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For the purpose of dealing with the subalgebras of Sheer stroke BCK-algebras associated with the YJϱ-fuzzy set, the concept of YJϱ-fuzzy subalgebras in Sheffer stroke BCK-algebras is introduced and the properties involved are investigated. Conditions for creating a YJϱ fuzzy subalgebra from a given fuzzy are explored. The relationship between fuzzy subalgebra and the YJϱ fuzzy subalgebra is discussed, and conditions are given for the YJϱ-fuzzy subalgebra to be a fuzzy subalgebra. The task of creating a new YJϱ-fuzzy subalgebra is established using the given fuzzy subalgebra. Two types of level sets are created and the conditions under which they become subalgebras are explored. [ABSTRACT FROM AUTHOR]

Dry reforming of methane (DRM) is an environmentally friendly technology for producing syngas while consuming CO 2. However, the short lifespan of catalysts due to metal sintering, coke deposition, and sulfur poisoning hinders its widespread adoption. To address such issues, perovskite catalysts, which have shown superior performance and resistance to coke formation and poisoning, were developed. In this study, a comprehensive simulation model of a DRM reactor that employs Sr 0·92 Y 0·08 Ti 0·95 Ru 0·05 O 3-d (SYTRu5) using COMSOL Multiphysics software was developed. The objective of this study is to contribute to the understanding of the intricate dynamics of DRM process via utilizing simulation models. The simulation model considered five main reactions and calculated the properties of the gas mixture considering temperatures and compositions. Using the simulation model, the distribution of gas mole fractions and temperatures were obtained. According to the results, the H 2 yield and CO 2 conversion rate increased with increasing operating temperature. The temperature of the catalyst bed decreased rapidly owing to the endothermicity of the reaction. Additionally, the CH 4 conversion rate increased with increasing proportion of CO 2 , whereas the reaction converged to an equilibrium state and the temperature difference in the catalyst bed decreased with decreasing gas flow rate. [Display omitted] • Simulation model of dry reforming with an SYTRu5 catalyst was developed. • Experimental and simulation results showed good agreements. • CH 4 conversion rates were 58% in experiments and. 59.44% in simulation at 650 °C. • Reaction characteristics were predicted under various temperatures and gas conditions. • High H 2 yield results in decrease of temperature due to endothermic reaction. [ABSTRACT FROM AUTHOR]

The bipolar-valued fuzzy filter in Sheffer stroke BL-algebras is defined, and several properties are investigated. Various characterizations of the bipolar-valued fuzzy filter are discussed. It is shown that the intersection of bipolar-valued fuzzy filters is also a bipolar-valued fuzzy filter, and an example to show that the union of bipolar-valued fuzzy filters is not a bipolar-valued fuzzy filter is provided. [ABSTRACT FROM AUTHOR]

The notions of intuitionistic fuzzy quasi-subalgebras and intuitionistic fuzzy (ultra) filters are defined and examined on Sheffer stroke BL-algebras in detail. Then we characterize the properties of these intuitionistic fuzzy structures, and show the relationships between intuitionistic fuzzy quasi-subalgebras and intuitionistic fuzzy (ultra) filters. Also, it is stated that the affiliations between aforementioned intuitionistic fuzzy structures and ordinary fuzzy structures on Sheffer stroke BL-algebras, and that the upper and lower level sets defining intuitionistic fuzzy (ultra) filters are (ultra) filters on these algebraic structures. At the end of the study, the process of building new intuitionistic fuzzy filters is presented by means of homomorphisms of Sheffer stroke BL-algebras. [ABSTRACT FROM AUTHOR]

In this paper, the notions of ideals in NBCK-algebras are presented and some properties of such ideals are analyzed. Essentially, our approach is to define NBCK-algebras of all cosets by considering an operation on the set of all cosets defined via ideals. Afterwards, our aim is to study ideal theorems on NBCK-algebras. [ABSTRACT FROM AUTHOR]

The concept of a (strong) set-valued BCK/BCI-morphism in BCK/BCI-algebras is considered, and several properties are investigated. Conditions for a set-valued mapping to be a set-valued BCK/BCI-morphism are given. Using the concept of generalized approximation space, generalized rough subalgebra (ideal) in BCK/BCI-algebras are introduced, and investigate their properties. Using the concept of generalized approximation space and ideal of BCK/bCI-algebra, another type of generalized lower and upper approximations based on the ideal is considered, and then several properties are investigated. [ABSTRACT FROM AUTHOR]

