16 research outputs found
Distance and Similarity Measures for Soft Sets
In [P. Majumdar, S. K. Samanta, Similarity measure of soft sets, New
Mathematics and Natural Computation 4(1)(2008) 1-12], the authors use matrix
representation based distances of soft sets to introduce matching function and
distance based similarity measures. We first give counterexamples to show that
their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma
4.4 making it a corllary of our result. The fundamental assumption of Majumdar
et al has been shown to be flawed. This motivates us to introduce set
operations based measures. We present a case (Example 28) where
Majumdar-Samanta similarity measure produces an erroneous result but the
measure proposed herein decides correctly. Several properties of the new
measures have been presented and finally the new similarity measures have been
applied to the problem of financial diagnosis of firms.Comment: 14 pages, accepted manuscript, to appear in New Mathematics and
Natural Computatio
Mappings on Fuzzy Soft Classes
We define the concept of a mapping on classes of fuzzy soft sets and study the properties of fuzzy soft images and fuzzy soft inverse images of fuzzy soft sets, and support them with examples and counterexamples
DISTANCE AND SIMILARITY MEASURES FOR SOFT SETS
In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corollary of our result. The fundamental assumption of Ref. 7 has been shown to be flawed. This motivates us to introduce set operations-based measures. We present a case (Example 6.7) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed here decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.Applied soft sets, similarity measure, distance measure, financial diagnosis, similarity based decision making
A Study of Frontier and Semifrontier in Intuitionistic Fuzzy Topological Spaces
Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms