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Mathematics 2018, 6(9), 146; https://doi.org/10.3390/math6090146

L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New?

1
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, 4040 Linz, Austria
2
Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, 810 05 Bratislava, Slovakia
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 23 June 2018 / Revised: 19 August 2018 / Accepted: 20 August 2018 / Published: 23 August 2018
(This article belongs to the Special Issue Fuzzy Mathematics)
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Abstract

We review several generalizations of the concept of fuzzy sets with two- or three-dimensional lattices of truth values and study their relationship. It turns out that, in the two-dimensional case, several of the lattices of truth values considered here are pairwise isomorphic, and so are the corresponding families of fuzzy sets. Therefore, each result for one of these types of fuzzy sets can be directly rewritten for each (isomorphic) type of fuzzy set. Finally we also discuss some questionable notations, in particular, those of “intuitionistic” and “Pythagorean” fuzzy sets. View Full-Text
Keywords: fuzzy set; interval-valued fuzzy set; “intuitionistic” fuzzy set; “pythagorean” fuzzy set; isomorphic lattices; truth values fuzzy set; interval-valued fuzzy set; “intuitionistic” fuzzy set; “pythagorean” fuzzy set; isomorphic lattices; truth values
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Klement, E.P.; Mesiar, R. L-Fuzzy Sets and Isomorphic Lattices: Are All the “New” Results Really New? . Mathematics 2018, 6, 146.

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