Given a set X , conditions for the neutrosophic quadruple X -set to be a (positive implicative) neutrosophic quadruple BCK -algebra are considered. The notion of (positive implicative) neutrosophic quadruple ideal is introduced, and the extended neutrosophic quadruple BCK/BCI -algebra is established. Several properties are investigated. [ABSTRACT FROM AUTHOR]

Some kinds of pseudo valuations such as positive implicative pseudo valuation, (weak) implicative pseudo valuation, and commutative pseudo valuation of various types are introduced. Several examples, properties and characterizations of them are given as well. The relationships between them and the substructures of hyper BCK -algebras are investigated, too. Finally, by giving various examples and theorems, the relationships among the proposed pseudo valuations are investigated and characterized, especially in hyper BCK -algebras with three elements. [ABSTRACT FROM AUTHOR]

Using the notion of the Łukasiewicz fuzzy set, we study the filter theory of Sheffer stroke Hilbert algebras. Here's what we're trying to do. 1. We first introduce the Łukasiewicz fuzzy filter of Sheffer stroke Hilbert algebras. 2. We provide an example to illustrates the Łukasiewicz fuzzy filter. 3. We examine the various properties of the Łukasiewicz fuzzy filter. 4. We discuss characterizations of the Łukasiewicz fuzzy filter. 5. We explore the conditions under which Łukasiewicz fuzzy set can be Łukasiewicz fuzzy filter. 6. We discuss the relationship between fuzzy filter and Łukasiewicz fuzzy filter. 7. We use the given filter to creates a Łukasiewicz fuzzy filter. 8. We present conditions for the three subsets, called ∈-set, q-set and O-set, to be filters. [ABSTRACT FROM AUTHOR]

The notion of eventful element and eventful set is introduced, and its application is considered in BCI and/or BCK algebras. Several properties are investigated, and (positive implicative) ideal in an eventful BCK algebra and closed ideal in an eventful BCI algebra are discussed. Given the subsets A and B of a BCI and/or BCK algebra, the eventful subset E (A , B) which consists of BCI and/or BCK events with a condition is established. Conditions for the eventful subset E (A , B) to be a (positive implicative) ideal of an eventful BCK algebra are provided, and conditions for the eventful subset E (A , B) to be a (closed) ideal of an event BCI algebra are given. An example to show that the set { 0 ̃ } is not a positive implicative ideal in an eventful BCK algebra is provided, and then the conditions for the set { 0 ̃ } to be a positive implicative ideal in an eventful BCK algebra are considered. [ABSTRACT FROM AUTHOR]

Lattice implication algebra is a new logical algebraic system which is established by combining lattice and implication algebra. As a generalization of intuitionistic fuzzy set, neutrosophic set is introduced which deals with indeterminate membership in addition to degree of membership and degree of non-membership. In this article, the notion of neutrosophic set theory is applied to lattice implication algebras. The concept of implicative neutrosophic LI-ideals of a lattice implication algebra is introduced, and several properties are investigated. Relationship between a neutrosophic LI-ideal and an implicative neutrosophic LI-ideal is discussed, and conditions for a neutrosophic LI-ideal to be an implicative neutrosophic LI-ideal are provided. Characterizations of an implicative neutrosophic LI-ideal are considered, and the extension property of an implicative neutrosophic LI-ideal is studied. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of how to define Γ -nearness ring in the sense of Nobusawa theory which extends the notion of a nearness ring and Γ -rings [N. Nobusawa, Osaka J. Math.1 (1964) 81–89; M. A. Öztürk and E. İnan, Annals of Fuzzy Mathematics and Informatics17(2) (2019) 115–131]. Also, we introduce some properties of approximations and these algebraic structures. [ABSTRACT FROM AUTHOR]

