Weak Hyper Research Articles

Looking at Two Ways of Constructing Quotient Hyper $BN$-algebras and Some Notes on Hyper $BN$-ideals

A hyper $BN$-algebra is a nonempty set $H$ together with a hyperoperation ``$\circledast$'' and a constant $0$ such that for all $x, y, z \in H$: $x \ll x$, $x \circledast 0 = \{x\}$, and $(x \circledast y) \circledast z = (0 \circledast z) \circledast (y \circledast x)$, where $x \ll y$ if and only if $0 \in x \circledast y$. We investigated the structures of ideals in the Hyper $BN$-algebra setting. We established equivalency of weak hyper $BN$-ideals and hyper sub$BN$-algebras. Also, we found a condition when a strong hyper $BN$-ideal become a hyper $BN$-ideal. Finally, we looked at two ways in constructing the quotient hyper $BN$-algebras and investigated the relationship between the two constructions.

Acute metabolic responses of two marine brachyuran crabs to dilute seawater: The aerobic cost of hyper regulation.

Hepatuspudibundus ("flecked box crab") is a stenohaline osmoconfomer, and restricted to marine habitats. Callinectes danae ("swimming crab Dana") lives in coastal/estuarine waters and is a weak hyper regulator. There is no consensus on which strategy is more expensive metabolically face salinity challenges: conformation with higher dependence on cell volume regulation, or hyper regulation, alleviating the need for intense cell volume regulation. Crabs were probed for their acute response to dilute seawater through exposures to salinities 35‰, 30‰, 25‰, and 20‰for 2, 4, and 6 h. Hemolymph osmolality, lactate, and ions (chloride, sodium, magnesium, potassium) were assayed, as well as muscle water content. Water dissolved oxygen, ammonia, and pH levels were also measured. H. pudibundus conformed for osmolality and displayed increase in muscle hydration along the decrease in salinity down to 25‰, while C. danae efficiently maintained hemolymph osmo ionic stability, consumed more oxygen, acidified more the water, and released more ammonia. In 25‰,both species spent energy: H. pudibundus putatively controlling cell volume, and C. danae regulating hemolymph concentrations. In 20‰, H. pudibundus closed itself, avoiding the contact of the interface epithelia with the external environment and producing much lactate, whereas C. danae spent more energy (aerobic) in extracellular osmo ionic stability. Under these conditions, anisosmotic extracellular regulation (together with additional cell volume regulation) is more oxygen consuming than osmoconformation with a putatively more intense challenge to cell volume. The exposure to hyposalinity limits the occupation of estuarine environments by H. pudibundus in short and middle term.

Fuzzy Soft Positive Implicative Hyper BCK-Ideals

In this paper, the author contributed the concepts of fuzzy soft positive implicative hyper BCK-ideal of types \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\) are introduced some related properties are considered. Relations between double-framed soft hyper BCK-ideal and double-framed soft strong hyper BCK-ideal are discussed. Additionally, the author demonstrate that the level set of fuzzy soft positive implicative hyper BCK-ideal of types \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\) are positive implicative hyper BCK ideal of types \((\ll ,\subseteq ,\subseteq)\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\), respectively. The conditions for a fuzzy soft set to be a fuzzy soft positive implicative hyper BCK-ideal of types \((\ll ,\subseteq ,\subseteq )\), \((\ll ,\ll ,\subseteq )\) and \((\subseteq ,\ll ,\subseteq )\), are initiated respectively, and the circumstances for a fuzzy soft set to be a fuzzy soft weak hyper BCK-ideal are also considered.

MBJ-neutrosophic hyper $ BCK $-ideals in hyper $ BCK $-algebras

In 2018, Takallo et al. introduced the concept of an MBJ-neutrosophic structure, which is a generalization of a neutrosophic structure, and applied it to a $ BCK/BCI $-algebra. The aim of this study is to apply the notion of an MBJ-neutrosophic structure to a hyper $ BCK $-algebra. The notions of the MBJ-neutrosophic hyper $ BCK $-ideal, the MBJ-neutrosophic weak hyper $ BCK $-ideal, the MBJ-neutrosophic s-weak hyper $ BCK $-ideal and the MBJ-neutrosophic strong hyper $ BCK $-ideal are introduced herein, and their relations and properties are investigated. These notions are discussed in connection with the MBJ-neutrosophic level cut sets.

Multipolar Intuitionistic Fuzzy Hyper BCK-Ideals in Hyper BCK-Algebras

In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzzy reflexive hyper BCK-ideal are introduced herein, and their relations and properties are investigated. These concepts are discussed in connection with the k-polar lower level set and the k-polar upper level set.

