
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01 Feb 2001
TL;DR: The proposed linguistic hedge fuzzy logic controller has the following advantages: it needs only the simple-shape membership functions rather than the carefully designed ones for characterizing the related variables, and it performs better than the conventional fuzzy logic controllers do.
Abstract: In this paper, we propose a novel fuzzy logic controller, called linguistic hedge fuzzy logic controller, to simplify the membership function constructions and the rule developments. The design methodology of linguistic hedge fuzzy logic controller is a hybrid model based on the concepts of the linguistic hedges and the genetic algorithms. The linguistic hedge operators are used to adjust the shape of the system membership functions dynamically, and ran speed up the control result to fit the system demand. The genetic algorithms are adopted to search the optimal linguistic hedge combination in the linguistic hedge module, According to the proposed methodology, the linguistic hedge fuzzy logic controller has the following advantages: 1) it needs only the simple-shape membership functions rather than the carefully designed ones for characterizing the related variables; 2) it is sufficient to adopt a fewer number of rules for inference; 3) the rules are developed intuitionally without heavily depending on the endeavor of experts; 4) the linguistic hedge module associated with the genetic algorithm enables it to be adaptive; 5) it performs better than the conventional fuzzy logic controllers do; and 6) it can be realized with low design complexity and small hardware overhead. Furthermore, the proposed approach has been applied to design three well-known nonlinear systems. The simulation and experimental results demonstrate the effectiveness of this design,.
136 citations
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TL;DR: The results show empirically that the use of the methodology outperforms the initial Fuzzy Rule-Based Classification System and also improves the behavior of the genetic tuning based on the 3-tuples fuzzy linguistic representation.
136 citations
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TL;DR: A modified area method is proposed to rank fuzzy numbers with the area between the centroid point and original point that can effectively rank various fuzzy numbers and their images.
Abstract: Ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems. Many methods have been proposed to deal with ranking fuzzy numbers. Chu pointed out some shortcomings of the existing distance method and proposed to rank the fuzzy numbers with the area between the centroid point and original point. However, drawbacks are also found in the area method. For example, it cannot rank fuzzy numbers when some fuzzy numbers have the same centroid point. In this paper, we propose a modified area method to rank fuzzy numbers. The modified method can effectively rank various fuzzy numbers and their images. We also used some comparative examples to illustrate the advantage of the proposed method.
136 citations