In 2022, Öztürk defined the nearness equivalence classes and nearness cosets of the nearness groups (see [10]). Furthermore, he showed a nearness group G induced by a nearness subgroup H can not be written two different decompositions of G by separate left (right) cosets [10]. In other words, if H is a nearness subgroup of a nearness group G, then G may be shown as a union of different non-discrete left (right) cosets of H in G. Also, it is given that Lagrange's theorem does not work in the nearness subgroups as usual subgroups. Our purpose in this paper is to introduce normal nearness subgroups and quotient nearness groups. Besides which, it is given an example of a nearness group that has nearness subgroup but not normal nearness subgroup. Also, a criterion that satisfies the condition of being a normal subgroup is investigated. It is shown that the multiplication of the two right near-cosets (left near-cosets) is again a right near-coset (left near-coset) is valid in normal nearness subgroups under certain conditions. Moreover, examples of normal nearness subgroups and quotient nearness groups are given. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the concept of cubic intuitionistic sets in B-algebras. We consider the cubic intuitionistic subalgebras, the cubic intuitionistic ideals and also the cubic intuitionistic closed ideals of a B-algebra. Further properties and relationships of the above algebraic structures are discussed and investigated. [ABSTRACT FROM AUTHOR]

As a foundation to study the similarity measure with applications in pattern recognition, (normalized) Hamming distances and (normalized) Euclidean distances between hyper structures based on two and three parameters are established. An example to show that these distances are not metrics in general is provided, and conditions for these distances to be metrics are considered. The notions of length fuzzy ideals with four types are introduced, and related properties and their relations are investigated. Relations between length fuzzy ideals and length fuzzy subalgebras are investigated. Conditions for a length fuzzy subalgebra to be a length fuzzy ideal are provided. Characterizations of a length fuzzy ideal are considered. [ABSTRACT FROM AUTHOR]

The concept and properties of cubic sets were first introduced and investigated by Jun et al. in 2011. In this paper, we first introduce the concept of cubic sets in UP-subalgebras and consider the UP-ideals of a UP-algebra. Relationships between the cubic UP-subalgebras and the cubic UP-ideals of a UP-algebra are investigated. In addition, the homomorphic images and the inverse images of the cubic UP-subalgebras and the cubic UP-ideals are also studied. Related properties of UP -algebras and their UP-ideals are explored and discussed. Finally, the Cartesian product of cubic UP-algebras are investigated. [ABSTRACT FROM AUTHOR]

As a new extension of a cubic set, the notion of a cubic interval-valued intuitionistic fuzzy set is introduced, and its application in BCK/BCI-algebra is considered. The notions of α-internal, β-internal, α-external and b-external cubic IVIF set are introduced, and the P-union, P-intersection, R-union and R-intersection of α-internal and α-external cubic IVIF sets are discussed. The concepts of cubic IVIF subalgebra and ideal in BCK/BCI-algebra are introduced, and related properties are investigated. Relations between cubic IVIF subalgebra and cubic IVIF ideal are considered, and characterizations of cubic IVIF subalgebra and cubic IVIF ideal are discussed. [ABSTRACT FROM AUTHOR]

The notion of a neutrosophic positive implicative N-ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N-ideal and a neutrosophic positive implicative N-ideal are discussed. Characterizations of a neutrosophic positive implicative N-ideal are considered. Conditions for a neutrosophic N-ideal to be a neutrosophic positive implicative N-ideal are provided. An extension property of a neutrosophic positive implicative N-ideal based on the negative indeterminacy membership function is discussed. [ABSTRACT FROM AUTHOR]

As a generalization of interval-valued fuzzy sets and fuzzy sets, the concept of hyperfuzzy sets was introduced by Ghosh and Samanta in the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012), 27-37]. The aim of this manuscript is to introduce the length-fuzzy set and apply it to BCK/BCI-algebras. The notion of length-fuzzy subalgebras in BCK/BCI-algebras is introduced, and related properties are investigated. Characterizations of a length-fuzzy subalgebra are discussed. Relations between length-fuzzy subalgebras and hyperfuzzy subalgebras are established. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the concept of cubic sets to the neutrosophic sets. The notions of truth-internal (indeterminacy-internal, falsity-internal) neutrosophic cubic sets and truth-external (indeterminacy-external, falsity-external) neutrosophic cubic sets are introduced, and related properties are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we define the concept of generalized cubic subsemigroups (ideals) of a semigroup and investigate some of its related properties. In particular, we introduce the concept of $(\in _{(\widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma}_{1},\gamma _{2}) }\vee q_{(\widetilde{\delta }_{1},\delta _{2})})$-cubic ideal, $(\in _{( \widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma }_{1},\gamma _{2}) }\vee q_{(\widetilde{\delta }_{1},\delta _{2}) })$-cubic quasi-ideal, $(\in _{( \widetilde{\gamma }_{1},\gamma _{2}) },\in _{(\widetilde{\gamma }_{1},\gamma _{2}) }\vee q_{( \widetilde{\delta }_{1},\delta _{2})})$-cubic bi-ideal and $(\in _{( \widetilde{\gamma }_{1},\gamma _{2})},\in _{(\widetilde{\gamma } _{1},\gamma _{2})}\vee q_{(\widetilde{\delta }_{1},\delta _{2})})$-cubic prime/semiprime ideal of a semigroup. [ABSTRACT FROM AUTHOR]

