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Journal articles on the topic 'P-Fuzzy Set'
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1
Norahun, Wondwosen Zemene. "P-Fuzzy Ideals and P-Fuzzy Filters in P-Algebras." Advances in Fuzzy Systems 2021 (June 30, 2021): 1–9. http://dx.doi.org/10.1155/2021/4561087.
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In this paper, we introduce the concept of p-fuzzy ideals and p-fuzzy filters in a p-algebra. We provide a set of equivalent conditions for a fuzzy ideal to be a p-fuzzy ideal and a p-algebra to be a Boolean algebra. It is proved that the class of p-fuzzy ideals forms a complete distributive lattice. Moreover, we show that there is an isomorphism between the class of p-fuzzy ideals and p-fuzzy filter.
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S., Subramanian, and Seethalakshmi E. "CERTAIN APPLICATIONS OF P- FUZZY SOFT STRUCTURES." International Journal of Applied and Advanced Scientific Research 2, no. 2 (2017): 294–98. https://doi.org/10.5281/zenodo.1115610.
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In this paper, we investigate the notion of P-fuzzy soft intersection groups which is a generalization of that fuzzy soft groups is provided. By introducing the notion soft fuzzy cosets, soft fuzzy quotient groups based on P-fuzzy soft intersection ideals are established. Finally, isomorphism theorems of P-fuzzy soft intersection groups related to invariant fuzzy soft sets are discussed.
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V., Ramadas, and Anitha B. "ON PSEUDO COMPATIBLE P-FUZZY SOFT RELATIONS." International Journal of Applied and Advanced Scientific Research 3, no. 1 (2017): 7–11. https://doi.org/10.5281/zenodo.1133940.
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MIRANDA, PEDRO, MICHEL GRABISCH, and PEDRO GIL. "p-SYMMETRIC FUZZY MEASURES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, supp01 (2002): 105–23. http://dx.doi.org/10.1142/s0218488502001867.
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In this paper we propose a generalization of the concept of symmetric fuzzy measure based in a decomposition of the universal set in what we have called subsets of indifference. Some properties of these are studied, as well as their Choquet integral. Finally, a degree of interaction between the subsets of indifference is defined.
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V., Ramadas, and P. Antony Samy V. "P-FUZZY LEVEL SUBMODULES OF NEAR RINGS." International Journal of Applied and Advanced Scientific Research 3, no. 1 (2018): 84–88. https://doi.org/10.5281/zenodo.1165264.
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A Technique of generating of P- fuzzy R- sub module by a given arbitrary P- fuzzy set is provided. It is shown that (i) The sum of two P- fuzzy R- sub module of a module M is the P- fuzzy R- sub module generated by their union and (ii) The set of all P- fuzzy sub module of a given module forms a complete lattice. Consequently it is established that the collection of all P- fuzzy R- sub module, having the same values at zero, of M of the lattice of P- fuzzy R- sub module of M. Interrelationship of these finite range sub lattices is established. Finally it is shown that the lattice of all P- fuzzy R- sub module of M can be embedded into a lattice of P- fuzzy R- sub module of M. Through out this paper , M denote as P- fuzzy R- sub module where R is the commutative near ring with unity. Characterization of P- fuzzy left R- sub modules with respect to t- norm are also given.
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Zhang, Qiuxiang, and Lili Wei. "Testing fuzzy hypotheses with crisp data based on p-value." Advances in Engineering Technology Research 7, no. 1 (2023): 171. http://dx.doi.org/10.56028/aetr.7.1.171.2023.
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In this paper, we propose the p-value of fuzzy hypothesis by the concept of projection of the fuzzy relation, the small p-value gives evidence that research hypothesis is true. For the crisp hypothesis, we give the fuzzy set description of the test and prove that the rejection region of the test is the cut set of the fuzzy set. Finally, the p-values of fuzzy hypothesis are given by specific examples.
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Haso, Kardo Sleman, and Alias Barakat Khalaf. "On Cubic Fuzzy Groups and Cubic Fuzzy Normal Subgroups." Science Journal of University of Zakho 10, no. 3 (2022): 105–11. http://dx.doi.org/10.25271/sjuoz.2022.10.3.907.
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In this paper, the notions of cubic fuzzy groups and cubic fuzzy normal subgroups are introduced. The internal, external of cubic sets, (P-,R-) order, (P-,R-) intersection and (P-,R-) union of cubic fuzzy groups are investigated and some related properties were obtained. It is proved that a cubic fuzzy group which is both (internal, external) cubic set. Also we provide condition on cubic fuzzy group to be an internal cubic set. We show that (P-,R-) intersection and (P-,R-) union of cubic fuzzy groups are also cubic fuzzy groups. Also the (P-,R-) intersection, (P-,R-) union of cubic fuzzy normal subgroups are proved to be cubic fuzzy normal subgroup.
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Daraby, Bayaz, та S. B. Nimse. "On fuzzy generalized α-closed set and its applications". Filomat 21, № 2 (2007): 99–108. http://dx.doi.org/10.2298/fil0702099d.
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In this paper, we define and study fuzzy generalized ?-closed sets and r-open sets of a given L-fuzzy topological space and prime element r ? P(L) and coprime element a ? M(L). The concept of L-fuzzy r-open sets was introduced in [10], and it was proved that all r-open sets for L-fuzzy topological space form a new L-fuzzy topology, which is called stratiform L-fuzzy topology. Making use of the fuzzy generalized ?-closed sets, fuzzy generalized ?-continuous map is presented. .
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Hameed, M. Shazib, Zaheer Ahmad, Salman Mukhtar та Asad Ullah. "Some results on χ-single valued neutrosophic subgroups". Indonesian Journal of Electrical Engineering and Computer Science 23, № 3 (2021): 1583. http://dx.doi.org/10.11591/ijeecs.v23.i3.pp1583-1589.
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<p>In this study, we develop a novel structure χ-single valued neutrosophic set, which is a generalization of the intuitionistic set, inconsistent intuitionistic fuzzy set, Pythagorean fuzzy set, spherical fuzzy set, paraconsistent set, etc. Fuzzy subgroups play a vital role in vagueness structure, it differ from regular subgroups in that it is impossible to determine which group elements belong and which do not. In this paper, we investigate the concept of a χ-single valued neutrosophic set and χ-single valued neutrosophic subgroups. We explore the idea of χ-single valued neutrosophic set on fuzzy subgroups and several characterizations related to χ-single valued neutrosophic subgroups are suggested.</p>
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Mehmood, Faisal, Tahir Mahmood, and Qaisar Khan. "Cubic Hesitant Fuzzy Sets and Their Applications to Multi Criteria Decision Making." International Journal of Algebra and Statistics 5, no. 1 (2016): 19. http://dx.doi.org/10.20454/ijas.2016.1055.
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In this paper we introduced cubic hesitant fuzzy set and defined internal (external) cubic hesitant fuzzy set, P(R)-union and P(R)-intersection of cubic hesitant fuzzy sets. Furthermore we defined P(R)-addition and P(R)-multiplication of cubic hesitant fuzzy sets. By using the defined operations of cubic hesitant fuzzy sets we proved their different results. We also defined R-weighted averaging and R-weighted geometric operators for cubic hesitant fuzzy sets and practiced it in multi-criteria decision making problem.
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Gubena, Yeshiwas Mebrat, and Teferi Getachew Alemayehu. "Fuzzy Spectral Spaces and Fuzzy Congruences of a Heyting ADL." Journal of Mathematics 2023 (January 13, 2023): 1–12. http://dx.doi.org/10.1155/2023/4926900.
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In this paper, the space F p of fuzzy prime ideals of Heyting almost distributive lattice H is studied, and it is shown that the collection of all sets M η is a topology on F p , where η is a fuzzy ideal on H and M η = θ ∈ F p | η ⊈ θ . The only compact subset of the space F p is given. A fuzzy congruence relation Θ on H is defined, and the homomorphism between the set of all fuzzy ideals of H and the set of all fuzzy ideals of H / Θ is established. Furthermore, we established an isomorphism between fuzzy spectrum of H and fuzzy spectrum of H / Θ .
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Alghazzawi, Dilshad, Wafaa H. Hanoon, Muhammad Gulzar, Ghazanfar Abbas та Nasreen Kausar. "Certain properties of ω-Q-fuzzy subrings". Indonesian Journal of Electrical Engineering and Computer Science 21, № 2 (2021): 822. http://dx.doi.org/10.11591/ijeecs.v21.i2.pp822-828.
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<p>In this paper, we define the - -fuzzy subring and discussed various fundamental aspects of - -fuzzy subrings. We introduce the concept of - -level subset of this new fuzzy set and prove that - -level subset of - -fuzzy subring form a ring. We define - -fuzzy ideal and show that set of all - -fuzzy cosets form a ring. Moreover, we investigate the properties of homomorphic image of - -fuzzy subring.</p>
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JANSSEN, JEROEN, DIRK VERMEIR, STEVEN SCHOCKAERT, and MARTINE DE COCK. "Reducing fuzzy answer set programming to model finding in fuzzy logics." Theory and Practice of Logic Programming 12, no. 6 (2011): 811–42. http://dx.doi.org/10.1017/s1471068411000093.
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AbstractIn recent years, answer set programming (ASP) has been extended to deal with multivalued predicates. The resulting formalismsallow for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining thestable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where manyefficient solvers have been constructed, to date there is no efficient fuzzy ASP solver. A well-knowntechnique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactlycorrespond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the wayto implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners.
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Farhadinia, Bahram, and Francisco Chiclana. "Extended Fuzzy Sets and Their Applications." Mathematics 9, no. 7 (2021): 770. http://dx.doi.org/10.3390/math9070770.
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This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense.
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Anushka, A. Patil, and S. Patil Pramod. "Evaluation Of Soil Nutrients By Using Type-1 Fuzzy Set." International Journal of Advance and Applied Research 10, no. 3 (2023): 281 to 285. https://doi.org/10.5281/zenodo.7678201.
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<em>To study the status and quantity of available soil nutrients in soil study was conducted in typical farm of Miraj, Sangli district in Maharashtra sample from each farm were collected and scientifically analysed. The subjective information is quantified by using fuzzy sets. The problem of selection of soil containing “high” availability of Nitrogen ( N ), Phosphate ( P ) and “medium” Potassium ( K ) is demonstrated as application of type-1 fuzzy set.</em>
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Alohali, Hanan, Muhammad Bilal Khan, Jorge E. Macías-Díaz, and Fahad Sikander. "On $ \left(\mathit{p}, \mathit{q}\right) $-fractional linear Diophantine fuzzy sets and their applications via MADM approach." AIMS Mathematics 9, no. 12 (2024): 35503–32. https://doi.org/10.3934/math.20241685.
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<p>The integration of internationally sustainable practices into supply chain management methodologies is known as "green supply chain management". Reducing the supply chain's overall environmental impact is the main objective in order to improve corporate connections and the social, ecological, and economic ties with other nations. To accomplish appropriate and accurate measures to address the issue of emergency decision-making, the paper is divided into three major sections. First, the $ \left(p, q\right) $-fractional linear Diophantine fuzzy set represents a new generalization of several fuzzy set theories, including the Pythagorean fuzzy set, $ q $-rung orthopair fuzzy set, linear Diophantine fuzzy set, and $ q $-rung linear Diophantine fuzzy set, with its key features thoroughly discussed. Additionally, aggregation operators are crucial for handling uncertainty in decision-making scenarios. Consequently, algebraic norms for $ \left(p, q\right) $-fractional linear Diophantine fuzzy sets were established based on operational principles. In the second part of the study, we introduced a range of geometric aggregation operators and a series of averaging operators under the $ \left(p, q\right) $-fractional linear Diophantine fuzzy set, all grounded in established operational rules. We also explained some flexible aspects for the invented operators. Furthermore, using the newly developed operators for $ \left(p, q\right) $-fractional linear Diophantine fuzzy information, we constructed the multi-attribute decision-making ($ MADM $) technique to assess the green supply chain management challenge. Last, we compared the ranking results of the produced approaches with the obtained ranking results of the techniques using several numerical instances to demonstrate the validity and superiority of the developed techniques. Finally, a few comparisons between the findings were made.</p>
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Lee, Jeong-Gon, Mohammad Fozouni, Kul Hur, and Young Bae Jun. "A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets." Mathematics 8, no. 6 (2020): 993. http://dx.doi.org/10.3390/math8060993.
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In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.
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Gundeti, Soujanya, and Surender Reddy B. "N-Cubic Picture Fuzzy Linear Spaces." Indian Journal of Science and Technology 17, no. 31 (2024): 3228–43. https://doi.org/10.17485/IJST/v17i31.1793.
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Abstract <strong>Objectives:</strong> The major objective of the present work is to apply the concept of N-cubic structure to N-Picture Fuzzy Linear Spaces. It also examines the fundamental operations such as P-union, P-intersection, R-union and R- intersection of N-Cubic Picture Fuzzy Linear Spaces, ENCPFLS and INCPFLS, and discusses in detail both of them with examples.<strong> Methods:</strong> We define P(R)-union and P(R)- intersection of N- Cubic Picture Fuzzy Linear Spaces and its properties by giving few examples with the motivation of the notion of Cubic Picture Fuzzy Linear Space (CPFLS). <strong>Findings:</strong> The notion of external and internal N-Cubic Picture Fuzzy Linear Spaces including their properties are derived. <strong>Novelty:</strong> For the first time, we present the idea of N-Cubic Picture Fuzzy Linear Spaces (NCPFLS), which has been developed on the basis of interval valued N- Picture fuzzy linear spaces (IVNPFLS) and N-Picture fuzzy linear spaces (NPFLS). In addition, we have studied the basic operations which includes P(R)-union and P(R)- intersection on ENCPFLS and INCPFLS. <strong>Keywords:</strong> N­-picture fuzzy set, N-­cubic set, N-Picture fuzzy linear space, Interval valued N-Picture fuzzy linear spaces, P(R)­ union, P(R)­intersection AMS Subject Classification: 08A72, 03E72
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Shagari, Mohammed Shehu, Saima Rashid, Khadijah M. Abualnaja, and Monairah Alansari. "On nonlinear fuzzy set-valued $ \Theta $-contractions with applications." AIMS Mathematics 6, no. 10 (2021): 10431–48. http://dx.doi.org/10.3934/math.2021605.
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<abstract><p>Among various improvements in fuzzy set theory, a progressive development has been in process to investigate fuzzy analogues of fixed point theorems of the classical fixed point results. In this direction, taking the ideas of $ \theta $-contractions as well as Feng-Liu's approach into account, some new fuzzy fixed point results for nonlinear fuzzy set-valued $ \theta $-contractions in the framework of metric-like spaces are introduced in this paper without using the usual Pompeiu-Hausorff distance function. Our established concepts complement, unify and generalize a few important fuzzy and classical fixed point theorems in the corresponding literature. A handful of these special cases of our notions are pointed and analyzed. Some of the main results herein are further applied to derive their analogues in metric-like spaces endowed with partial ordering and binary relations. Comparisons and nontrivial examples are given to authenticate the hypotheses and significance of the obtained ideas.</p></abstract>
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Prasertpong, Rukchart. "Roughness of soft sets and fuzzy sets in semigroups based on set-valued picture hesitant fuzzy relations." AIMS Mathematics 7, no. 2 (2022): 2891–928. http://dx.doi.org/10.3934/math.2022160.
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<abstract><p>In the philosophy of rough set theory, the methodologies of rough soft sets and rough fuzzy sets have been being examined to be efficient mathematical tools to deal with unpredictability. The basic of approximations in rough set theory is based on equivalence relations. In the aftermath, such theory is extended by arbitrary binary relations and fuzzy relations for more wide approximation spaces. In recent years, the notion of picture hesitant fuzzy relations by Mathew et al. can be considered as a novel extension of fuzzy relations. Then this paper proposes extended approximations into rough soft sets and rough fuzzy sets from the viewpoint of its. We give corresponding examples to illustrate the correctness of such approximations. The relationships between the set-valued picture hesitant fuzzy relations with the upper (resp., lower) rough approximations of soft sets and fuzzy sets are investigated. Especially, it is shown that every non-rough soft set and non-rough fuzzy set can be induced by set-valued picture hesitant fuzzy reflexive relations and set-valued picture hesitant fuzzy antisymmetric relations. By processing the approximations and advantages in the new existing tools, some terms and products have been applied to semigroups. Then, we provide attractive results of upper (resp., lower) rough approximations of prime idealistic soft semigroups over semigroups and fuzzy prime ideals of semigroups induced by set-valued picture hesitant fuzzy relations on semigroups.</p></abstract>
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Macodi-Ringia, Amila Pagadilan, and Gaudencio Cempron Petalcorin. "On Intuitionistic Fuzzy Hyper GR-ideals in Hyper GR-algebras." European Journal of Pure and Applied Mathematics 13, no. 2 (2020): 246–57. http://dx.doi.org/10.29020/nybg.ejpam.v13i2.3660.