Fuzzy weak hyper deductive systems of hyper equality algebras and their measures

Fuzzy weak hyper deductive systems of hyper equality algebras and their measures

PRIME WEAK HYPER BCK-IDEALS OF LOWER HYPER BCK-SEMI LATTICE

In this manuscript, we introduce the concept of a prime weak hyper BCK- ideal of a lower hyper BCK-semi lattice and consider its property. Also, we introduce the concept of an irreducible weak hyper BCK-ideal of a lower hyper BCK-semi lattice and investigate its relation with the prime weak hyper BCK-ideal.

Multipolar fuzzy hyper BCK-ideals of hyper BCK-algebras

In this paper, we apply m-polar fuzzy set to hyper BCKalgebra. We introduce the notions of k-polar fuzzy hyper BCK-ideal, k-polar fuzzy weak hyper BCK-ideal, k-polar fuzzy s-weak hyper BCK-ideal, k-polar fuzzy strong hyper BCK-ideal and k-polar fuzzy reflexive hyper BCKideal, and investigate related properties and their relations. We discuss k-polar fuzzy (weak, s-weak, strong, reflexive) hyper BCK-ideal in relation to k-polar level set

Bipolar-valued fuzzy soft hyper BCK ideals in hyper BCK algebras

Using the notion of bipolar-valued fuzzy soft set, the concepts of bipolar-valued fuzzy soft (weak, [Formula: see text]-weak, strong) hyper BCK ideal are introduced, and related properties and relations are investigated. Characterizations of bipolar-valued fuzzy soft (weak) hyper BCK ideal are considered. Conditions for a bipolar-valued fuzzy soft weak hyper BCK ideal to be a bipolar-valued fuzzy soft [Formula: see text]-weak hyper BCK ideal are provided. Conditions for a bipolar-valued fuzzy soft set to be a bipolar-valued fuzzy soft strong hyper BCK ideal are displayed.

Weak hyper semi-quantales and weak hypervalued topological spaces

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued topology (or many-valued topology). Some properties of weak hyper semi-quantales and weak hypervalued-topologies will be studied. An adjunction between the category of weak hyper semi-quantales and the category of weak hypervalued quasi-topological spaces will be established.

Int-soft Implicative hyper $BCK$-ideals in hyper $BCK$-algebras

The notion of an int-soft (weak) implicative hyper BCK-ideal is introduced, and related properties are investigated. Relations between an int-soft weak implicative hyper BCK-ideal, an int-soft implicative hyper BCK-ideal, an int-soft hyper BCK-ideal, and an int-soft strong hyper BCK-ideal are considered, and characterizations of an int-soft weak implicative hyper BCK-ideal are discussed. Conditions for an int-soft hyper BCK-ideal to be an int-soft weak implicative hyper BCK-ideal are provided. Using an int-soft weak implicative hyper BCK-ideal, a new int-soft weak implicative hyper BCK-ideal is established. Finally, we show the hyper homomorphic preimage of an int-soft implicative hyper BCK-ideal is also an int-soft implicative hyper BCK-ideal.

Intuitionistic Fuzzy Soft Hyper BCK Algebras

Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets, and presented an application of fuzzy soft sets in a decision-making problem. Maji et al. also introduced the notion of intuitionistic fuzzy soft sets in the paper [P.K. Maji, R. Biswas and A.R. Roy, Intuitionistic fuzzy soft sets, The Journal of Fuzzy Mathematics, 9 (2001), no. 3, 677–692]. The aim of this manuscript is to apply the notion of intuitionistic fuzzy soft set to hyper BCK algebras. The notions of intuitionistic fuzzy soft hyper BCK ideal, intuitionistic fuzzy soft weak hyper BCK ideal, intuitionistic fuzzy soft s-weak hyper BCK-ideal and intuitionistic fuzzy soft strong hyper BCK-ideal are introduced, and related properties and relations are investigated. Characterizations of intuitionistic fuzzy soft (weak) hyper BCK ideal are considered. Conditions for an intuitionistic fuzzy soft weak hyper BCK ideal to be an intuitionistic fuzzy soft s-weak hyper BCK ideal are provided. Conditions for an intuitionistic fuzzy soft set to be an intuitionistic fuzzy soft strong hyper BCK ideal are given.

Fuzzy hyper h-ideals of hyper BCK-algebras

The fuzzification of (weak, strong, reflexive) hyper h-ideals in hyper BCK-algebras is considered. It is shown that every fuzzy (weak, strong, reflexive) hyper h-ideal is a fuzzy (weak, strong, reflexive) hyper BCK-ideal. Relations among (fuzzy) weak hyper h-ideals, (fuzzy) hyper h-ideals, (fuzzy) strong hyper h-ideals and fuzzy reflexive hyper h-ideals are given. The hyper homomorphic pre-image of a fuzzy hyper h-ideal is discussed. It is proved that the product of fuzzy hyper h-ideals is also a fuzzy hyper h-ideal.

