Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Fuzzy Set Theory: Foundations and Applications

Abstract: Information, uncertainty and complexity classical logic basic concepts and notation fuzzy sets - basic concepts and properties fuzzy sets - further properties classical relations fuzzy relations fuzzy logic applications - a survey an historical overview established applications prospective applications illustrative examples

A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making

Abstract: The objective of this article is to extend and present an idea related to weighted aggregated operators from fuzzy to Pythagorean fuzzy sets PFSs. The main feature of the PFS is to relax the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted averaging PFEWA, Pythagorean fuzzy Einstein ordered weighted averaging PFEOWA, generalized Pythagorean fuzzy Einstein weighted averaging GPFEWA, and generalized Pythagorean fuzzy Einstein ordered weighted averaging GPFEOWA, are proposed in this article. Some desirable properties corresponding to it have also been investigated. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.

Fuzzy Relation Equations and Their Applications to Knowledge Engineering

Abstract: 1: Introductory Remarks on Fuzzy Sets.- 2: Fuzzy Relation Equations in Residuated Lattices.- 3: Lower Solutions of Max-Min Fuzzy Equations.- 4: Measures of Fuzziness of Solutions of Max-Min Fuzzy Relation Equations on Linear Lattices.- 5: Boolean Solutions of Max-Min Fuzzy Equations.- 6: ?-Fuzzy Relation Equations and Decomposable Fuzzy Relations.- 7: Max-Min Decomposition Problem of a Fuzzy Relation in Linear Lattices.- 8: Fuzzy Relation Equations with Lower and Upper Semicontinuous Triangular Norms.- 9: Fuzzy Relation Equations with Equality and Difference Composition Operators.- 10: Approximate Solutions of Fuzzy Relation Equations.- 11: Handling Fuzziness in Knowledge-Based Systems.- 12: Construction of Knowledge Base, Its Validation and Optimization.- 13: Inference Algorithms in Knowledge-Based Systems.- 14: A Fuzzy Controller and Its Realization.- 15: Bibliographies.- Author Index.

Ranking fuzzy numbers with an area between the centroid point and original point

Abstract: To improve the ranking method of Lee and Li [1], Cheng [2] proposed the coefficient of variation (CV index). Shortcomings are also found in the CV index. Cheng [2] also proposed the distance method to improve the ranking method of Murakami et al. However, the distance method is not sound either. Moreover, the CV index contradicts the distance method in ranking some fuzzy numbers. Therefore, to overcome the above shortcomings, we propose ranking fuzzy numbers with the area between the centroid point and original point.