# Abd Ghafur AhmadUniversiti Kebangsaan Malaysia | ukm

Abd Ghafur Ahmad

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138

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## Publications

Publications (138)

A bipolar-valued fuzzy set (BVFS) is a generalization of the fuzzy set (FS). It has been applied to a wider range of problems that cannot be represented by FS. New forms of the bipolar-valued fuzzy Cartesian product (BVFCP), bipolar-valued fuzzy relations (BVFRs), bipolar-valued fuzzy equivalence relations (BVFERs), and Bipolar-valued fuzzy functio...

This study investigates the challenges to the digitalization technology adoption in Malaysia agriculture sector by using the DEMATEL (Decision-Making Trial and Evaluation Laboratory) approach, which will give a complete knowledge of the interdependencies among the barriers. The research objectives are to determine the cause and effect of digital ag...

DEMATEL serves as a tool for addressing multi-criteria decision-making problems, primarily by identifying critical factors that exert the most significant influence on a specific system. To enhance its capabilities in handling contextual decision problems, DEMATEL has been further developed through integration with various other MCDM methods. The i...

The neutrosophic soft set emerges as a highly valuable and efficient adaptation of soft sets, specifically addressing parameterized values of alternatives. However, numerous decision-making algorithms rooted in neutrosophic soft sets often neglect the external factors impacting their effectiveness. This paper introduces the innovative concept of an...

The Neutrosophic Soft Set (NSS) is an advanced and highly effective expansion of soft sets, specifically designed to handle parameterized values of alternatives. As an enhanced version of fuzzy soft sets, it provides a novel mathematical framework that offers significant advantages in dealing with uncertain information. This model is created by mer...

1 | Introduction The conception of a fuzzy set was created as a generalization of a crisp set by Zadeh [1], which led to the foundation of fuzzy set theory. These sets characterize a membership function that assigns each object a grade of membership between 0 and 1. Followed by the studies of fuzzy subgroup by Rosenfeld [2] which utilized the notio...

In this paper, we defined the complex intuitionistic fuzzy subring and introduced some new concepts like Intuitionistic fuzzy sets and homogeneous complex intuitionistic fuzzy sets. Then, we investigated some of characteristics of complex intuitionistic fuzzy subring. The relationship between complex intuitionistic fuzzy subring and intuitionistic...

This paper presents the concepts of a complex intuitionistic fuzzy subfield (CIFSF) and the direct product of a complex intuitionistic fuzzy subfield which is generalized from the concept of a complex fuzzy subfield by adding the notion of intuitionistic fuzzy into a complex fuzzy subfield. The main contribution and originality of this research are...

Most complex problems in the real-world typically involve uncertain,incomplete and indeterminate two-dimen
sional data i.e. information pertaining to the attributes and the periodicity of the problem parameters. To meet
the demand for models that has the ability to handle these information with these characteristics, the introduction
of neutrosophi...

The main objective of this study is to propose a new notion of a complex intuitionistic $ Q $-fuzzy subfield of a field $ F $ that is developed from the concept of a complex fuzzy subfield of a field $ F $ by adding the notion of intuitionistic $ Q $-fuzzy into a complex fuzzy subfield. We establish a new structure of complex fuzzy subfields which...

We introduce the concept of an effective neutrosophic soft set, which aims to capture the influence on three independent membership functions representing degrees of truth (T), indeterminacy (I) and falsity (F). We go further by presenting a generalization of the effective neutrosophic soft set, which includes the incorporation of a degree to signi...

In this paper, we generalize direct product of finite intuitionistic anti fuzzy normal subrings over normed rings. In particular, we discuss the relation between intuitionistic anti characteristic function and direct product of finite intuitionistic anti fuzzy normed normal subrings. Finally, we give characterizations of direct product of finite in...

The neutrosophic idea is a fertile environment adaptable to different mathematical tools. This paper aims to introduce the mapping of complex interval neutrosophic soft sets (MI-CNSSs). Further, the images and inverse images of complex interval neutrosophic soft sets and their properties are explored. These will be supported by concrete examples, a...

