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  1. 2 Open Mathematics

Autorzy help

  1. 2 Wang Q.

  2. 2 Zhan J.

  3. 1 Borzooei R. A.

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  1. 1 2017

  2. 1 2016

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Rough semigroups and rough fuzzy semigroups based on fuzzy ideals

100%
Wang Q., Zhan J.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1114-1121
EN
In this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups, fuzzy semigroups and rough fuzzy semigroups, and some relative properties are also discussed.
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A study on soft rough semigroups and corresponding decision making applications

81%
Wang Q., Zhan J., Borzooei R. A.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1400-1413
EN
In this paper, we study a kind of soft rough semigroups according to Shabir’s idea. We define the upper and lower approximations of a subset of a semigroup. According to Zhan’s idea over hemirings, we also define a kind of new C-soft sets and CC-soft sets over semigroups. In view of this theory, we investigate the soft rough ideals (prime ideals, bi-ideals, interior ideals, quasi-ideals, regular semigroups). Finally, we give two decision making methods: one is for looking a best a parameter which is to the nearest semigroup, the other is to choose a parameter which keeps the maximum regularity of regular semigroups.
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