Papers by Dr. Noor Rehman
Scientific Reports, Apr 28, 2022
Scientific Reports
The precise selection of suppliers to fulfill production requirements is a fundamental component ... more The precise selection of suppliers to fulfill production requirements is a fundamental component of all manufacturing and process industries. Due to the increasing consumption levels, green supplier selection (GSS) has been one of the most important issues for environmental preservation and sustainable growth. The present work aims to develop a technique based on Fermatean hesitant fuzzy rough set (FHFRS), a robust fusion of Fermatean fuzzy set, hesitant fuzzy set, and rough set for GSS in the process industry. On the basis of the operational rules of FHFRS, a list of innovative Fermatean hesitant fuzzy rough weighted averaging operators has been established. Further, several intriguing features of the proposed operators are highlighted. To cope with the ambiguity and incompleteness of real-world decision-making (DM) challenges, a DM algorithm has been developed. To illustrate the applicability of the methodology, a numerical example for the chemical processing industry is presented...
International Journal of Fuzzy Systems
The core contribution of this study is to develop a novel generalized idea of q-rung orthopair pr... more The core contribution of this study is to develop a novel generalized idea of q-rung orthopair probabilistic hesitant fuzzy rough set (q-ROPHFRS) which is hybrid structure of the q-rung orthopair fuzzy set, probabilistic hesitant fuzzy set, and rough set. The q-ROPHFRS covers the positive and negative membership grades in the form of probabilistic hesitant fuzzy rough information to address the uncertainties in real-world decision-making problems. This paper proposes a list of novel q-rung orthopair probabilistic hesitant fuzzy rough averaging/geometric aggregation operators to handle the uncertainty effectively and reliably to aggregate the uncertain information under q-ROPHFRSs. Several interesting elementary properties have been investigated. Furthermore, a novel multi-attribute decision-making approach based on the proposed aggregation information is presented. Finally, a numerical application regarding selecting a medical oxygen supplier to the hospital is presented to illustrate the consistency of the developed decision-making technique. The comparison of the proposed technique with B Noor Rehman
The concept of q ,-fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a tern... more The concept of q ,-fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by q ,-fuzzy left (right, lateral) ideals, q ,-fuzzy quasi-ideals and q ,-fuzzy bi-(generalized bi-) ideals.
Computational Intelligence and Neuroscience
Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. T... more Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. The striking framework of the FFS is keen to provide the larger preference domain for the modeling of ambiguous information deploying the degrees of membership and nonmembership. Furthermore, FFSs prevail over the theories of intuitionistic fuzzy sets and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being a significant part of the literature, are crucial and beneficial tools that are widely applied in decision-making, data mining, medical diagnosis, and pattern recognition. This paper aims to expand the literature on FFSs by proposing many innovative Fermatean fuzzy sets-based information measures, namely, distance measure, similarity measure, entropy measure, and inclusion measure. We investigate the relationship between distance, similarity, entropy, and inclusion measures for FFSs. Anoth...
Journal of the National Science Foundation of Sri Lanka, 2018
LA-semigroups are non-associative sturctures of great importance. Study of generalised roughness ... more LA-semigroups are non-associative sturctures of great importance. Study of generalised roughness for fuzzy algebraic substrucures of LA-semigroups has been initiated. Many different kinds of set valued maps are needed to preserve an algebraic substrucure, while considering its lower and upper approximations. In the present paper generalised lower and upper approximations in
Computational Intelligence and Neuroscience
The main purpose of this manuscript is to present a novel idea on the q-rung orthopair fuzzy roug... more The main purpose of this manuscript is to present a novel idea on the q-rung orthopair fuzzy rough set (q-ROFRS) by the hybridized notion of q-ROFRSs and rough sets (RSs) and discuss its basic operations. Furthermore, by utilizing the developed concept, a list of q-ROFR Einstein weighted averaging and geometric aggregation operators are presented which are based on algebraic and Einstein norms. Similarly, some interesting characteristics of these operators are initiated. Moreover, the concept of the entropy and distance measures is presented to utilize the decision makers’ unknown weights as well as attributes’ weight information. The EDAS (evaluation based on distance from average solution) methodology plays a crucial role in decision-making challenges, especially when the problems of multicriteria group decision-making (MCGDM) include more competing criteria. The core of this study is to develop a decision-making algorithm based on the entropy measure, aggregation information, and...