In this paper, as a further generalization of m-polar fuzziness subalgebras, we present the conception of an m-polar (ω,θ)-fuzzy subalgebra in BCK/BCI-algebras and discuss some interesting properties of it. We define an m-polar (∈γˆ,∈γˆ∨qδˆ)-fuzzy subalgebras and explore some of its significant attributes. Certain features of m-polar (∈γˆ,∈γˆ∨qδˆ)-...

Interval complex neutrosophic soft set (ICNSS) is the generalization of complex neutrosophic soft set (CNSS) as it provides an interval-based membership structure to handle the complex neutrosophic soft data. However, in the definition of the ICNSS, parameters set is a classical set, and the parameters have the same degree of importance which is co...

The idea of an interval complex neutrosophic soft set (I-CNSS) emerges from the interval neutrosophic soft set (I-NSS) by the extension of its three membership functions (T, I, F) from real space to complex space (unit disc) to better handle uncertainties, vagueness, indeterminacy, and imprecision of information in the periodic nature. The novelty...

In this paper we characterize strongly g(x)-invo clean rings and specify the relation between strongly g(x)-invo clean rings and strongly clean rings. Further, some general properties and relevant examples of strongly g(x)-invo clean rings are presented.

In this work, we introduced the concepts of fuzzy measure algebra of the M-polar electrode ambiguous ideals, and many of them have been investigated properties. Characterizations of the blurry M-polar measure sub-algebra and fuzzy (commutative) ideals of polarity are also looked at. Also, the relationships between M-polar fuzzy measure subalgebras,...

Interval complex neutrosophic soft sets (I-CNSSs) are interval neutrosophic soft sets (I-NSSs) described by three two-dimensional independent membership functions which are uncertainty interval, indeterminacy interval, and falsity interval respectively. Relation is a tool that helps in describing consistency and agreement between objects. Throughou...

A fuzzy system is a novel computing technique that accesses uncertain information by fuzzy representation. In the decision-making process, fuzzy system and soft computing are effective tools that are tolerant to imprecision, uncertainty, and partial truths. Evolutionary fuzzy systems have been developed with the appearance of interval fuzzy, dual f...

In this paper, we initiate the notion of intuitionistic anti fuzzy normed normal subrings and generalize various related properties. We extend the notion of intuitionistic fuzzy normed subrings to intuitionistic anti fuzzy normed normal subrings. Further, we study the algebraic nature of direct product of intuitionistic anti fuzzy normed normal sub...

In this paper, we define the notion of Q-neutrosophic normal soft groups and discuss several related structural characteristics and properties. Additionally, we discuss the relation between Q-neutrosophic normal soft groups and normal soft groups. Furthermore, we define the concept of Q-neutrosophic soft cosets and discuss several relevant attribut...

In this paper, we define the notion of Q-neutrosophic normal soft groups and discuss several related structural characteristics and properties. Additionally, we discuss the relation between Q-neutrosophic normal soft groups and normal soft groups. Furthermore, we define the concept of Q-neutrosophic soft cosets and discuss several relevant attribut...

Interval complex neutrosophic soft sets (I-CNSSs) are interval neutrosophic soft sets (I-NSSs) described by three two-dimensional independent membership functions which are uncertainty interval, indeterminacy interval, and falsity interval respectively. A relation is a tool that helps in describing consistency and agreement between objects. Through...

This paper is a combination of time neutrosophic soft sets and Q-neutrosophic soft expert sets. We define the general concept of time Q-neutrosophic soft expert sets and study its properties. Some operations such as complement, union, and intersection are explored. Then a hypothetical application of this concept in the decision-making problem is gi...

This paper presents the notion of intuitionistic fuzzy normed normal subrings. We investigate the concept of intuitionistic fuzzy normal subrings over normed rings and characterize relevant properties of such subrings. Further, we define direct product of fuzzy normal subrings over normed rings and investigate some related fundamental properties.

The hesitant fuzzy set (HFS) concept as an extension of fuzzy set (FS) in which the membership degree of a given element, called the hesitant fuzzy element (HFE), is defined as a set of possible values. A large number of studies are concentrating on HFE and HFS measurements. It is not just because of their crucial importance in theoretical studies,...