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Let $P(H)$ be the power set of $H$. Consider $\ds P^*(H)=P(H)\setminus\{\phi\}$. A hyperoperation on a nonempty set $H$ is a function $\ds\circledast:H\times H\rightarrow P^*(H).$ A set $H$ endowed with a family $\Gamma$ of hyperoperations is called ahyperstructure. Hyperstructures have many applications to several sectors of both pure and applied sciences. One of the well developed hyperstructures is the hyper BCI-algebra. Recently, by following this hyperstructure, a new hyperstructure was created by Indangan et al., named as hyper GR-algebras. In this paper, fuzzy set and intuitionistic fuzzy set are applied to hyper GR-algebra. Particularly, the fuzzy hyper GR-ideal of type 1 and the intuitionistic fuzzy hyper GR-ideal are introduced, and a relationship between them are obtained. Moreover, some of their characterizations are established by the use of their level subsets.
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Kim, Jin Bai, and Kern O. Kymn. "Rational choice function derived from a fuzzy preference." International Journal of Mathematics and Mathematical Sciences 11, no. 1 (1988): 43–45. http://dx.doi.org/10.1155/s0161171288000080.
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We shall prove that every fuzzy rational choice function is fuzzy regular (see Richter [6, p. 36] ), count the total number of the fuzzy rational choice ftmctions on a set of four elements and consider a semigroup of all fuzzy rational choice functions on a set.
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Balamurugan, M., Khalil H. Hakami, Moin A. Ansari, Anas Al-Masarwah, and K. Loganathan. "Quadri-Polar Fuzzy Fantastic Ideals in BCI-Algebras: A TOPSIS Framework and Application." European Journal of Pure and Applied Mathematics 17, no. 4 (2024): 3129–55. http://dx.doi.org/10.29020/nybg.ejpam.v17i4.5429.
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A quadri-polar fuzzy ($q\mathcal{P}$-$\mathcal{F}$) set is an extension of a traditional fuzzy set that uses four degrees of membership to represent different aspects of belonging to provide a more detailed framework for handling uncertainty and vagueness. In this paper, we propose the notion of quadri-polar-$(\varpi,\vartheta)$-fuzzy fantastic ideals ($q\mathcal{P}$-$(\varpi,\vartheta)$-$\mathcal{FFI}(s)$) in BCI-algebras based on $q\mathcal{P}$-$\mathcal{F}$ set. Also, the notion of quadri-polar-$(\in_{\tilde{\sigma}}, \in_{\tilde{\sigma}} \vee q_{\tilde{\tau}})$-fuzzy fantastic ideals ($q\mathcal{P}$-$(\in_{\tilde{\sigma}}, \in_{\tilde{\sigma}} \vee q_{\tilde{\tau}})$-$\mathcal{FFI}(s)$) is introduced, and the characterizations for an $\in_{\tilde{\sigma}}$-$q\mathcal{P}$-$\mathcal{F}$ set and $q_{\tilde{\tau}}$-$q\mathcal{P}$-$\mathcal{F}$ set to be quadri-polar fuzzy ideals ($q\mathcal{P}$-$\mathcal{FI}$) in BCI-algebras are established. Furthermore, we present the $q\mathcal{P}$-$\mathcal{F}$ TOPSIS technique for multi-criteria Group decision-making (MCGDM), which is a natural extension of the TOPSIS method and used to rank and choose the best alternatives under $q\mathcal{P}$-$\mathcal{F}$ positive and negative ideal solutions. Finally, practical examples interpreting the applicability of our proposed $q\mathcal{P}$-$\mathcal{F}$-TOPSIS are solved.
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Rahman, Atiqe Ur, Muhammad Saeed, Hamiden Abd El-Wahed Khalifa, and Walaa Abdullah Afifi. "Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets." AIMS Mathematics 7, no. 3 (2022): 3866–95. http://dx.doi.org/10.3934/math.2022214.
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<abstract><p>Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.</p></abstract>
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Kaur, Sandeep, Alkan Özkan, and Faizah D. Alanazi. "A new perspective on fuzzy mapping theory with invertedly open and closed mappings." AIMS Mathematics 10, no. 1 (2025): 921–31. https://doi.org/10.3934/math.2025043.
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<p>In fuzzy mapping theories, we examine fuzzy closedness and fuzzy continuity of a mapping $ \phi $, characterized respectively by $ \overline{\phi(M)} \subseteq \phi(\overline{M}) $ and $ \phi(\overline{M}) \subseteq \overline{\phi(M)} $, for every fuzzy set $ M $ in $ V $. Here, $ (V, \tau) $ represents a fuzzy topological space (FTs), where $ V = \{v\} $ denotes a set of points. This reveals a fundamental symmetry between the two mappings in connection with the closure operator. On the other hand, the fuzzy openness of a mapping $ \phi $ is characterized by $ \phi(M^\circ) &lt; (\phi(M))^\circ $ for every fuzzy set $ M $ in $ V $. Considering the above statements, it is logical to explore how fuzzy continuity relates to the interior operator. Building on this, we introduce the notion of the invertedly fuzzy open mapping, defined as $ (\phi(M))^\circ &lt; \phi(M^\circ) $ for any fuzzy set $ M $ in $ V $, and discuss its relationship with fuzzy continuity. In our study, we define and analyze invertedly fuzzy open and invertedly fuzzy closed mappings, along with their respective properties. We also delve into how these mappings connect with fuzzy continuous mappings. Furthermore, we examine a characterization of fuzzy homeomorphism for bijective mappings concerning the interior operator.</p>
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Jawad, Muhammad, Niat Nigar, Sarka Hoskova-Mayerova, Bijan Davvaz, and Muhammad Haris Mateen. "Fundamental theorems of group isomorphism under the framework of complex intuitionistic fuzzy set." AIMS Mathematics 10, no. 1 (2025): 1900–1920. https://doi.org/10.3934/math.2025088.
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<p>Algebraic homomorphisms are essential mathematical structures that sustain operations across algebraic systems such as groups, rings, and fields. These mappings not only preserve the validity of algebraic operations but also make it easier to investigate structural similarities and equivalences across distinct algebraic entities. In this article, we establish the group isomorphism under the complex intuitionistic fuzzy set, an extended form of the complex fuzzy set that adds the complex degree of non-membership functions, which plays a significant role in the decision-making process. The complex algebraic structure provides effective tools for understanding complex phenomena. We discuss the more intricate features of homomorphism and isomorphism in the framework of a complex intuitionistic fuzzy set. In addition, we introduce the complex intuitionistic fuzzy normal subgroups. We establish the relationship between two complex intuitionistic fuzzy subgroups and analyze of complex intuitionistic fuzzy isomorphisms among these subgroups, proving the important theorems. Furthermore, we establish examples to explore the concept of complex intuitionistic fuzzy subgroups.</p>
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Razaq, Abdul, and Ghaliah Alhamzi. "On Pythagorean fuzzy ideals of a classical ring." AIMS Mathematics 8, no. 2 (2023): 4280–303. http://dx.doi.org/10.3934/math.2023213.
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<abstract><p>The Pythagorean fuzzy set is an extension of the intuitionistic fuzzy set and is an effective approach of handling uncertain situations. Ring theory is a prominent branch of abstract algebra, vibrant in wide areas of current research in mathematics, computer science and mathematical/theoretical physics. In the theory of rings, the study of ideals is significant in many ways. Keeping in mind the importance of ring theory and Pythagorean fuzzy set, in the present article, we characterize the concept of Pythagorean fuzzy ideals in classical rings and study its numerous algebraic properties. We define the concept of Pythagorean fuzzy cosets of a Pythagorean fuzzy ideal and prove that the set of all Pythagorean fuzzy cosets of a Pythagorean fuzzy ideal forms a ring under certain binary operations. Furthermore, we present Pythagorean fuzzy version of the fundamental theorem of ring homomorphism. We also introduce the concept of Pythagorean fuzzy semi-prime ideals and give a detailed exposition of its different algebraic characteristics. In the end, we characterized regular rings by virtue of Pythagorean fuzzy ideals.</p></abstract>
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Höhle, Ulrich, Hans-E. Porst, and Alexander P. Sostak. "Fuzzy functions: a fuzzy extension of the category SET and some related categories." Applied General Topology 1, no. 1 (2000): 115. http://dx.doi.org/10.4995/agt.2000.3028.
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<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -&gt; L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>
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Alemayehu, Teferi Getachew. "Fuzzy Ideals in Pseudo-Hoop Algebras." International Journal of Mathematics and Mathematical Sciences 2022 (September 23, 2022): 1–10. http://dx.doi.org/10.1155/2022/4643252.
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In this study, fuzzy ideals in pseudo-hoop algebras are presented. Also, we investigate fuzzy congruences relations on pseudo-hoop algebras induced by fuzzy ideals. By using fuzzy ideals, we create the fuzzy quotient pseudo-hoop algebras and identify and demonstrate the one-to-one relationship between the set of all normal fuzzy ideals of a pseudo-hoop algebra H with conditions p D N and the set of all fuzzy congruences relation on H . Additionally, we investigate the relationship between fuzzy ideals and fuzzy filters in pseudo-hoop algebras by considering the set of complement elements of pseudo-hoop algebras. Lastly, we study fuzzy prime ideals and fuzzy ⊙ -prime ideals and their relation.
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Soujanya, Gundeti, and B. Surender Reddy. "N-Cubic Picture Fuzzy Linear Spaces." Indian Journal Of Science And Technology 17, no. 31 (2024): 3228–43. http://dx.doi.org/10.17485/ijst/v17i31.1793.
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Objectives: The major objective of the present work is to apply the concept of N-cubic structure to N-Picture Fuzzy Linear Spaces. It also examines the fundamental operations such as P-union, P-intersection, R-union and R- intersection of N-Cubic Picture Fuzzy Linear Spaces, ENCPFLS and INCPFLS, and discusses in detail both of them with examples. Methods: We define P(R)-union and P(R)- intersection of N- Cubic Picture Fuzzy Linear Spaces and its properties by giving few examples with the motivation of the notion of Cubic Picture Fuzzy Linear Space (CPFLS). Findings: The notion of external and internal N-Cubic Picture Fuzzy Linear Spaces including their properties are derived. Novelty: For the first time, we present the idea of N-Cubic Picture Fuzzy Linear Spaces (NCPFLS), which has been developed on the basis of interval valued N- Picture fuzzy linear spaces (IVNPFLS) and N-Picture fuzzy linear spaces (NPFLS). In addition, we have studied the basic operations which includes P(R)-union and P(R)- intersection on ENCPFLS and INCPFLS. Keywords: N-picture fuzzy set, N-cubic set, N-Picture fuzzy linear space, Interval valued N-Picture fuzzy linear spaces, P(R) union, P(R)intersection AMS Subject Classification: 08A72, 03E72
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Riaz, Muhammad, Aurang Zeb, Fawad Ali, Muhammad Naeem, and Sama Arjika. "Fermatean Cubic Fuzzy Aggregation Operators and Their Application in Multiattribute Decision-Making Problems." Journal of Function Spaces 2022 (November 30, 2022): 1–18. http://dx.doi.org/10.1155/2022/3664302.
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The purpose of aggregation methods is to convert a list of objects of a set into a single object of the same set usually by an n -arry function, so-called aggregation operator. The key features of this work are the aggregation operators, because they are based on a novel set called Fermatean cubic fuzzy set (F-CFS). F-CFS has greater spatial scope and can deal with more ambiguous situations where other fuzzy set extensions fail to support them. For this purpose, the notion of F-CFS is defined. F-CFS is the transformation of intuitionistic cubic fuzzy set (I-CFS), Pythagorean cubic fuzzy set (P-CFS), interval-valued cubic fuzzy set, and basic orthopair fuzzy set and is grounded on the constraint that “the cube of the supremum of membership plus nonmembership degree is ≤ 1 ”. We have analyzed some properties of Fermatean cubic fuzzy numbers (F-CFNs) as they are the alteration of basic properties of I-CFS and P-CFS. We also have defined the score and deviation degrees of F-CFNs. Moreover, the distance measuring function between two F-CFNs is defined which shows the space between two F-CFNs. Based on this notion, the aggregation operators namely Fermatean cubic fuzzy-weighted averaging operator (F-CFWA), Fermatean cubic fuzzy-weighted geometric operator (F-CFWG), Fermatean cubic fuzzy-ordered-weighted averaging operator (F-CFOWA), and Fermatean cubic fuzzy-ordered-weighted geometric operator (F-CFOWG) are developed. Furthermore, the notion is applied to multiattribute decision-making (MADM) problem in which we presented our objectives in the form of F-CFNs to show the effectiveness of the newly developed strategy.
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Kanwal, Shazia, Asif Ali, Abdullah Al Mazrooei, and Gustavo Santos-Garcia. "Existence of fuzzy fixed points of set-valued fuzzy mappings in metric and fuzzy metric spaces." AIMS Mathematics 8, no. 5 (2023): 10095–112. http://dx.doi.org/10.3934/math.2023511.
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<abstract> <p>A contemporary fuzzy technique is employed in the current study to generalize some established and recent findings. For researchers, fixed point (FP) procedures are highly advantageous and appealing mechanisms. Discovering fuzzy fixed points of fuzzy mappings (FM) meeting Nadler's type contraction in complete fuzzy metric space (FMS) and?iri? type contraction in complete metric spaces (MS) is the core objective of this research. The outcomes are backed up by example and applications that highlight these findings. There are also preceding conclusions that are given as corollaries from the relevant literature. In this mode, numerous consequences exist in the significant literature are extended and combined by our findings.</p> </abstract>
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Qiyas, Muhammad, Muhammad Naeem, and Neelam Khan. "Fractional orthotriple fuzzy Choquet-Frank aggregation operators and their application in optimal selection for EEG of depression patients." AIMS Mathematics 8, no. 3 (2023): 6323–55. http://dx.doi.org/10.3934/math.2023320.
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<abstract><p>The fractional orthotriple fuzzy sets (FOFSs) are a generalized fuzzy set model that is more accurate, practical, and realistic. It is a more advanced version of the present fuzzy set models that can be used to identify false data in real-world scenarios. Compared to the picture fuzzy set and Spherical fuzzy set, the fractional orthotriple fuzzy set (FOFS) is a powerful tool. Additionally, aggregation operators are effective mathematical tools for condensing a set of finite values into one value that assist us in decision making (DM) challenges. Due to the generality of FOFS and the benefits of aggregation operators, we established two new aggregation operators in this article using the Frank t-norm and conorm operation, which we have renamed the fractional orthotriple fuzzy Choquet-Frank averaging (FOFCFA) and fractional orthotriple fuzzy Choquet-Frank geometric (FOFCFG) operators. A few of these aggregation operators' characteristics are also discussed. To demonstrate the efficacy of the introduced work, the multi-attribute decision making (MADM) algorithm is discussed along with applications. To demonstrate the validity and value of the suggested work, a comparison of the proposed work has also been provided.</p></abstract>
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Al-Qudah, Yousef, Mazlan Hassan, and Nasruddin Hassan. "Fuzzy Parameterized Complex Multi-Fuzzy Soft Expert Set Theory and Its Application in Decision-Making." Symmetry 11, no. 3 (2019): 358. http://dx.doi.org/10.3390/sym11030358.
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Contemporary research has refined systems with complex fuzzy sets in order to improve the design and model of real-life applications. Symmetry and antisymmetry are basic characteristics of binary relations used when modeling the decision maker’s preferences. A recent focus has been the analysis of a complex data set using the properties of fuzzy concept lattice and the complex soft set. We will introduce a new concept to represent the information which utilizes the time factor, called fuzzy parameterized complex multi-fuzzy soft expert set ( F P - CMFSES ), and investigate part of its fundamental properties. This F P - CMFSES model allows us to validate the information provided by an expert, at a given phase of time, using the properties of complex fuzzy sets. We then construct an algorithm based on this concept by converting it from the complex state to the real state. Eventually, we implement it to a decision-making problem to demonstrate the applicability of the suggested method. A comparison among F P - CMFSES and other existing methods is made to expose the dominance of the suggested method. Apart from that, we also propose the weighted fuzzy parameterized complex multi-fuzzy soft expert set and investigate its application to decision-making.