Scientific Reports, 2022
Wind power is often recognized as one of the best clean energy solutions due to its widespread av... more Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q-rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q-rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power pl...
Complexity, 2022
In our current era, a new rapidly spreading pandemic disease called coronavirus disease (COVID-19... more In our current era, a new rapidly spreading pandemic disease called coronavirus disease (COVID-19), caused by a virus identified as a novel coronavirus (SARS-CoV-2), is becoming a crucial threat for the whole world. Currently, the number of patients infected by the virus is expanding exponentially, but there is no commercially available COVID-19 medication for this pandemic. However, numerous antiviral drugs are utilized for the treatment of the COVID-19 disease. Identification of the appropriate antivirus medicine to treat the infection of COVID-19 is still a complicated and uncertain decision. This study’s key objective is to develop a novel approach called q-rung orthopair probabilistic hesitant fuzzy rough set (q-ROPHFRS), which incorporates the q-rung orthopair fuzzy set, probabilistic hesitant fuzzy set, and rough set structures. New q-ROPHFR aggregation operators have been established: the q-ROPHFR Einstein weighted averaging (q-ROPHFREWA) operator and the q-ROPHFR Einstein w...
Mathematical Problems in Engineering, 2022
Industrial control system (ICS) attacks are usually targeted attacks that use the ICS entry appro... more Industrial control system (ICS) attacks are usually targeted attacks that use the ICS entry approach to get a foothold within a system and move laterally throughout the organization. In recent decades, powerful attacks such as Stuxnet, Duqu, Flame, and Havex have served as wake-up calls for industrial units. All organizations are faced with the rise of security challenges in technological innovations. This paper aims to develop aggregation operators that can be used to address the decision-making problems based on a spherical fuzzy rough environment. Meanwhile, some interesting properties of idempotence, boundedness, and monotonicity for the proposed operators are analyzed. Moreover, we use this newly constructed framework to select ICS security suppliers and validate its acceptability. Furthermore, a different test has been performed based on a new operator to strengthen the suggested approach. Additionally, comparative analysis based on the novel extended TOPSIS method is presente...
Generalizing the concepts of , q-fuzzy (left, right, lateral) ideals, , q-fuzzy... more Generalizing the concepts of , q-fuzzy (left, right, lateral) ideals, , q-fuzzy quasi-ideals and , q-fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of , q-fuzzy (left, right, lateral) ideals, , q-fuzzy quasi-ideals and , q-fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. Some new results are obtained.
Abstract: The concept of, q-fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal ... more Abstract: The concept of, q-fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by, q-fuzzy left (right, lateral) ideals, , q-fuzzy quasi-ideals and, q-fuzzy bi-(generalized bi-) ideals.
In this paper, we introduced the concepts of roughness and fuzziness in ordered ternary semigroup... more In this paper, we introduced the concepts of roughness and fuzziness in ordered ternary semigroups. We proved that the lower and upper approximation of an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal) in an ordered ternary semigroup is an ordered ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal). Finally, we define fuzzy ternary subsemigroup (resp. left ideal, right ideal, lateral ideal, bi-ideal, interior ideal) in an ordered ternary semigroup. 2010 mathematics subject classification: 20N99 • 06F99 • 06D72 • 08A72
Scientific Reports
The classical theory of rough set was established by Pawlak, which mainly focusses on the approxi... more The classical theory of rough set was established by Pawlak, which mainly focusses on the approximation of sets characterized by a single equivalence relation over the universe. However, most of the current single granulation structure models cannot meet the user demand or the target of solving problems. Multigranulation rough sets approach can better deal with the problems, where data might be spread over various locations. In this article, we present the idea of soft preference and soft dominance relation for the development of soft dominance rough set in an incomplete information system. Subsequently, several important structural properties and results of the proposed model are carefully analyzed. After employing soft dominance based rough set approach to it for any times, we can only get six different sets at most in an incomplete information system. That is to say, every rough set in a universe can be approximated by only six sets, where the lower and upper approximations of ea...
