Fuzzy Hyper Research Articles

BIPOLAR FUZZY HYPER BCK-IDEALS IN HYPER BCK-ALGEBRAS

Using the notion of bipolar-valued fuzzy sets, the concepts of bipo- lar fuzzy (weak, �� -weak, strong) hyper BCK-ideals are introduced, and their relations are discussed. Moreover, several related properties are investigated.

BIPOLAR FUZZY HYPER MV-DEDUCTIVE SYSTEMS OF HYPER MV-ALGEBRAS

The notions of bipolar fuzzy hyper MV-subalgebras, (weak) bipolar fuzzy hyper MV-deductive system and precisely weak bipolar fuzzy hyper MV-deductive system are introduced, and their relations are investigated. Characterizations of bipolar fuzzy hyper MV-subalgebras and weak bipolar fuzzy hyper MV-deductive systems are provided.

Fuzzy hyperrings ( Hv-rings) based on fuzzy universal sets

The aim of this paper is to define and study the concept of a fuzzy hyperring, which depends on the concept of a fuzzy universal set. A correspondence relation between a fuzzy hyperring based on a fuzzy universal set and both ordinary and fuzzy hyperideal in the sense of Davvaz is obtained.

Fuzzy Point Hyper BCK-algebras

By using the concept of fuzzy points, we generalize the notion of hyper BCK-algebra and the notions of fuzzy point hyper BCK-(sub) algebras, fuzzy point (weak, strong) hyper BCK-ideals, quasi hyper BCK-(sub) algebras and quasi (weak, strong) hyper BCK-ideals are introduced. The relationship between these notions are stated and proved. Finally, we study the condition QH on quasi hyper BCK-algebras.

Product structure of the fuzzy n-ary factor polygroup

Fuzzy n-ary hypergroups were introduced as suitable generalizations of fuzzy polygroups and a special case of fuzzy n-ary hyper groups. The aim of this paper is to introduce the notion of fuzzy n-ary factor polygroups of a polygroup. Based on the fuzzy n-ary factor group, we also study the product structures of the generating fuzzy factor n-ary groups. At the end of the paper, we prove the fundamental theorem of isomorphism of fuzzy n-ary groups.

The L-fuzzy hypermodules

In this paper, we introduce the concept of L -fuzzy hypermodules over an L -fuzzy hyperring and investigate some of their properties. We provide the notion of L -fuzzy R -subhypermodules of an L -fuzzy R -hypermodule and derive a kind of L -fuzzy quotient hypermodule by using an L -fuzzy R -subhypermodule. We also study the properties of L -fuzzy α -regular relation on L -fuzzy R -hypermodules and investigate L -fuzzy hypermodule (strong) homomorphism.

Fuzzy hyperrings

In this paper we introduce and analyze the fuzzy hyperring notion. We consider and study the subfuzzy-structures of a such notion and homomorphisms between fuzzy hyperrings. Finally, fundamental relations on fuzzy hyperrings are analyzed. In all the paper, we follow a connection between hyperrings and fuzzy hyperrings.

Intuitionistic fuzzy strong hyper K-subalgebras in Hyper K-algebras

Intuitionistic fuzzifications of (strong) hyper K-subalgebras in hyper K-algebras are discussed, and related properties are investigated. Relations between intuitionistic fuzzy hyper K-subalgebras and intuitionistic fuzzy strong hyper K-subalgebras are provided.

SOME RESULTS OF INTUITIONISTIC FUZZY WEAK DUAL HYPER K-IDEALS

In this note we consider the notion of intuitionistic fuzzy (weak) dual hyper K-ideals and obtain related results. Then we classify this notion according to level sets. After that we determine the relationships between in- tuitionistic fuzzy (weak) dual hyper K-ideals and intuitionistic fuzzy (weak) hyper K-ideals. Finally, we define the notion of the product of two intu- itionistic fuzzy (weak) dual hyper K-ideals and prove several Decomposition Theorems.

