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: In this paper, the concepts of statistically convergent and statis tically Cauchy sequences of fuzzy numbers have been introduced and discussed and also /(p)-spaces of sequences of fuzzy numbers have be introduced.
Abstract: In this paper, the concepts of statistically convergent and statis tically Cauchy sequences of fuzzy numbers have been introduced and discussed. Also /(p)-spaces of sequences of fuzzy numbers have been introduced.
191 citations
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TL;DR: The problem of how to permit a patron to represent the relative importance of various index terms in a Boolean request while retaining the desirable properties of a Boolean system is concerned.
Abstract: This article concerns the problem of how to permit a patron to represent the relative importance of various index terms in a Boolean request while retaining the desirable properties of a Boolean system. The character of classical Boolean systems is reviewed and related to the notion of fuzzy sets. The fuzzy set concept then forms the basis of the concept of a fuzzy request in which weights are assigned to index terms. The properties of such a system are discussed, and it is shown that such systems retain the manipulability of traditional Boolean requests.
191 citations
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TL;DR: F fuzzy theory is applied to eliminate the conversion debate by directly evaluating the linguistic assessment of factors, and grey theory is used to obtain risk priority number by assigning relative weighting coefficient without any utility function.
Abstract: Traditional failure mode and effects analysis (FMEA) determines the risk priority number by finding the multiplication of factor scores that are converted from the probability or degree of problem occurrence without considering the relative importance of factors. This study applies fuzzy theory to eliminate the conversion debate by directly evaluating the linguistic assessment of factors, and uses grey theory to obtain risk priority number by assigning relative weighting coefficient without any utility function. Results of the illustrative example show that concurrent application of fuzzy method and grey theory can solve the problems that have arisen from conventional FMEA, and can efficiently discover the potential failure modes and effects. Indicates that, as a result, the stability of product and process can be assured.
191 citations
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TL;DR: This paper presents a geometrical interpretation of picture fuzzy sets, and proposes correlation coefficients forPicture fuzzy sets which considers the degree of positive membership, degree of neutral membership,degree of negative membership and thedegree of refusal membership.
Abstract: Picture fuzzy sets are extension of Atanassov's intuitionistic fuzzy sets. Picture fuzzy set based models may be adequate in situations when we face human opinions involving more answers of types: yes, abstain, no, refusal. It can be considered as a powerful tool represent an uncertain information in the process of cluster analysis. In this paper, we present a geometrical interpretation of picture fuzzy sets. We propose correlation coefficients for picture fuzzy sets which considers the degree of positive membership, degree of neutral membership, degree of negative membership and the degree of refusal membership. Effectiveness of the proposed correlation coefficient has been established in a bidirectional approximate reasoning systems. We apply the correlation coefficient to clustering analysis under picture fuzzy environments. Advantages of proposed correlation coefficients and drawbacks of existing correlation coefficients have been discussed.
190 citations
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TL;DR: Fuzzy logic adds to bivalent logic an important capability-a capability to reason precisely with imperfect information, which comes into play when precise reasoning is infeasible, excessively costly or unneeded.
190 citations