In this article, we study some properties of anti-fuzzy sub-semigroup, anti fuzzy left (right, two sided) ideal, anti fuzzy ideal, anti fuzzy generalized bi-ideal, anti fuzzy interior ideals and anti fuzzy two sided ideal of regular semigroup. Also, we characterized regular LA-semigroup in terms of their anti fuzzy ideal.

The last decade of this 20th century provides a wide spread of applications of one of the computer techniques, which is called Fuzzy Logic. This technique depends mainly on the fuzzy set theory, which is considered as a general domain with respect to the conventional set theory. This paper presents in initiative the fuzzy sets theory and fuzzy logic as a complete mathematics system. Here it was explained the concept of fuzzy set and defined the operations of fuzzy logic. It contains eleven operations beside the other operations which related to fuzzy algebra. Such search is considered as an enhancement for supporting the others waiting search activities in this field.

The notion of interval value fuzzy k-ideal of KU-semigroup was studied as a generalization of afuzzy k-ideal of KU-semigroup. Some results of this idea under homomorphism are discussed. Also, we presented some properties about the image (pre-image) for interval~ valued fuzzy~k-ideals of a KU-semigroup. Finally, the~ product of~ interval valued fuzzyk-ideals is established.

Producing pseudo-random numbers (PRN) with high performance is one of the important issues that attract many researchers today. This paper suggests pseudo-random number generator models that integrate Hopfield Neural Network (HNN) with fuzzy logic system to improve the randomness of the Hopfield Pseudo-random generator. The fuzzy logic system has been introduced to control the update of HNN parameters. The proposed model is compared with three state-ofthe-art baselines the results analysis using National Institute of Standards and Technology (NIST) statistical test and ENT test shows that the projected model is statistically significant in comparison to the baselines and this demonstrates the competency of neuro-fuzzy based model to produce

In thisˑ paperˑ, we apply the notion ofˑ intuitionisticˑ fuzzyˑ n-fold KU-ideal of KU-algebra. Some types of ideals such as intuitionistic fuzzy KU-ideal, intuitionisticˑ fuzzy closed idealˑ and intuitionistic fuzzy n-fold KU-ideal are studied. Also, the relations between intuitionistic fuzzy n-fold KU-ideal and intuitionistic fuzzy KU-ideal are discussed. Furthermore, aˑ fewˑ results of intuitionisticˑ fuzzyˑ n-ˑfold KU-ideals of a KU-algebra underˑ homomorphismˑ are discussed.

This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given.  As the first result, it has been proved that every  σ-algebra over a fuzzy set x*  is a  fuzzy σ-ring-over a fuzzy set x*  and construct their converse by example. Furthermore, the fuzzy ring  concept has been studied to generalize fuzzy algebra and its relation. Investigating  that the concept of fuzzy  σ-Ring is a stronger form of a fuzzy ring  that is every fuzzy σ-Ring over a fuzzy set x* is a fuzzy ring over a fuzzy set x* and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied