Papers by Lemnaouar ZEDAM
Kragujevac journal of mathematics, 2022
In the present paper, we introduce the notion of (F, G)-derivation on a lattice as a generalizati... more In the present paper, we introduce the notion of (F, G)-derivation on a lattice as a generalization of the notion of (∧, ∨)-derivation. This newly notion is based on two arbitrary binary operations F and G instead of the meet (∧) and the join (∨) operations. Also, we investigate properties of (F, G)-derivation on a lattice in details. Furthermore, we define and study the notion of principal (F, G)derivations as a particular class of (F, G)-derivations. As applications, we provide two representations of a given lattice in terms of its principal (F, G)-derivations.
Revue Africaine de Recherche en Informatique et Mathématiques Appliquées
In this paper we introduce the notions of intuitionistic weak alpha-cut and untuitionistic strong... more In this paper we introduce the notions of intuitionistic weak alpha-cut and untuitionistic strong alpha-cut of intuitionistic fuzzy subsets of a universe X. These notions lead us to show that the set IF(X) of all intuitionistic fuzzy subsets on a universe X can be equipped with a structure of involutive theta-valued Lukasiewicz-Moisil algebra. Conversely, we show that every involutive theta-valued Lukasiewicz-Moisil algebra can be embedded into an algebra of intuitionistic fuzzy subsets. Dans ce travail nous introduisons les notions de alpha-coupes et de alpha-coupes strictes d'un ensemble flou intuitionsiste d'un référentiel X. A l'aide de ces notions, nous montrons que l'ensemble IF(X) des sous-ensembles flous intuitionistes d'un référentiel X admet une structure d'algèbre de Moisil-Lukasiewicz. theta-valente involutive. Réciproquement, nous montrons que toute algèbre de Moisil-Lukasiewicz theta-valente involutive se plonge dans une algèbre des sous-ensembl...
International Journal of Information Technology & Decision Making
The concepts of relations and information measures have importance whenever we deal with medical ... more The concepts of relations and information measures have importance whenever we deal with medical diagnosis problems. The aim of this paper is to investigate the global pandemic COVID-19 scenario using relations and information measures in an interval-valued T-spherical fuzzy (IVTSF) environment. An IVTSF set (IVTSFS) allows describing four aspects of human opinions i.e., membership, abstinence, non-membership, and refusal grade that process information in a significant way and reduce information loss. We propose similarity measures and relations in the IVTSF environment and investigate their properties. Both information measures and relations are applied in a medical diagnosis problem keeping in view the global pandemic COVID-19. How to determine the diagnosis based on symptoms of a patient using similarity measures and relations is discussed. Finally, the advantages of dealing with such problems using the IVTSF framework are demonstrated with examples.
International Journal of Fuzzy System Applications
In this study, the authors explore the complex q-rung orthopair fuzzy sets, which are preferred t... more In this study, the authors explore the complex q-rung orthopair fuzzy sets, which are preferred to be enhanced of the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets, individually. The intention is regarding the buildup of certain innovative operational laws and their related weighted aggregation operators based on the complex q-rung orthopair fuzzy (CQROF) information. In this regard, they characterize certain original neutral or fair operational laws that involve the model of proportional distribution to accomplish a neutral or fair usage to the truth and falsity functions of CQROFSs. Consequently, with these operations, they acquire CQROF weighted fairly aggregation (CQROFWFA) and CQROF ordered weighted fairly aggregation (CQROFOWFA) operators which can neutrally or fairly provide the truth and falsity degrees. They implement an MADM (multi-attribute decision-making) methodology with multiple decision makers and partial weight knowledge in the structure o...
Background/ introduction : To analyze the symptoms of brain cancer in the presence of the strateg... more Background/ introduction : To analyze the symptoms of brain cancer in the presence of the strategic decision-making method under the consideration of human cognitive process, and its basic idea is to divide a universal set into three pair-wise disjoint regions to cognitive information processing. As the ambiguity and complexity of the decision-making environment, cognitive information about alternatives given by decision-makers is ambiguous and contradictory. Brain Carcinoma is one of the massive dangerous diseases in the human body and certain intellectuals have been affected by them. Methods A bunch of intellectuals has generalized the concept of fuzzy set, but the methodology of complex q-rung orthopair fuzzy set (Cq-ROFS) has gotten a huge attraction from different scholars. In the presence of the above theory, this study aims to employ the principle of variation coefficient and generalized variation coefficient similarity measures for Cq-ROFSs and exemplify their properties. To...
International Journal of Analysis and Applications
Recently, Mishra and Srivastava have introduced and studied the notion of fuzzy topology generate... more Recently, Mishra and Srivastava have introduced and studied the notion of fuzzy topology generated by fuzzy relation and several properties were proved. In this paper, we mainly investigate the lattice structure of fuzzy open sets in this topology, and show its various properties and characteristics. Additionally, we extend to this lattice the notions of fuzzy ideal and fuzzy filter. For each of these notions, we fully characterize them in terms of this lattice meet and join operations.
International Journal of Fuzzy Systems
Journal of Function Spaces, 2022
This manuscript is aimed at developing some novel operational laws named scalar neutrality operat... more This manuscript is aimed at developing some novel operational laws named scalar neutrality operation and neutrality addition on picture fuzzy numbers (PFNs). The main focus of this work is to involve the neutral behaviour of the experts towards the priorities of entities where it presents equal degrees to independent membership functions. Moreover, based on these operations, some novel aggregation operators are established to aggregate the different priorities of experts. Some useful relations and characteristics are examined thoroughly. Lastly, the multiattribute group decision-making algorithm in accordance with the suggested operation is illustrated and examined a case study in order to choose a suitable mining company for a mining project along with several numerical examples. The advantages, as well as the superiority of the suggested approach, are exhibited by comparing the results with a few existing methods.
Journal of Mathematics, 2021
The theory of complex dual type-2 hesitant fuzzy sets (CDT-2HFSs) is a blend of two different mod... more The theory of complex dual type-2 hesitant fuzzy sets (CDT-2HFSs) is a blend of two different modifications of fuzzy sets (FSs), called complex fuzzy sets (CFSs) and dual type-2 hesitant fuzzy sets (DT-2HFSs). CDT-2HFS is a proficient technique to cope with unpredictable and awkward information in realistic decision problems. CDT-2HFS is composed of the grade of truth and the grade of falsity, and the grade of truth (also for grade of falsity) contains the grade of primary and secondary parts in the form of polar coordinates with the condition that the sum of the maximum of the real part (also for the imaginary part) of the primary grade (also for the secondary grade) cannot exceed the unit interval [0, 1]. The aims of this manuscript are to discover the novel approach of CDT-2HFS and its operational laws. These operational laws are also justified with the help of an example. Additionally, based on a novel CDT-2HFS, we explored the correlation coefficient (CC) and entropy measures (...
In this paper, we introduced a new concept of single valued neutrosophic graph (SVNG) known as co... more In this paper, we introduced a new concept of single valued neutrosophic graph (SVNG) known as constant single valued neutrosophic graph (CSVNG). Basically, SVNG is a generalization of intuitionistic fuzzy graph (IFG). More specifically, we described and explored somegraph theoretic ideas related to the introduced concepts of CSVNG. An application of CSVNG in a Wi-Fi network system is discussed and a comparison of CSVNG with constant IFG is established showing the worth of the proposed work. Further,<br> several terms like constant function and totally constant function are investigated in the frame-work of CSVNG and their characteristics<br> are studied.
Kybernetika, 2021
In this paper, we introduce six basic types of composition of ternary relations, four of which ar... more In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension.
Iranian Journal of Fuzzy Systems, 2016
In a recent paper, De Baets et al. have characterized the fuzzytolerance and fuzzy equivalence re... more In a recent paper, De Baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. In this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. The reasoninglargely draws upon the notion of the clone relation of a (crisp) relation,introduced recently by Bouremel et al., and the partition of this clone relationin terms of three diff erent types of pairs of clones. More specifi cally, reflexive related clones and irreflexive unrelated clones turn out to play a key role in thecharacterization of the fuzzy tolerance and fuzzy equivalence relations that agiven (crisp) relation is compatible with.
In this paper we study a -fuzzy orders. First, we establish some results which enable us to build... more In this paper we study a -fuzzy orders. First, we establish some results which enable us to build new a -fuzzy orders from crisp order relations. Secondly, we give a result concerning compatible a -fuzzy orders defined on real vector spaces. Also, we characterize a subcategory of totally a -fuzzy orders which are compatible with the usual addition and multiplication on the real line.
Iranian Journal of Fuzzy Systems, 2013
In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As ... more In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.
Problem statement: In this study, we characterize a subcategory of fu zzy orders which were compa... more Problem statement: In this study, we characterize a subcategory of fu zzy orders which were compatible with the usual addition and the mul tiplication by scalar on the real line R. esults and Conclusion: All possible forms of fuzzy orders of this subcateg ory are given.