Intuitionistic fuzzy commutative hyper K-ideals

In this paper first we introduce the notion of intuitionistic fuzzy (weak)hyperK-ideals and also commutative hyperK-ideals of types 1–4 and by some examples we show that there are different notions. Then we obtain some relationships between these notions. Finally by given the notion of the product of two intuitionistic fuzzy commutative hyperK-ideals we give a Decomposition Theorem.

FUZZY (WEAK) IMPLICATIVE HYPER K-IDEALS

Fuzzy (weak) implicative hyper K-ideals are introduc- ed, and relations among fuzzy weak implicative hyper K-ideals, fuzzy implicative hyper K-ideals and fuzzy hyper K-ideals are dis- cussed.

Spinorial content of the standard model, a different look at super-symmetry and fuzzy E-infinity hyper Kähler

Abstract The paper is written partially very informal with one formal section about hyper Kahler manifolds of the E-infinity fuzzy type. We discuss spinors and the particle content of minimally extended super-symmetric standard model.

A comparative study of cluster validation indices applied to genotyping data

Clustering is the most important task in unsupervised learning and cluster validation plays a very important role in cluster analysis. In this paper, we compared the performance of 7 major validation indices designed for Fuzzy- c Means: Partition Coefficient (PC), Partition Entropy (PE), Fukuyama-Sugeno index (F-S), Xie and Beni index (X-B), Compose Within and Between scattering (CWB), SC and Fuzzy hyper volume (FHV) on genotyping data obtained from single nucleotide polymorphism analysis. We first find there are three factors (the fuzzy factor m, the number of variables p and the maximum number of clusters c max) that may influence validation indices' performance. A validation scheme was designed to optimize the performance of these indices. Finally, we test the indices on a total of 18 datasets and compared their performance. PC and CWB showed the best overall performance. CWB only failed on one dataset and PC failed on 2.

FUZZY (POSITIVE, WEAK) IMPLICATIVE HYPER BCK-IDEALS

In this note first we define the notions of fuzzy positive implicative hyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems which characterize the above notions according to the level subsets. Also we obtain the relationships among these notions, fuzzy (strong, weak, reflexive) hyper BCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7 and 8. Then, we define the notions of fuzzy (weak) implicative hyper BCK- ideals and we obtain some related results. Finally, by considering the product of two hyper BCK-algebras we give some theorems which show that how the projections of a fuzzy (positive implicative, implicative) hyper BCK-ideal is again a fuzzy (positive implicative, implicative) hyper BCK-ideal.

INTUITIONISTIC FUZZY HYPER BCK-IDEALS OF HYPER BCK-ALGEBRAS

The intuitionistic fuzzification of (strong, weak, s-weak) hyper BCK-ideals is introduced, and related properties are investigated. Character- izations of an intuitionistic fuzzy hyper BCK-ideal are established. Using a collection of hyper BCK-ideals with some conditions, an intuitionistic fuzzy hyper BCK-ideal is built.

Fuzzy multiply positive implicative hyper BCK‐ideals of hyperBCK‐algebras

We consider the fuzzification of the notion of fuzzy multiply positive implicative hyper BCK‐ideals of BCK‐algebras and then some related results are obtained. Using the concept of level subsets, we give a characterization of a fuzzy multiply positive implicative hyper BCK‐ideal. We state a relation between a fuzzy hyper BCK‐ideal and a fuzzy multiply positive implicative hyper BCK‐ideal. Moreover, we introduce the notions of Noetherian hyper BCK‐algebras and hyper homomorphisms of hyper BCK‐algebras and investigate some related properties. Finally, we introduce the concept of hyper normalization of hyper BCK‐algebras and discuss related properties.

Fuzzy implicative hyper BCK‐ideals of hyper BCK‐algebras

We consider the fuzzification of the notion of implicative hyper BCK‐ideals, and then investigate several properties. Using the concept of level subsets, we give a characterization of a fuzzy implicative hyper BCK‐ideal. We state a relation between a fuzzy hyper BCK‐ideal and a fuzzy implicative hyper BCK‐ideal. We establish a condition for a fuzzy hyper BCK‐ideal to be a fuzzy implicative hyper BCK‐ideal. Finally, we introduce the notion of hyper homomorphisms of hyper BCK‐algebras, and discuss related properties.