$\sigma$-algebra of complex fuzzy subgroups associated with a finite group and the measure on the $\sigma$-algebra
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Abstract
Complex fuzzy subgroups of a finite group are fuzzy subgroups in which the membership values are in the unit disc. In this paper we introduce the term $\sigma$-algebra of complex fuzzy subgroups associated with a finite group by using the discussion in [3]. We prove that the collection of complex fuzzy subgroups associated with a finite group will form a $\sigma$-algebra of complex fuzzy sets. Also, we define measures on this newly introduced $\sigma$-algebra.
Keywords:
Complex fuzzy sets, Fuzzy subgroups, Complex fuzzy subgroups, Similarity measure, Coherence MeasureMathematics Subject Classification:
Mathematics- Pages: 1176-1180
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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D. E. Tamir, Lu Jin and Abraham Kandel, A new interpretation of complex membership grade, Int. J. Intell. System, $26(2011) 285-312$.
Mikhled Okleh Alsarahead and Abd Ghafur Ahmad, Complex Fuzzy Subgroup, Applied Mathematical Sciences, $11(41)(2017), 2011-2021$.
T. David H. Glass, Coherence measures and their relation to fuzzy similarity and inconsistency in knowledge bases, Arti. Intell. Rev., 26(2006), 227-249.
A Sancho- Royo and J. L. Verdegay, On the definition of coherence measure for fuzzy sets, Int. J. of Uncertainty, $12(2)(2004), 129-144$.
D. Ramot, Menahem Friedman, Menahem Friedman, G. Langholz, A. Kandel, On complex fuzzy sets, Fuzzy Syslems, 2001, 1-10.
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