Motivated by the new notion of intuitionistic fuzzy normed ideal, we present and investigate some associated properties of intuitionistic fuzzy normed ideals. We describe the intrinsic product of any two intuitionistic fuzzy normed subsets and show that the intrinsic product of intuitionistic fuzzy normed ideals is a subset of the intersection of t...

In this paper, we define direct product of finite intuitionistic fuzzy normed normal subrings and investigate relevant properties. We also provide some essential operations specially subset, complement and intersection related to direct product of finite intuitionistic fuzzy normed normal subrings. Then we generalize the relation between the intuit...

In this paper, we introduce the notion of intuitionistic anti fuzzy normed subrings and intuitionistic anti fuzzy normed ideals and various properties of intuitionistic anti fuzzy normal subrings and ideals are examined. Also, we prove that the intersection of two intuitionistic anti fuzzy normed ideals is also an intuitionistic anti fuzzy normed i...

In this article, a new idea of BMBJ-neutrosophic hyper-BCK-algebras is introduced and some of its properties are investigated. Here, BMBJ-neutrosophic hyper-BCK-ideal, BMBJ-neutrosophic weak hyper-BCK-ideal, BMBJ-neutrosophic s-weak hyper-BCK-ideal, and BMBJ-neutrosophic strong hyper-BCK-ideal are presented, and some relevant results and relations...

Dual hesitant fuzzy set (DHFS) consists of two parts: membership hesitant function and non-membership hesitant function. This set supports more exemplary and flexible access to set degrees for each element in the domain and can address two types of hesitant in this situation. It can be considered a powerful tool for expressing uncertain information...

In this paper, the notion of the interval valued complex neutrosophic soft set (IV-CNSS) is
defined as a combination of interval valued complex neutrosophic set and soft set. Then, we introduce
the IV-CNSS’s operations such as union, intersection and complement. To explore the study further, we
present some basic operational rules, and investigate...

This study focuses on combining the theories of m-polar fuzzy sets over BCK-algebras and establishing a new framework of m-polar fuzzy BCK-algebras. In this paper, we define the idea of m-polar fuzzy positive implicative ideals in BCK-algebras and investigate some related properties. Then, we introduce the concepts of m-polar $(\in,\in \vee q)$-fuz...

The main goal of this paper is to introduce the notion of intuitionistic fuzzy normed rings and to establish basic properties related to it. We extend normed rings by incorporating the idea of intuitionistic fuzzy to normed rings, we develop a new structure of fuzzy rings which will be called an intuitionistic fuzzy normed ring. As an extension of...

The notions of doubt N-subalgebras and doubt N-ideals in BCK-algebras are introduced, and related properties are investigated. Characterizations of a doubt N-subalgebra and a doubt N-ideal are given, and relations between them are discussed.

Smarandache implemented the idea of neutrosophic set theory as a method for dealing undetermined
data. Neutrosophic set theory is commonly used in various algebric structures, such as groups, rings and
BCK/BCI-algebras. At present, there exist no results on doubt neutrosophic ideals of BCK/BCI-algebras
using t-conorm and t-norm. First, the notions...

In this research, we suggest the theory of FPHFLTSSs. This theory is combination of hesitant fuzzy linguistic term soft sets (HFLTSSs) and weights of criteria in the set namely fuzzy parameterized where all the information are given in a single set. Then, we address several related concepts and the fundamental operations of this theory, namely the...

In this paper, by combining hesitant fuzzy soft sets (HFSSs) and fuzzy parameterized, we introduce the idea of a new hybrid model, fuzzy parameterized hesitant fuzzy soft sets (FPHFSSs). The benefit of this theory is that the degree of importance of parameters is being provided to HFSSs directly from decision makers. In addition, all the informatio...

As an extension of neutrosophic soft sets, Q-neutrosophic soft sets were established to deal with twodimensional indeterminate data. Different hybrid models of fuzzy sets were utilized to different algebraic structures,
for example groups, rings, fields and lie-algebras. A field is an essential algebraic structure, which is widely used
in algebra a...

In this article, we present the idea of quasi-coincidence of an m-polar fuzzy point with an m-polar fuzzy subset. By utilizing this new idea, we further introduce the notion of m-polar (α,β)fuzzy subalgebras in BCK/BCI-algebras which is a generalization of the idea of (α,β)-bipolar fuzzy subalgebras in BCK/BCI-algebras. Some interesting results of...