Hyper BCK-ideals based on soft set theory

The notions of int-soft hyper [Formula: see text]-ideals, int-soft strong hyper [Formula: see text]-ideals, int-soft [Formula: see text]-weak hyper [Formula: see text]-ideals, int-soft weak hyper [Formula: see text]-ideals and int-soft reflexive hyper [Formula: see text]-ideals are introduced, and related properties and relations are investigated. Using the notion of inclusive sets, characterizations of an int-soft (weak, strong, reflexive) hyper [Formula: see text]-ideal are provided.

State operators and state-morphism operators on hyper BCK-algebras

In this paper, we first introduce the notion of state operators on a hyper BCK-algebra and investigate some properties of them. Also we introduce the notions of state hyper (weak hyper, strong hyper) BCK-ideals and discuss relations among them. Moreover we study state congruences on state hyper BCK-algebra (X, σ) and show that there exists a bijection between all state regular strong congruence relations and all state hyper reflexive strong BCK-ideals on (X, σ). Then, we induce quotient state hyper BCK-algebra on a bounded hyper BCK-algebra by the kernel of regular commutative state operator and prove that it is a bounded commutative BCK-algebra, that is an MV-algebra. Furthermore, we introduce (strong) state-morphism operators on hyper BCK-algebras and discuss the relationship between (strong) state-morphism operators and state operators. We also introduce the adjoint pairs on a hyper BCK-algebra and obtain that there is a one-to-one correspondence between the regular adjoint pairs and the regular state-morphism operators on a hyper BCK-algebra.

Some Results on Fuzzy Hyper BCK-ideals of Hyper CK-algebras

The fuzzification of (weak, strong, reflexive) hyper BCK-positive implicative ideals in hyper BCK-algebras is considered. It is shown that every fuzzy (weak, strong, reflexive) hyper BCK-positive implicative ideal is a fuzzy (weak, strong, reflexive) hyper BCK-ideal. Relations among weak hyper BCK-positive implicative ideals, hyper BCK-positive implicative ideals, strong hyper BCK-positive implicative ideals and reflexive hyper BCK-positive implicative ideals are given. It is proved that the product of fuzzy (weak, strong, reflexive) hyper BCK-positive implicative ideals is also a fuzzy (weak, strong, reflexive) hyper BCK-positive implicative ideal. Lastly the relations among fuzzy (weak, strong, reflexive) hyper BCK-(implicative, positive implicative, commutative) ideals are being discussed. Keywords: Hyper Bck-Algebra, (Fuzzy) Hyper Bck-Positive Implicative Ideal, (Fuzzy) Reflexive Hyper Bck-Positive Implicative Ideal, (Fuzzy) Strong Hyper Bck-Positive Implicative Ideal, (Fuzzy) Weak Hyper Bck-Positive Implicative Ideal

Classification of Proper Hyper BCI-Algebras of Order 3

We consider the notion of an isomorphism between two hyper BCI-algebras and obtain all of the hyper BCI-algebras of order 3. It is shown that there exist 14 proper hyper BCI-algebras and 5 proper weak hyper BCI-algebras of order 3 up to isomorphism. Finally, further study on the theory of hyper BCI-algebra and its related hyper structure and applications of our result s in information sciences are discussed.

HYPER MV-DEDUCTIVE SYSTEMS OF HYPER MV-ALGEBRAS

The notions of (weak) hyper MV-deductive systems and (weak) implicative hyper MV-deductive systems are introduced, and several properties are investigated. Relations among hyper MV-deductive systems, weak hyper MV-deductive systems, implicative hyper MV-deductive systems and weak implicative hyper MV-deductive systems are discussed. A characterization of a hyper MV-deductive system is provided. A condition for a weak hyper MV-deductive system to be a weak implicative hyper MV-deductive system is given.

New types of hyper MV-deductive systems in hyper MV-algebras

The notions of a (weak) hyper MV-deductive system, a (⊆, ⊆; ⊆)-hyper MV-deductive system, a (≪, ⊆; ⊆)- hyper MV-deductive system, a (≪, ≪; ⊆)-hyper MV-deductive system, a (≪, ≪; ≪)-hyper MV-deductive system and a (∩, ∩; ∩)-hyper MV-deductive system are introduced, and then their relations are investigated (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Hyper MV ‐ideals in hyper MV ‐algebras

AbstractIn this paper we define the hyper operations ⊗, ∨ and ∧ on a hyper MV ‐algebra and we obtain some related results. After that by considering the notions ofhyper MV ‐ideals and weak hyper MV ‐ideals, we prove some theorems. Then we determine relationships between (weak) hyper MV ‐ideals in a hyper MV ‐algebra (M, ⊕, *, 0) and (weak) hyper K ‐ideals in a hyper K ‐algebra (M, °, 0). Finally we give a characterization of hyper MV ‐algebras of order 3 or 4 based on the (weak) hyper MV ‐ideals (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)