The notions of falling fuzzy (implicative, positive implicative and fantastic) filters of a BL-algebra are introduced based on the theory of falling shadows and fuzzy sets. The relations between fuzzy (implicative, positive implicative and fantastic) filters and falling fuzzy (implicative, positive implicative and fantastic) filters are provided. Finally, we apply the concept of falling fuzzy inference relations to BL-algebras and obtain some related results. [ABSTRACT FROM AUTHOR]

This feeding trial was carried out to evaluate the effects of different dietary cadmium levels on growth and tissue cadmium content in juvenile parrotfish, Oplegnathus fasciatus, using cadmium chloride (CdCl2) as the cadmium source. Fifteen fish averaging 5.5±0.06 g (mean±SD) were randomly distributed into each of twenty one rectangular fiber tanks of 30 L capacity. Each tank was then randomly assigned to one of three replicates of seven diets containing 0.30 (C0), 21.0 (C21), 40.7 (C41), 83.5 (C83), 162 (C162), 1,387 (C1,387) and 2,743 (C2,743) mg cadmium/kg diet. At the end of sixteen weeks of feeding trial, weight gain (WG), specific growth rate (SGR) and feed efficiency (FE) of fish fed C21 were significantly higher than those of fish fed C83, C162, C1,387 and C2,743 (p<0.05). Weight gain, SGR and FE of fish fed C0, C21 and C41 were significantly higher than those of fish fed C162, C1,387 and C2,743. Protein efficiency ratio of fish fed C0, C21 and C41 were significantly higher than those of fish fed C1,387 and C2,743. Average survival of fish fed C0, C21, C41 and C162 were significantly higher than that of fish fed C2,743. Tissue cadmium concentrations increased with cadmium content of diets. Cadmium accumulated the most in liver, followed by gill and then muscle. Muscle, gill and liver cadmium concentrations of fish fed C0, C21, C41 and C83 were significantly lower than those of fish fed C162, C1,387 and C2,743. Based on the ANOVA results of growth performance and tissue cadmium concentrations the safe dietary cadmium level could be lower than 40.7 mg Cd/kg diet while the toxic level could be higher than 162 mg Cd/kg diet. [ABSTRACT FROM AUTHOR]

In this article, we first introduce the concept of quasi-coincidence of an interval valued fuzzy point with an interval valued fuzzy subset. This concept is a generalization of the concept of quasi-coincidence of a fuzzy point within a fuzzy subset. By using this new idea, we introduce the concept of an interval valued (α, β)-fuzzy bi-ideals in ordered semigroups. Which is a generalization of the idea of an (α, β)-fuzzy bi-ideals in ordered semigroups. Some interesting results of the algebraic ordered semigroups in terms of interval valued (α, β)-fuzzy bi-ideals are given. By using interval valued ($ε, ε $\vee$ q)-fuzzy bi-ideals some interesting results are obtained. [ABSTRACT FROM AUTHOR]

In the paper [B. Davvaz and A. Khan, Generalized fuzzy filters in ordered semigroups, IJST (2012) Vol. 36, A1: 77-86], Davvaz and Khan discussed the notion of (∈, ∈ ∨ q)-fuzzy left (right) filters as a generalization of the notion of fuzzy left (right) filters of ordered semigroups. In this article, we try to obtain a more general form than (∈, ∈ ∨ q)-fuzzy left (right) filters in ordered semigroups. The notion of an (∈, ∈ ∨ qk)-fuzzy left (right) filter is introduced, and several properties are investigated. Characterizations of an (∈, ∈ ∨ qk)-fuzzy left (right) filter are established. A condition for an (∈, ∈ ∨ qk)-fuzzy left (right) filter to be a fuzzy left (right) filter is provided. Using implication operators and the notion of implication-based fuzzy left (resp. right) filters, characterizations of a fuzzy left (resp. right) filter and an (∈, ∈ ∨ qk)-fuzzy left (resp. right) filter are considered. [ABSTRACT FROM AUTHOR]