The purpose of this work is to present a new theory namely fuzzy parameterized dual hesitant fuzzy soft sets (FPDHFSSs). This theory is an extension of the existing dual hesitant fuzzy soft set whereby the set of parameters have been assigned with respective weightage accordingly. We also introduced the basic operation functions for instance inters...

The notions of m-polar fuzzy subalgebras and m-polar fuzzy (closed, commutative) ideals are introduced, and related properties are investigated. Characterizations of m-polar fuzzy subalgebras and m-polar fuzzy (commutative) ideals are considered. Relations between m-polar fuzzy subalgebras, m-polar fuzzy ideals and m-polar fuzzy commutative ideals...

In this paper, we introduce the notion of Q-neutrosophic soft rings and discuss some of its related properties. Next, we discuss the cartesian product of Q-neutrosophic soft rings and homomorphic images and preimages of Q-neutrosophic soft rings. Moreover, Q-neutrosophic soft ideals are defined and some of their related properties are explored.

In this work, we introduce the concept of centroid quasi-centroid for Leibniz algebras and study some of their properties. Then, we determine the quasi-centroid of four-dimensional Leibniz algebras and give their classification.

In this paper, we introduce the concepts of normal m-polar fuzzy subalgebras, maximal m-polar fuzzy subalgebras and completely normal m-polar fuzzy subalgebras in BCK/BCI-algebras. We discuss some properties of normal (resp., maximal, completely normal) m-polar fuzzy subalgebras. We prove that any non-constant normal m-polar fuzzy subalgebra which...

The objective of the current work is to extend the thought of Q-neutrosophic soft sets to fields. In this paper, we define the notion of Q-neutrosophic soft fields. Structural characteristics of it are investigated.

In this paper, the idea of (S, T) -normed doubt neutrosophic ideals of BCK/BCI-algebras is introduced and the characteristic properties are described. Then, images and preimages of (S, T) -normed doubt neutrosophic ideals under homomorphism are considered.

Multi-polar vagueness in data plays a prominent role in several areas of the sciences. In recent years, the thought of m-polar fuzzy sets has captured the attention of numerous analysts, and research in this area has escalated in the past four years. Hybrid models of fuzzy sets have already been applied to many algebraic structures, such as BCK/BCI...

In this paper, we introduce the notion of doubt bipolar fuzzy H-ideals of BCK/BCI-algebras and investigate some interesting properties. We characterize strong doubt positive t-level cut set, strong doubt negative s-level cut set, homomorphism and equivalence relation by considering doubt bipolar fuzzy H-ideals of BCK/BCI-algebras. Characterization...

In this research article, we study some properties of doubt bipolar fuzzy H-ideals inBCK/ BCI-algebras. Doubt bipolar fuzzy H-ideals are connected with doubt bipolar fuzzy subalgebras and doubt bipolar fuzzy ideals. Moreover, doubt bipolar fuzzy H-ideals are characterized using doubt positive t-level cut set, doubt negative s-level cut set and H-Ar...

In this paper, we defined complex intuitionistic fuzzy ideal and investigated some of its characteristics.

The notions of doubt bipolar fuzzy subalgebras and (closed) doubt
bipolar fuzzy ideals are introduced, and related properties are investigated.
Characterizations of a doubt bipolar fuzzy subalgebra and a doubt bipolar
fuzzy ideal are given, and relations between a doubt bipolar fuzzy subalgebra
and a doubt bipolar fuzzy ideal are discussed. The con...

Let M signifies smooth, non-compact manifold without boundary of dimension greater or equal to 5. Assuming that M has a finite number of tame ends and a neighbourhood U of infinity at each end, let D (M) be the simplicial group of self-diffeomorphisms of M. The results showed the existence of a fibration map from D (M) to the disjoint union of D (U...

In [1], Čerin introduced the homotopy theory for topological semigroups and the concept of the S-fibration. The lifting function for the S-fibration was given in [7]. In this paper, we build upon these results and introduce the concept of (Formula Presented) -fiber homotopy equivalence for (Formula Presented) -fibrations in the homotopy theory of P...

