Rough semigroups and rough fuzzy semigroups based on fuzzy ideals
Qiumei Wang,Jianming Zhan +1 more
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A special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S is introduced and the lower and upper approximations based on a fuzzy Ideal in semigroups are defined.Abstract:
Abstract 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.read more
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Rough fuzzy ternary subsemigroups based on fuzzy ideals with three-dimensional congruence relation
TL;DR: This research proposes the three-dimensional k-level relation and proved that this relation is a congruence relation on a ternary semigroup and proves by counterexamples that converses of many parts of many results do not hold which have negated the results proved in Q. Wang's paper.
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On rough sets induced by fuzzy relations approach in semigroups
TL;DR: A rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation is introduced, and some interesting properties are investigated.
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Generalizations of rough sets induced by binary relations approach in semigroups
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The properties of rough v-coexact sequence in rough group
TL;DR: In this paper , the authors investigated the characteristics of a rough V-coexact sequence in rough groups and showed that it can be used to define a rough set theory for groups, rings, and modules.
References
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Book
Fuzzy sets
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
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Rough sets
TL;DR: This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition.
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Fuzzy invariant subgroups and fuzzy ideals
TL;DR: This paper will give a characteristic of a field by a fuzzy ideal, as fuzzy invariant subgroups, fuzzy ideals, and to prove some fundamental properties of fuzzy algebra.