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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: This paper focuses on the correlation and correlation coefficient of SVNHFSs and investigates their some basic properties in detail and establishes a decision-making method to handling the single-valued neutrosophic hesitant fuzzy information.
Abstract: As a combination of the hesitant fuzzy set (HFS) and the single-valued neutrosophic set (SVNS), the single-valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompasses the fuzzy set, intuitionistic fuzzy set (IFS), HFS, dual hesitant fuzzy set (DHFS) and SVNS. Correlation and correlation coefficient have been applied widely in many research domains and practical fields. This paper, motivated by the idea of correlation coefficients derived for HFSs, IFSs, DHFSs and SVNSs, focuses on the correlation and correlation coefficient of SVNHFSs and investigates their some basic properties in detail. By using the weighted correlation coefficient information between each alternative and the optimal alternative, a decision-making method is established to handling the single-valued neutrosophic hesitant fuzzy information. Finally, an effective example is used to demonstrate the validity and applicability of the proposed approach in decision making, and the relationship between the each existing method and the developed method is given as a comparison study.
109 citations
TL;DR: This paper presents a new approach for stability analysis and controller design of Takagi-Sugeno (TS) models that considers information derived from existing or induced order relations among the membership functions.
109 citations
TL;DR: This introduction to the R package sets is a (slightly) modied version of Meyer and Hornik (2009a), published in the Journal of Statistical Software.
Abstract: This introduction to the R package sets is a (slightly) modied version of Meyer and Hornik (2009a), published in the Journal of Statistical Software. We present data structures and algorithms for sets and some generalizations thereof (fuzzy sets, multisets, and fuzzy multisets) available for R through the sets package. Fuzzy (multi-)sets are based on dynamically bound fuzzy logic families. Further extensions include user-denable iterators and matching functions.
109 citations
01 May 2010
TL;DR: The proposed method provides a useful way to handle fuzzy multiple criteria hierarchical group decision-making problems and can handle evaluating values represented by nonnormal interval type-2 fuzzy sets.
Abstract: In this paper, we present a new method for handling fuzzy multiple criteria hierarchical group decision-making problems based on arithmetic operations and fuzzy preference relations of interval type-2 fuzzy sets. Because the time complexity of the proposed method is O(nk), where n is the number of criteria and k is the number of decision-makers, it is more efficient than Wu and Mendel's method, whose time complexity is O(mnk), where m is the number of α-cuts, n is the number of criteria and k is the number of decision-makers. Moreover, the proposed method can overcome another drawback of Wu and Mendel's method, i.e., it can handle evaluating values represented by nonnormal interval type-2 fuzzy sets. The proposed method provides us with a useful way to handle fuzzy multiple criteria hierarchical group decision-making problems.
109 citations
01 Jun 2000
TL;DR: A four-step approach to build a fuzzy system automatically is presented, and the results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography.
Abstract: In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A four-step approach to build a fuzzy system automatically is presented: Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration. Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation. Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography.
109 citations