The notion of rough sets was introduced by Z. Pawlak in the year 1982. The notion of a i-semigroup was introduced by M. K. Sen in the year 1981. In 2003, Y. B. Jun studied the roughness of subi- semigroups, ideals and bi-ideals in i-semigroups. In this paper, we study rough prime ideals and rough fuzzy prime ideals in i-semigroups.

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Rough prime ideals and rough fuzzy prime ideals in gamma-semigroups

Based on big data, this paper studies the influence of new type of filling pneumonia on the development of sports industry When selecting the typical economic indicators that reflect the development trend of sports industry, it is found that the data is huge according to the big industrial data, but the information that can be reflected is poor and complex Therefore, it is necessary to process these big economic data in order to obtain the impact of new coronary pneumonia on the development of sports industry This paper studies the feature selection algorithm of big data samples, so as to select typical economic indicators from many economic indicators of sports industry to reflect the development trend of sports industry A deep learning algorithm based on feature selection of big data is proposed Firstly, a feature selection framework for big data is constructed, and then data fusion and deep learning are carried out Experiments show that the algorithm can solve the contradiction between large data and poor information This method has a certain forward-looking, and has a certain reference value for the information discrimination of the development trend of sports industry © 2020 - IOS Press and the authors All rights reserved

Development of sports industry under the influence of COVID-19 epidemic situation based on big data

A ternary semigroup is a nonempty set equipped with an associative ternary operation. A Pythagorean fuzzy set is one of the generalizations of the fuzzy set. The aim of this paper is to study rough Pythagorean fuzzy ideals in ternary semigroups. This idea is extended to the lower and upper approximations of Pythagorean fuzzy ideals.

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Rough Pythagorean fuzzy ideals in ternary semigroups

We give the relation between the semilattice congruence N and the set of prime ideals of the ordered -semigroup M.

THE FILTERS OF THE ORDERED $\Gamma$-SEMIGROUPS

In this paper the terms; a completely prime po-Γ-ideal, c-system,a prime po-Γ-ideal, m-system of a po-Γ-semigroup are introduced. It is proved that every poΓ-subsemigroup of a po-Γ-semigroup is a c-system. It is also proved that a po-Γ-ideal P of a po-Γ-semigroup S is completely prime if and only if S\P is either a c-system or empty. It is proved that if P is a po-Γ-ideal of a po-Γ-semigroup S, then the conditions (1) if A, B are po-Γ-ideals of S and AΓB⊆P then either A⊆P or B⊆P, (2) if a, b ∈ S such that aΓSΓb ⊆ P, then either a ∈ P or b ∈ P, are equivalent. It is proved that every completely prime po-Γ-ideal of a po-Γ-semigroup S is a prime po-Γ-ideal of S. It is also proved that in a commutative po-Γ-semigroup S, a po-Γ-ideal P is a prime po-Γ-ideal if and only if P is a completely prime po-Γ-ideal. Further it is proved that a po-Γ-ideal P of a po-Γ-semigroup S is a prime po-Γ-ideal of S if and only if S\P is an m-system or empty. In a globally idempotent po-Γ-semigroup, it is proved that every maximal poΓ-ideal is a prime poΓ-ideal. It is also proved that a globally idempotent po-Γ-semigroup having a maximal po-Γ-ideal, contains semisimple elements. The terms completely semiprime poΓ-ideal,a semiprime po-Γ-ideal, n-system, d-system are introduced. It is proved that (1) every completely semiprime po-Γ-ideal of a po-Γ-semigroup is a semiprime po-Γ-ideal, (2) every completely prime poΓ-ideal of a poΓ-semigroup is a completely semiprime po-Γ-ideal. It is also proved that the nonempty intersection of any family of (1) completely prime po-Γ-ideals of a po-Γ-semigroup is a completely semiprime po-Γ-ideal, (2) prime poΓ-ideals of a po-Γ-semigroup is a semiprime po-Γ-ideal. It is also proved that a poΓ-ideal Q of a po-Γ-semigroup S is a semiprime iff S\Q is either an n-system or empty. Further it is proved that if N is an n-system in a po-Γ-semigroup S and a ∈ N, then there exists an m-system M of S such that a ∈ M and M ⊆ N. Mathematics Subject Clasification (2010) : 06F05, 06F99, 20M10, 20M99

http://www.iosrjournals.org/iosr-jm/papers/vol1-issue6/H0163951.pdf

Po--Ideals in Po--Semigroups

In 1981, Sen [4] have introduced the concept of -semigroups. We have known that -semigroups are a generalization of semigroups. In this paper, we introduce the concepts of the extensions of s-prime ideals, prime ideals, s-semiprime ideals and semiprime ideals in -semigroups and characterize the relationship between the extensions of ideals and some congruences in -semigroups.

On the Ideal Extensions in Γ-Semigroups

A semigroup S is an E-inversive E-semigroup if for every a ∈ S, there exists an element x ∈ S such that ax is idempotent and the set of all idempotents of S forms a subsemigroup. The aim of this paper is to investigate the maximum idempotent separating congruence on E-inversive E-semigroups by using a full and weakly self-conjugate subsemigroup.

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The Maximum Idempotent Separating Congruence on E-inversive E-semigroups

Abstract In this paper, we introduce 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, and some interesting properties are investigated. Based on this point, we propose a rough completely prime ideal in a semigroup structure under a compatible preorder fuzzy relation, including the rough semigroup and rough ideal. Then we provide sufficient conditions for them. Finally, the relationships between rough completely prime ideals (rough semigroups and rough ideals) and their homomorphic images are verified.

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On rough sets induced by fuzzy relations approach in semigroups

The motivation mainly comes from the conditions of the (ordered) ideals to be prime or semiprime that are of importance and interest in (ordered) semigroups and in (ordered) -semigroups In 1981, Sen [8] has introduced the concept of the -semigroups We can see that any semigroup can be considered as a -semigroup The concept of ordered ideal extensions in ordered -semigroups was introduced in 2007 by Siripitukdet and Iampan [12] Our purpose in this paper is to introduce the concepts of the ordered n-prime ideals and the ordered n-semiprime ideals in ordered -semigroups and to characterize the relationship between the ordered n-prime ideals and the ordered ideal extensions in ordered -semigroups

Manoj Siripitukdet

Papers

On the Ideal Extensions in Γ-Semigroups

The Maximum Idempotent Separating Congruence on E-inversive E-semigroups

On rough sets induced by fuzzy relations approach in semigroups

ON THE ORDERED n-PRIME IDEALS IN ORDERED Γ-SEMIGROUPS

Generalizations of rough sets induced by binary relations approach in semigroups