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What is Picture Fuzzy Set

Chapter 12
Handbook of Research on Advances and Applications of Fuzzy Sets and Logic
Like intuitionistic fuzzy sets, picture fuzzy sets have the previous two functions: one for membership and another for non-membership. The major difference is that picture fuzzy sets have one more function: for abstinence. This value indicates that the grade of abstinence. This concept of having abstinence value can be particularly useful when one cannot be very confident on the membership or non-membership values for alternative/object.
Published in Chapter:
Tanimoto Similarity Coefficients Measuring Bipolar q-Rung Picture Fuzzy Information and Their Applications
Hüseyin Kamacı (Yozgat Bozok University, Turkey) and Subramanian Petchimuthu (University College of Engineering, Nagercoil, India)
Copyright: © 2022 |Pages: 30
DOI: 10.4018/978-1-7998-7979-4.ch012
Abstract
In this chapter, the concepts of bipolar q-rung picture fuzzy set and bipolar q-rung picture fuzzy number are introduced. Moreover, the fundamentals of bipolar q-rung picture fuzzy sets and bipolar q-rung picture fuzzy numbers are studied. Relatedly, some basic operations, aggregation operators, and relations on the bipolar q-rung picture fuzzy sets/numbers are derived. The intuitive definition of Tanimoto's similarity coefficient is proposed to measure the similarity between two bipolar q-rung picture fuzzy sets. Finally, it is shown that the proposed Tanimoto similarity measures can be used to deal with the problems of medical diagnosis and pattern recognition under the bipolar q-rung picture fuzzy environment.
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