We introduce the concept of centroid and quasicentroids for Leibniz algebras and study some of their properties. Then we determine the centroids of low-dimensional Leibniz algebras and give their classification.

In this paper we continue the study of complex intuitionistic fuzzy groups by introducing the notion of complex intuitionistic fuzzy normal subgroup based on complex intuitionistic fuzzy space as a generalisation of intuitionistic fuzzy normal subgroup.

In this paper, we define the complex fuzzy subring and complex fuzzy ideal and study some of their characteristics.

The article is concerned with homotopy in the category Pwhose objects are the pairs (X,∗)consisting of a Polish space X and a closed binary operation ∗. Homomorphisms in Pare continuous maps compatible with the operations. The result showed that the category Padmits the structure of a fibration category in the sense of H. Baues. The notions of fibr...

In this paper we present a new concept of complex intuitionistic fuzzy subrings based on the notion of complex intuitionistic fuzzy subspace, This concept generalize the concept of intuitionistic fuzzy space from the real range of membership function and non-membership, [0,1], to complex range of membership function and, non-membership unit disc in...

Conditions for an infinite dimensional topological transformation group acting transitively on a smooth open manifold to have a slice at each point were given. The results showed that for a manifold whose dimension is finite and greater than 5, the slice exists at each point of the manifold including points near the infinity, provided that the grou...

Complex fuzzy sets, which include complex-valued grades of memberships, are extensions of standard fuzzy sets that better represent time-periodic problem parameters. However, the membership functions of complex fuzzy sets are difficult to enumerate, as they are subject to personal preferences and bias. To overcome this problem, we generalize comple...

In this paper we present a new formulation of complex intuitionistic fuzzy rings based on the notion of complex intuitionistic fuzzy space.

We consider the relative group presentation $\mathcal{P} = \langle G, \mathbf{x} | \mathbf{r} \rangle$ where $\mathbf{x} = \{ x \}$ and $\mathbf{r} = \{ xg_1 xg_2 xg_3 x^{-1} g_4 \}$. We show modulo a small number of exceptional cases exactly when $\mathcal{P}$ is aspherical. If $H = \langle g_1^{-1} g_2, g_1^{-1} g_3 g_1 , g_4 \rangle \leq G$ then...

This paper gives generalization of a notion of supplemented module. Here, we utilize some algebraic properties like supplemented, amply supplemented and local modules in order to obtain the generalization. Other properties that are instrumental in this generalization are $D_{i}$, $SSP$ and $SIP$. If a module $M$ is $Rad$-$D_{11}$-module and has $D_...

The aim of this study is to introduce the notion of complex intuitionistic fuzzy groups based on the notion of complex intuitionistic fuzzy space this concept generaleis the concept of intuitionistic fuzzy space from the real range of membership function and non-membership, to complex range of membership function and, non-membership unit disc in th...

In this paper, using the context of 0-σ-complete metric-like spaces, some common fixed point results of maps that satisfy the generalized so-called (F, ψ, ϕ)-weak contractive conditions are obtained. Our results generalize, extend, unify and complement many existing results in the literature. Examples are given to show the validity of our results.

In this paper, we proved common coupled fixed point results for mixed g-monotone and w-compatible mappings in ordered cone b-metric spaces. Our results extend and generalize several well-known comparable results in literature.

In this paper, we proved common coupled fixed point results for mixed g-monotone and w-compatible mappings in ordered cone b-metric spaces. Our results extend and generalize several well-known comparable results in literature.

Problem statement: In 1999 Molodtsov introduced the concept of a soft set as a general mathematical tool for dealing with uncertainty. The solutions of such problems involve the use of mathematical principles based on uncertainty and imprecision. Approach: In this study we recall the definition of a soft set, its properties and its operations. Resu...

In this paper, we consider, discuss and generalize some recent fixed point results for mappings in 2-metric and b2 -metric spaces established by Mustafa et al. [31]. By using one new lemma all our results are with much shorter proofs. One example shows that our generalizations are genuine. © 2015, Pushpa Publishing House. Allahabad, India. All righ...

In this paper, we introduce the concept of monotone mappings and monotone mapping with respect to other mapping to obtain some coupled, tripled and n-tupled coincidence and fixed point results in partially ordered abstract metric spaces. Our results generalize, extend, complement and improve various comparable results in the existing literature. Th...

