Mathematics

In this paper, we introduce the concept of bipolar fuzzy subquasigroups and investigate some of
their important properties. Using bipolar fuzzy subquasigroups, characterizations of Artinian and Noetherian
subquasigroups are also discussed.

In this paper, we introduce the concept of generalized doubt fuzzy ideals(and q-ideals) of
BCI-algebras and present some fundamental properties. We characterize the generalized doubt fuzzy
q-ideals of BCI-algebras by their level subsets. We also discuss doubt fuzzy q-ideals of BCI-algebras with
thresholds.

In the present paper, we introduce the notion of left derivation of a BCIalgebra
and investigate some related properties. A condition for left derivation to be
regular is given. Finally, we give a characterization of a p-semisimple BCI-algebra
which admits left derivation

In this paper, we introduce the notion of derivation for an MV-
algebra and discuss some related properties. Using the notion of an isotone
derivation we give some characterizations of a derivation of an MV-algebra.
Moreover, we de…ne an additive derivation of an MV-algebra and investigate
some of its properties. Also,we prove that an additive derivation of a linearly
ordered MV- algebral is an isotone.

The notion of left-right (resp. right-left) derivation of Balgebra
is introduced and some related properties are investigated.
Also the notion of derivation of 0-commutative B-algebra is studied
and some of its properties are investigated.

In this paper we introduce the notion of soft incline algebras and filter soft incline algebras, and investigate some of their properties. Moreover, we introduce the notions of prime and maximal soft ideal and quotient of soft incline algebras.

We introduce the concept of fuzzy soft incline algebras and investigate some of their properties. We discuss fuzzy soft images and fuzzy soft inverse images of fuzzy soft incline algebras. We introduce the notion of an (∈, ∈ ∨q)− fuzzy soft incline algebra which is a generalization of a fuzzy soft incline algebras.

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty and vagueness. In this paper, we apply the concept of soft sets to K-algebras and investigate some properties of Abelian soft K-algebras. We also introduce the concept of soft intersection K-algebras and investigate some of their properties.

We introduce the notion of derivation for an MV-algebra and discuss some related properties. Using the notion of an isotone derivation, we give some characterizations of a derivation of an MV-algebra. Moreover, we define an additive derivation of an MV-algebra and investigate some of its properties. Also, we prove that an additive derivation of a linearly ordered MV-algebral is an isotone.

We define a ranked trigroupoid as a natural followup on the idea of a ranked bigroupoid. We consider the idea of a derivation on such a trigroupoid as representing a two-step process on a pair of ranked bigroupoids where the mappingdis a self-derivation at each step. Following up on this idea we obtain several results and conclusions of interest. We also discuss the notion of a couplet(D,d)onX, consisting of a two-step derivationdand its squareD=d∘d, for example, whose defining property leads to further observations on the underlying ranked trigroupoids also.

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty and vagueness. In this paper, we apply the concept of soft sets toK-algebras and investigate some properties of Abelian softK-algebras. We also introduce the concept of soft intersectionK-algebras and investigate some of their properties.

The notion of int-soft subfields, int-soft algebras over int-soft subfields, and int-soft hypervector spaces are introduced, and their properties and characterizations are considered. In connection with linear transformations, int-soft hypervector spaces are discussed.

We propose certain types of interval-valued fuzzy graphs including balanced interval-valued fuzzy graphs, neighbourly irregular interval-valued fuzzy graphs, neighbourly total irregular interval-valued fuzzy graphs, highly irregular interval-valued fuzzy graphs, and highly total irregular interval-valued fuzzy graphs. Some interesting properties associated with these new interval-valued fuzzy graphs are investigated, and necessary and sufficient conditions under which neighbourly irregular and highly irregular interval-valued fuzzy graphs are equivalent are obtained. We also describe the relationship between intuitionistic fuzzy graphs and interval-valued fuzzy graphs.

Connectivity has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. The structural properties of intuitionistic fuzzy graphs provide a tool that allows for the solution of operations research problems. In this paper, we introduce various types of intuitionistic fuzzy bridges, intuitionistic fuzzy cut vertices, intuitionistic fuzzy cycles, and intuitionistic fuzzy trees in intuitionistic fuzzy graphs and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types.

We introduce the concept of(γ,δ)-bifuzzy Lie subalgebra, whereγ,δare any two of{∈,q,∈∨q,∈∧q}withγ≠∈∧q, by using belongs to relation(∈)and quasi-coincidence with relation(q)between bifuzzy points and bifuzzy sets and discuss some of its properties. Then we introduce bifuzzy soft Lie subalgebras and investigate some of their properties.

We introduce the concept of Cayley bipolar fuzzy graphs and investigate some of their properties. We present some interesting properties of bipolar fuzzy graphs in terms of algebraic structures. We also discuss connectedness in Cayley bipolar fuzzy graphs.

Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.