Abstract: In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, w... more Abstract: In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a generalization of fuzzy ideals in ternary semigroups. We investigate the related properties of ternary semigroups. The lower and upper parts of fuzzy subsets of a ternary semigroup are defined. Characterizations of regular ternary semigroups by the properties of the lower part of (∈,∈∨q)-fuzzy left (right) ideals, (∈,∈∨q)-fuzzy quasi ideals and (∈,∈∨q)-fuzzy bi-ideals are given. Key words: Ternary semigroups, (∈,∈∨q)-fuzzy ideals, (∈,∈∨q)-fuzzy left (right) ideals, (∈,∈∨q)-fuzzy quasi ideals and (∈,∈∨q)-fuzzy bi-ideals
The concept of q , -fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ter... more The concept of q , -fuzzy ternary subsemigroup (left, right, lateral, quasi-, bi-) ideal of a ternary semigroup is introduced and several related properties are investigated. We give some characterizations of regular and weakly regular ternary semigroups by q , -fuzzy left (right, lateral) ideals, q , -fuzzy quasi-ideals and q , -fuzzy bi-(generalized bi-) ideals.
Generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy... more Generalizing the concepts of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) ideals in ternary semigroups, the notions of -fuzzy (left, right, lateral) ideals, -fuzzy quasi-ideals and -fuzzy bi (generalized bi-) in ternary semigroups are introduced and several related properties are investigated. Some new results are obtained.
Journal of the National Science Foundation of Sri Lanka
The aim of this study is to introduce the concept of implication-based fuzzy ternary subsemigroup... more The aim of this study is to introduce the concept of implication-based fuzzy ternary subsemigroups in ternary semigroups. Using the four implication operators, that is, Gaines-Rescher implication operator, Gödel implication operator, the contraposition of Gödel implication operator and the Luckasiewicz implication operator, the implication-based fuzzy ternary subsemigroups are considered. Furthermore, based on this novel idea, relationships between fuzzy [resp.
In this paper we define anti fuzzy left (right, lateral) ideals, anti fuzzy quasi-ideals, anti fu... more In this paper we define anti fuzzy left (right, lateral) ideals, anti fuzzy quasi-ideals, anti fuzzy bi-ideals and anti fuzzy generalized bi-ideals in ternary semigroups. We also characterize different classes of ternary semigroups by the properties of these ideals. 2010 AMS Classification: 03E72, 20N10
In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a ... more In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a generalization of fuzzy ideals in ternary semigroups. We investigate the related properties of ternary semigroups. The lower and upper parts of fuzzy subsets of a ternary semigroup are defined. Characterizations of regular ternary semigroups by the properties of the lower part of (∈,∈∨ q)-fuzzy left (right) ideals, (∈, ∈∨ q)-fuzzy quasi ideals and (∈, ∈∨ q)-fuzzy bi-ideals are given. Dudek et al. (19) and Ma and Zhan (20) defined (α,β)-fuzzy ideals in hemirings, and investigated some related properties of hemirings. In (21), Jun and Song initiated the study of (α,β)-fuzzy interior ideals of a semigroup. Kazanci and Yamak (22), studied (∈,∈∨ q)- fuzzy bi-ideals of a semigroup. In (23), Wang and Chen defined (α,β)-fuzzy subalgebra of BCH-algebras. Recently, (∈,∈∨q)-fuzzy K-algebra has been studied by Akram (24). It is now natural to investigate similar type of generalizations of the existi...
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Papers by Dr. Noor Rehman