In this paper, we consider, discuss and complement fixed points results for mappings satisfying cyclical contractive conditions established by W. A. Kirk et al. [W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, Volume 4, No. 1, 2003, 79-89]. By using our new Lemma...

The existence and uniqueness of the common coupled and common triple fixed points in cone metric spaces have been studied. The concepts of coincidence point, point of coincidence and commonfixed point of N-order for mappings F: XN → X and g:X →X have been introduced recently in 2012. In this paper, we establish coincidence point of N-order theorem...

In this paper, we prove some common fixed point results with generalized contractive condition under the concept of a c-distance in cone metric spaces. Our results, extend and improve some well-known contractive conditions in literature.

In this paper, we give the idea of a generalized c-distance in a cone b-metric space. Then, we prove some common fixed point and fixed point theorems in cone b-metric spaces by using the distance.

In this paper, we prove the existence and uniqueness of the fixed point in some type of mappings which satisfy the T-Kannan contraction on generalized distance in cone metric spaces. The presented theorem extend and generalize several well-known comparable results in literature.

The purpose of this paper is to further the study of (fw) and (fwr)-supplemented module. We study the relation between generalized weakly supplemented module (briefly (
WGS
)-module) and weakly supplemented module and any amply supplemented module M is weakly supplemented. Also any semilocal and locally Noetherian with radical small in M is weakly...

In this paper we give explicit necessary and sufficient conditions for weak-⊕-supplemented module. If M is lifting module then it is weak-⊕-supplemented module. Moreover if we have an R-module M such that is generalized lifting module then M is weak-⊕-supplemented module. We prove that if M is supplemented and projective then M is weak-⊕-supplement...

Abstract: In this paper we give explicit necessary and sufficient conditions
for weak-L-supplemented module. If M is lifting module then it is weak-
L-supplemented module. Moreover if we have an R-module M such that is
generalized lifting module then M is weak-L-supplemented module. We prove
that if M is supplemented and projective then M is weak-L...

The purpose of this paper is to prove the existence of a unique fixed point of T-contraction type mappings under c-distance on complete cone metric spaces depended on another function.

The notion of length module was introduced by Lomp (1999) because of utmost importance to the topic of finite length we should be exposed of some modules which it is related to this property. In this article we introduce new conditions over semisimple, simple modules and we discuss some of the basic characterizations of these modules which show man...

In this paper, we establish common coupled fixed point and coupled fixed point theorems in cone b-metric spaces. The presented theorems extend and generalize several well-known comparable results in literature. We supply some examples to elucidate our obtained results.

The purpose of this paper is to further study the concept of a very important module theory namely principally supplemented modules. Therefore, our work presents some properties of the relation between lifting property and principally supplemented module. Also we will focus on quasi-discrete module to study principally supplemented in general way....

The concept of cone metric space has been introduced in 2007. The
existence and uniqueness of the fixed point and common fixed point have
been studied by considering different types of contractive conditions.
In this article, we generalize some fixed point theorems by replacing
the constants in contractive conditions with functions. Some supporting...

The existence and uniqueness of the coupled fixed points in cone metric spaces have been studied. Fixed point of N-order for the mapping F:X N →X has been introduced recently in 2010. In this paper, we establish a fixed point theorem of N-order for the mapping F in such spaces. The presented theorem extends and generalizes several well-known compar...

We generalize in this paper some results on common fixed points of two, respectively four, contractive-type mappings in abstract metric spaces by removing condition of normality of the cone in their formulations. Further, some results about periodic points of self-maps are extended to the setting of abstract metric spaces.

Competent lecturer with strong commitment in teaching and supervision should be able to cope with the vision of UniversitiKebangsaan Malaysia (UKM), particularly to produce graduates who are knowledgeable, confident and contributes productively to the existence of a dynamic society. Lecturer's roles to teach and supervise should be supported by a s...

This study was conducted to ascertain teaching Science and Mathematics in English will enhance English proficiency amongst the science stream students in UKM. The study found that the students agreed that the teaching of Science and Mathematics in English can improve their English proficiency. The results showed that teaching Science and Mathematic...