Topic
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: Multiattribute decision making using intuitionistic fuzzy sets is investigated, in which multiple criteria are explicitly considered, several linear programming models are constructed to generate optimal weights for attributes, and the corresponding decision-making methods have also been proposed.
577 citations
TL;DR: Fuzzy linear programming belongs to goal programming in the sense that implicitly or explicitly aspiration levels have to be defined at which the membership functions of the fuzzy sets reach their maximum or minimum.
574 citations
TL;DR: This work presented two new methods to deal with the multi‐attribute decision making problems under the fuzzy environment and used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.
Abstract: The q-rung orthopair fuzzy sets (q-ROFs) are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets and the Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we propose the q-rung orthopair fuzzy weighted averaging operator and the q-rung orthopair fuzzy weighted geometric operator to deal with the decision information, and their some properties are well proved. Further, based on these operators, we presented two new methods to deal with the multi-attribute decision making problems under the fuzzy environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.
567 citations
TL;DR: In this paper, the authors considered the problem of decomposition of the probability density function of the original set into the weighted sum of the component fuzzy set densities, which is done by optimization of some functional defined over all possible fuzzy classifications.
561 citations
TL;DR: New methods for measuring distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets, based on the Hausdorff metric, are suggested.
557 citations