In this paper, the notions of normal m-dominating set, normal m-domination number, inverse normal domination set (number) and inverse normal m-domination number are introduced, and some the related results are investigated. Finally, a utilization relevant to decision-making based on influencing factors the company's efficiency is presented. [ABSTRACT FROM AUTHOR]

In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double-framed soft sets is introduced, and applications in BCK/BCI-algebras are discussed. The notions of double-framed soft algebras in BCK/BCIalgebras are introduced, and related properties are investigated. Characterizations of doubleframed soft algebras are considered. Product and int-uni structure of double-framed soft algebras are discussed, and several examples are provided. [ABSTRACT FROM AUTHOR]

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notions of closed intersectional soft BCI-ideals and intersectional soft commutative BCI-ideals are introduced, and related properties are investigated. Conditions for an intersectional soft BCI-ideal to be closed are provided. Characterizations of an intersectional soft commutative BCI-ideal are established, and a new intersectional soft c-BCI-ideal from an old one is constructed. [ABSTRACT FROM AUTHOR]

Abstract: The notions of cubic -ideals and cubic -ideals are introduced, and several related properties are investigated. Characterizations of a cubic -ideal are established. Relations between cubic -ideals, cubic -ideals and cubic -ideals are discussed. The cubic extension property of a cubic -ideal is discussed. [Copyright &y& Elsevier]

Abstract: Xu et al. introduced the concept of vague soft sets, which is an extension to the soft set and the vague set. In this paper, we apply the concept of vague soft sets to hemiring theory. The notion of -vague (soft) left -ideals of a hemiring is introduced and some related properties are investigated. [Copyright &y& Elsevier]

Abstract: On the basis of the theory of a falling shadow, the notion of a falling fuzzy positive implicative ideal of a BCK-algebra is introduced. Relations between falling fuzzy positive implicative ideals and falling fuzzy ideals are given. Relations between fuzzy positive implicative ideals and falling fuzzy positive implicative ideals are provided. [ABSTRACT FROM AUTHOR]

Abstract: The fuzzification of generalized Tarski filters of generalized Tarski algebras is considered, and related properties are investigated. Characterizations of a fuzzy generalized Tarski filter are established. Based on the theory of a falling shadow, the notion of a falling fuzzy generalized Tarski filter of a generalized Tarski algebra is introduced. Relations between fuzzy generalized Tarski filters and falling fuzzy generalized Tarski filters are provided. A characterization of a falling fuzzy generalized Tarski filter is established. [ABSTRACT FROM AUTHOR]

Abstract: Generalizing the notions of -fuzzy ideal, -fuzzy quasi-ideal and -fuzzy bi-ideal, the concepts of -fuzzy ideal, -fuzzy quasi-ideal and -fuzzy bi-ideal are defined. Different classes of semigroups are characterized by the properties of these fuzzy ideals. [ABSTRACT FROM AUTHOR]

Abstract: A generalization of an -fuzzy ideal of a BCK/BCI-algebra is discussed. Characterizations of an -fuzzy ideal and an -fuzzy ideal are provided. Conditions for an -fuzzy ideal (resp. -fuzzy ideal) to be a fuzzy ideal are provided. Using the notion of a fuzzy ideal with thresholds, characterizations of a fuzzy ideal, an -fuzzy ideal and an -fuzzy ideal are discussed. [Copyright &y& Elsevier]

Abstract: In the paper [P.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (3) (2001) 589–602], 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. The aim of this manuscript is to apply fuzzy soft set for dealing with several kinds of theories in BCK/BCI-algebras. The notions of fuzzy soft BCK/BCI-algebras, (closed) fuzzy soft ideals and fuzzy soft -ideals are introduced, and related properties are investigated. [Copyright &y& Elsevier]

Abstract: Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. Recently, decision making based on (fuzzy) soft sets has found paramount importance. This paper aims to give deeper insights into decision making based on fuzzy soft sets. We discuss the validity of the Roy–Maji method and show its true limitations. We point out that the choice value designed for the crisp case is no longer fit to solve decision making problems involving fuzzy soft sets. By means of level soft sets, we present an adjustable approach to fuzzy soft set based decision making and give some illustrative examples. Moreover, the weighted fuzzy soft set is introduced and its application to decision making is also investigated. [Copyright &y& Elsevier]

