Similarity measures play an important role in different research topics such as image analysis, pattern ecognition,
decision making and market prediction. In the same way,
distance measure is an important tool which describes differences between two objects and considered as a dual
concept of similarity measure [12]. The choice of a similarity
measure or a distance measure for any fields of research is not trivial. Since Zadeh proposed fuzzy sets,
many scholars have conducted research on similarity
measures between fuzzy sets. Other similarity measures are proposed for Atanassov intuitionistic fuzzy sets
as a generalization of fuzzy sets.
In this paper, one presents a new measure of distance for the
interval [a,b]
and then for bipolar fuzzy values. Based on the new distance, the similarity of bipolar fuzzy values was
defined. Then, using the similarity or dissimilarity, the cardinality and entropy measures are constructed for bipolar fuzzy set. All these measures are done for bipolar fuzzy
values or bipolar fuzzy set in the framework of penta-valued
representation.
The paper has the following structure: section 2 presents the
fuzzy set and its extensions: intuitionistic fuzzy set,
paraconsistent fuzzy set and bipolar fuzzy set. Also, the main
operators for bipolar fuzzy sets are presented.
Presents the penta-valued representation of bipolar fuzzy sets
defining indexes of truth, falsity, unknowingness, contradiction and ambiguity.Presents a new
distance measure for the interval
[a,b] and its particular forms for [0,1]
and [1,1]
This arricle too presents distance and
similarity measures for bipolar fuzzy sets.
presents the measures for cardinality and entropy.
Sharing link:
Similarity, Cardinality and Entropy for Bipolar Fuzzy Set in the ... - arXiv
PDFhttps://arxiv.org › pdf
Have a look at:
Dubois, Didier, et al. "Terminological difficulties in fuzzy set theory—The case of “Intuitionistic Fuzzy Sets”." Fuzzy Sets and Systems 156.3 (2005): 485-491.
and
Benferhat, Salem, et al. "Bipolar possibility theory in preference modeling: Representation, fusion and optimal solutions." Information Fusion 7.1 (2006): 135-150.
Dubois and Prade are quite critical on intuitionistic fuzzy sets
For example, when we want to express effect and side eftect of a drug, we can use bipolar fuzzy valuations. Because side effect is a negative effect. In intuitionistic fuzzy set, we can not model negative effect. Non-membership degree of an element doesn't correspond to negative effect. So, bipolar fuzzy and intuitionistic fuzzy is different in terms of modeling of problems.
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