Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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TL;DR: The issue of having to choose a best alternative in multicriteria decision making leads the problem of comparing Pythagorean membership grades to be considered, and a variety of aggregation operations are introduced for these Pythagorian fuzzy subsets.
Abstract: We first look at some nonstandard fuzzy sets, intuitionistic, and interval-valued fuzzy sets. We note both these allow a degree of commitment of less then one in assigning membership. We look at the formulation of the negation for these sets and show its expression in terms of the standard complement with respect to the degree of commitment. We then consider the complement operation. We describe its properties and look at alternative definitions of complement operations. We then focus on the Pythagorean complement. Using this complement, we introduce a class of nonstandard Pythagorean fuzzy subsets whose membership grades are pairs, (a, b) satisfying the requirement a
2
+ b
2
≤ 1. We introduce a variety of aggregation operations for these Pythagorean fuzzy subsets. We then look at multicriteria decision making in the case where the criteria satisfaction are expressed using Pythagorean membership grades. The issue of having to choose a best alternative in multicriteria decision making leads us to consider the problem of comparing Pythagorean membership grades.
1,706 citations
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TL;DR: In this article, a hierarchical multiple criteria decision-making (MCDM) model based on fuzzy-sets theory is proposed to deal with the supplier selection problems in the supply chain system.
1,559 citations
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TL;DR: In this article, the authors describe a fuzzy vault construction that allows Alice to place a secret value /spl kappa/ in a secure vault and lock it using an unordered set A of elements from some public universe U. If Bob tries to "unlock" the vault using B, he obtains the secret value if B is close to A, i.e., only if A and B overlap substantially.
Abstract: We describe a simple and novel cryptographic construction that we call a fuzzy vault. Alice may place a secret value /spl kappa/ in a fuzzy vault and "lock" it using an unordered set A of elements from some public universe U. If Bob tries to "unlock" the vault using an unordered set B, he obtains /spl kappa/ only if B is close to A, i.e., only if A and B overlap substantially.
1,481 citations
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TL;DR: A general neural-network (connectionist) model for fuzzy logic control and decision systems is proposed, in the form of feedforward multilayer net, which avoids the rule-matching time of the inference engine in the traditional fuzzy logic system.
Abstract: A general neural-network (connectionist) model for fuzzy logic control and decision systems is proposed. This connectionist model, in the form of feedforward multilayer net, combines the idea of fuzzy logic controller and neural-network structure and learning abilities into an integrated neural-network-based fuzzy logic control and decision system. A fuzzy logic control decision network is constructed automatically by learning the training examples itself. By combining both unsupervised (self-organized) and supervised learning schemes, the learning speed converges much faster than the original backpropagation learning algorithm. The connectionist structure avoids the rule-matching time of the inference engine in the traditional fuzzy logic system. Two examples are presented to illustrate the performance and applicability of the proposed model. >
1,476 citations