Abstract: The notions of fuzzy hyper-MV-subalgebras, (weak, strong) fuzzy hyper-MV-deductive systems and previously weak fuzzy hyper-MV-deductive systems are introduced, and their relations/properties are investigated. [Copyright &y& Elsevier]

Abstract: In this paper, we show that Theorem 4.17 and Corollary 4.18 coincide with Theorem 4.11 and Corollary 4.12, respectively, in [W. A. Dudek, M. Shabir, M. Irfan Ali, -fuzzy ideals of hemirings, Comput. Math. Appl. 58 (2009) 310–321]. We discuss more updated results than Theorem 4.17 and Corollary 4.18 in the paper [W. A. Dudek, M. Shabir, M. Irfan Ali, -fuzzy ideals of hemirings, Comput. Math. Appl. 58 (2009) 310–321]. [Copyright &y& Elsevier]

Abstract: By means of -soft sets and -soft sets, some characterizations of (implicative, positive implicative and fantastic) filteristic soft -algebras are investigated. Finally, we prove that a soft set is an implicative filteristic soft -algebra if and only if it is both a positive implicative filteristic soft -algebra and a fantastic filteristic soft -algebra. [Copyright &y& Elsevier]

Abstract: Using the ideas of belonging and quasi-coincidence of a fuzzy point with a fuzzy set, the concepts of -fuzzy ideals and -fuzzy generalized bi-ideals, which are generalization of fuzzy ideals and fuzzy generalized bi-ideals, in a semigroup are introduced, and related properties are investigated. We also define the lower and upper parts of fuzzy subsets of a semigroup. Characterizations of regular semigroups by the properties of the lower part of -fuzzy left ideals, -fuzzy quasi-ideals and -fuzzy generalized bi-ideals are given. [Copyright &y& Elsevier]

Abstract: Molodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Jun [Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413] applied first the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. In this paper we introduce the notion of soft -ideals and -idealistic soft BCI-algebras, and then investigate their basic properties. Using soft sets, we give characterizations of (fuzzy) -ideals in BCI-algebras. We provide relations between fuzzy -ideals and -idealistic soft BCI-algebras. [Copyright &y& Elsevier]

Using the idea of a quasi-coincedence of a fuzzy point with a fuzzy set, the concept of an (α,β)-fuzzy bi-ideal in ordered semigroups is introduced, which is a generalization of the concept of a fuzzy bi-ideal in ordered semigroups and some interesting characterizations theorems are obtained. A special attention is given to (∊, ∊ ∨q)-fuzzy bi-ideals. [ABSTRACT FROM AUTHOR]

Abstract: More general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy set is considered, and generalizations of results in the papers [Y. B. Jun, On -fuzzy subalgebras of BCK/BCI-algebras, Bull. Korean Math. Soc. 42 (4) (2005) 703–711; Y. B. Jun, Fuzzy subalgebras of type in BCK/BCI-algebras, Kyungpook Math. J. 47 (2007) 403–410] are discussed. The notions of -fuzzy subalgebras and -fuzzy subalgebras in a BCK/BCI-algebra are introduced, and several properties are investigated. Characterizations of -fuzzy subalgebra in a BCK/BCI-algebra are discussed. [Copyright &y& Elsevier]

Abstract: The notions of (transitive) soft -algebras, soft edge -algebras, soft -algebras, soft -ideals, soft -ideals, soft -ideals, and -idealistic (-idealistic, or -idealistic) soft -algebras are introduced. Also, their related properties are surveyed. [Copyright &y& Elsevier]

Abstract: Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft semirings by using the soft set theory. The notions of soft semirings, soft subsemirings, soft ideals, idealistic soft semirings and soft semiring homomorphisms are introduced, and several related properties are investigated. [Copyright &y& Elsevier]

Abstract: Molodtsov [D. Molodtsov, Soft set theory — First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. The notion of soft BCK/BCI-algebras and soft subalgebras are introduced, and their basic properties are derived. [Copyright &y& Elsevier]

.We prove that there exists a maximal ideal of a BCI-algebra X in which each subalgebra is an ideal. [ABSTRACT FROM AUTHOR]