International Journal of Computational Intelligence Systems, 2021
Recently, we have introduced six types of composition of ternary fuzzy relations. These compositi... more Recently, we have introduced six types of composition of ternary fuzzy relations. These compositions are close in spirit to the composition of binary fuzzy relations. Based on these types of composition, we have introduced several types of transitivity of a ternary fuzzy relation and investigated their basic properties. In this paper, we prove additional properties and characterizations of these types of transitivity of a ternary fuzzy relation. Also, we provide a representation theorem for ternary fuzzy relations satisfying these types of transitivity. Finally, we focus on the problem of closing a ternary fuzzy relation with respect to the proposed types of transitivity.
Complex & Intelligent Systems, 2020
Recently, Yager has established that the notion of q-rung orthopair fuzzy set (q-ROFS) is more ac... more Recently, Yager has established that the notion of q-rung orthopair fuzzy set (q-ROFS) is more accomplished than pythagorean fuzzy set (PyFS) and intuitionistic fuzzy set (IFS) to cope with awkward and complicated information in real decision theory. This notion works with yes-, no- and refusal-type fuzzy information. The constraint of q-ROFS is that the sum of n-power of the truth grade and the n-power of the falsity grade is bounded to unit interval. Generalized dice similarity measures are complimentary concepts quantifying the difference and closeness of q-ROFSs. In this paper, we suggested a number of novel dice similarity measures (DSMs) in the surroundings of the q-ROFS, and we examined some prevailing dice similarity measures and their limitations. In addition, we took the DSMs broad view to some globalized dice similarity measures (GDSMs), and we examined some of their particular cases. We employed the novel suggested GDSMs to the best selections of items on identification ...
Journal of Ambient Intelligence and Humanized Computing, 2021
The concept of fuzzy graph (FG) and its generalized forms have been developed to cope with severa... more The concept of fuzzy graph (FG) and its generalized forms have been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems etc. This paper is based on some developments in generalization of FG theory to deal with situations where imprecision is characterized by four types of membership grades. A novel concept of the domination of T-spherical fuzzy graph (TSFG) is proposed as a common generalization of the domination of FG, intuitionistic fuzzy graph (IFG) and picture fuzzy graph (PFG) based on a recently introduced concept of T-spherical fuzzy set (TSFS). This paper aims to bring into focus the proposal of the graph of T-Spherical fuzzy sets. Moreover, this research analyzes the concepts of domination and double domination theory in T-spherical fuzzy environment. More precisely, the framework of T-spherical fuzzy graphs is introduced, and their related theory is provided with the help of illustrative examples. Further, the domination theory that attached to T-spherical fuzzy graphs is developed. Some cardinality, order, strength and completeness on domination, neighbors in a TSFG bipartite TSFG and double domination set and some results are also studied in the environment of T-spherical fuzzy graphs. As an application, a political campaign is modeled using the proposed work, and explored that how the double domination could deal with political campaign. Finally, a comparison amongst the proposed and the existing studies is developed and advantages of the work in the environment of T-spherical fuzzy graph are discussed.
Soft Computing, 2020
Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool f... more Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool for dealing with uncertainty. A noticeable progress is found concerning the practical use of soft set in decision-making problems. The purpose of this manuscript is to explore the novel of multi-valued picture fuzzy set (MPFS) and multi-valued picture fuzzy soft set (MPFSS) which are the generalizations of the notions of picture fuzzy soft set (PFSS) and multi-fuzzy soft set (MFSS). This notion can be used to express fuzzy information in more general and effective way. In particular, some basic operations such as union, intersection, complement and product of the proposed MPFSS are developed, and their properties are investigated. Furthermore, some aggregation operators corresponding to the proposed MPFSSs are called multi-picture fuzzy soft weighted averaging, multipicture fuzzy soft ordered weighted averaging and multi-picture soft hybrid weighted averaging operators for a collections of MPFSSs are also developed. Moreover, based on these operators, we presented a new method to deal with the multi-attribute group decision-making problems under the multi-valued picture fuzzy soft environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. The graphical interpretation of the explored approaches is also utilized with future directions. Keywords Multi-valued picture fuzzy sets Á Multi-valued picture fuzzy soft sets Á Multi-attribute group decision-making problems Communicated by V. Loia.
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Papers by Lemnaouar ZEDAM