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Saeed, Tareq. "Intuitionistic fuzzy variational inequalities and their applications." AIMS Mathematics 9, no. 12 (2024): 34289–310. https://doi.org/10.3934/math.20241634.
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<p>In this paper, a new class of generalized convex (concave) fuzzy mappings are introduced, which is called intuitionistic convex (concave) fuzzy mappings from the convex set $ {K\subseteq \mathbb{R}}^{n} $ to the set of intuitionistic fuzzy numbers. By using the concept of epigraph, the characterization of intuitionistic convex fuzzy mappings is also discussed. Different types of intuitionistic convex (concave) fuzzy mappings are defined and their properties are investigated. Then, we discuss some applications of intuitionistic fuzzy convex mappings in fuzzy optimization. Additionally, some variational inequalities, known as intuitionistic fuzzy variational inequality and intuitionistic fuzzy variational mixed inequalities, are introduced. The results obtained in this paper can be regarded as refinements and extensions of previously established results.</p>
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Al-Qurashi, Maysaa, Mohammed Shehu Shagari, Saima Rashid, Y. S. Hamed, and Mohamed S. Mohamed. "Stability of intuitionistic fuzzy set-valued maps and solutions of integral inclusions." AIMS Mathematics 7, no. 1 (2021): 315–33. http://dx.doi.org/10.3934/math.2022022.
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<abstract><p>In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $ b $-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $ (\alpha, \beta) $-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.</p></abstract>
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Wajiansyah, Agusma, Supriadi Supriadi, Syarifah Nur, and Arief Bramanto Wicaksono P. "Implementasi Fuzzy Logic Pada Robot Line Follower." Jurnal Teknologi Informasi dan Ilmu Komputer 5, no. 4 (2018): 395. http://dx.doi.org/10.25126/jtiik.201854747.
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<p>Pada penelitian ini, akan diterapkan konsep <em>fuzzy logic </em>sebagai kendali cerdas pada robot line follower. Aturan pada <em>fuzzy logic</em> menggunakan metode <em>mamdani</em>. Sebagai input kendali digunakan 2 nilai hasil pembacaan sensor garis yang merupakan data biner 6-bit, yaitu pembacaan pada saat sampling ke-(<em>k</em>)<em> </em>dan pembacaan pada saat sampling ke-(<em>k-1</em>). Hasil pembacaan sensor diberi bobot dengan range nilai dari 0 s/d 255 yang merupakan semesta pembicaraan dari fuzzy set input ini. Setiap fuzzy set input menggunakan 5 <em>membershif function, </em>dan <em>rule base </em>yang digunakan sebanyak 25. Pada fuzzy set output digunakan 5 <em>membership function </em>dengan semesta pembicaraan adalah -127 s/d +127. output fuzzy merupakan bilangan crips tunggal yang didapat dengan menggunakan metode COG (<em>Center of Gravity</em>). Nilai crips output ini digunakan sebagai nilai deviasi untuk mengatur nilai PWM pada motor penggerak roda kiri dan kanan dari robot line follower. Pengujian fungsi kendali menggunakan metode matematis dan simulasi berbasis Simulink. Dari hasil yang didapat menjelaskan bahwa robot dapat bergerak sesuai dengan desain rule base yang digunakan.</p><p> </p><p> </p><p><strong><em>Abstract</em></strong></p><p><strong><em> </em></strong><em>In this research, the fuzzy logic concept will be applied as intelligent control on line-follower robot. The rules on fuzzy logic use the Mamdani method. As control inputs, used 2 values of line sensor readings are in the form of 6-bit binary data. the input is the sensor reading at the time of the kth sampling and the reading at the k-sampling moment. The sensor readings are weighted with a range of values from 0 s / d 255 which is the universe of speech from the fuzzy set of these inputs. Each fuzzy set of inputs uses 5 membership function, and the base rule used is 25. In fuzzy set output used 5 membership functions with the universe of talk is -127 s / d +127. the fuzzy output is a single crips number obtained by using the COG (Center of Gravity) method. This output crips value is used as the deviation value to set the PWM value on the left and right wheel drive motor of the line follower robot. Tests of control functions using mathematical methods and Simulink based simulations. From the results obtained to explain that the robot can move in accordance with the design of the base rule used</em></p><p> </p>
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Hifza, Muhammad Gulistan, Zahid Khan, et al. "A new fuzzy decision support system approach; analysis and applications." AIMS Mathematics 7, no. 8 (2022): 14785–825. http://dx.doi.org/10.3934/math.2022812.
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<abstract> <p>The current study proposes the idea of the N-cubic Pythagorean fuzzy set with their basic arithmetic operations to aggregate these sets. We define the score and accuracy functions for the comparison purpose. Finally, we discuss Chang's extent analysis of AHP under the environment of the N-cubic Pythagorean fuzzy set using the idea of triangular N-cubic Pythagorean fuzzy set. As an application, we discuss the reason for the downfall of international airlines using the developed approach.</p> </abstract>
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Al-shami, Tareq M., José Carlos R. Alcantud, and Abdelwaheb Mhemdi. "New generalization of fuzzy soft sets: $ (a, b) $-Fuzzy soft sets." AIMS Mathematics 8, no. 2 (2023): 2995–3025. http://dx.doi.org/10.3934/math.2023155.
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<abstract><p>Many models of uncertain knowledge have been designed that combine expanded views of fuzziness (expressions of partial memberships) with parameterization (multiple subsethood indexed by a parameter set). The standard orthopair fuzzy soft set is a very general example of this successful blend initiated by fuzzy soft sets. It is a mapping from a set of parameters to the family of all orthopair fuzzy sets (which allow for a very general view of acceptable membership and non-membership evaluations). To expand the scope of application of fuzzy soft set theory, the restriction of orthopair fuzzy sets that membership and non-membership must be calibrated with the same power should be removed. To this purpose we introduce the concept of $ (a, b) $-fuzzy soft set, shortened as $ (a, b) $-FSS. They enable us to address situations that impose evaluations with different importances for membership and non-membership degrees, a problem that cannot be modeled by the existing generalizations of intuitionistic fuzzy soft sets. We establish the fundamental set of arithmetic operations for $ (a, b) $-FSSs and explore their main characteristics. Then we define aggregation operators for $ (a, b) $-FSSs and discuss their main properties and the relationships between them. Finally, with the help of suitably defined scores and accuracies we design a multi-criteria decision-making strategy that operates in this novel framework. We also analyze a decision-making problem to endorse the validity of $ (a, b) $-FSSs for decision-making purposes.</p></abstract>
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Jiang, Man. "Properties of <i>R<sub>0</sub></i>-algebra based on hesitant fuzzy MP filters and congruence relations." AIMS Mathematics 7, no. 7 (2022): 13410–22. http://dx.doi.org/10.3934/math2022741.
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<abstract><p>The hesitant fuzzy MP filter and the hesitant fuzzy congruence relation of algebra are introduced in this study, and their properties are investigated. The comparable characterization of a hesitant fuzzy MP filter is then provided. Furthermore, we established that the set of all hesitant fuzzy congruence relations and the set of all hesitant fuzzy MP filters of <italic>R<sub>0</sub></italic>-algebra are complete lattice isomorphism based on the features of the hesitant fuzzy congruence relation in <italic>R<sub>0</sub></italic>-algebra.</p></abstract>
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Jiang, Man. "Properties of <i>R<sub>0</sub></i>-algebra based on hesitant fuzzy MP filters and congruence relations." AIMS Mathematics 7, no. 7 (2022): 13410–22. http://dx.doi.org/10.3934/math.2022741.
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<abstract><p>The hesitant fuzzy MP filter and the hesitant fuzzy congruence relation of algebra are introduced in this study, and their properties are investigated. The comparable characterization of a hesitant fuzzy MP filter is then provided. Furthermore, we established that the set of all hesitant fuzzy congruence relations and the set of all hesitant fuzzy MP filters of <italic>R<sub>0</sub></italic>-algebra are complete lattice isomorphism based on the features of the hesitant fuzzy congruence relation in <italic>R<sub>0</sub></italic>-algebra.</p></abstract>
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Ihsan, Muhammad, Muhammad Saeed, Alhanouf Alburaikan, and Hamiden Abd El-Wahed Khalifa. "Product evaluation through multi-criteria decision making based on fuzzy parameterized Pythagorean fuzzy hypersoft expert set." AIMS Mathematics 7, no. 6 (2022): 11024–52. http://dx.doi.org/10.3934/math.2022616.
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<abstract><p>In many real-world decision-making situations, uncertain nature of parameters is to be discussed to have unbiased and reliable decisions. Most of the existing literature on fuzzy soft set and its related structures ignored the uncertain parametric attitudes. The concept of fuzzy parameterization is launched to tackle the limitations of existing soft set-like models. Several extensions have already been introduced by using the concept of fuzzy parameterization. In this research, a novel extension, fuzzy parameterized Pythagorean fuzzy hypersoft expert set is aimed to be characterized. This model is more flexible and reliable as compared to existing models because it addresses their insufficiencies for the consideration of multi-argument approximate function. With the entitlement of this function, it tackles the real-life scenarios where each attribute is meant to be further classified into its respective sub-attribute valued disjoint set. The characterization of fuzzy parameterized Pythagorean fuzzy hypersoft expert set is accomplished by employing theoretic, axiomatic and algorithmic approaches. In order to validate the proposed model, an algorithm is proposed to study its role in decision-making while dealing with real-world problem. Moreover, the proposed model is compared with the most relevant existing models to assess its advantageous aspects.</p></abstract>
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Thangammal, R., M. Saraswathi, A. Vadivel, et al. "Fuzzy Nano z-locally Closed Sets, Extremally Disconnected Spaces, Normal Spaces, and Their Application." Advances in Fuzzy Systems 2022 (May 11, 2022): 1–9. http://dx.doi.org/10.1155/2022/3364170.
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In this paper, we introduce fuzzy nano (resp. δ, δS, P and Z) locally closed set and fuzzy nano (resp. δ, δS, P and Z) extremally disconnected spaces in fuzzy nano topological spaces. Also, we introduce some new spaces called fuzzy nano (resp. δ, δS, P and Z) normal spaces and strongly fuzzy nano (resp. δ, δS, P and Z) normal spaces with the help of fuzzy nano (resp. δ, δS, P and Z)-open sets in fuzzy nano topological space. Numerical data is used to quantify the provided features. Furthermore, using fuzzy nano topological spaces, an algorithm for multiple attribute decision-making (MADM) with an application in medical diagnosis is devised.
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Ali, Sumbal, Asad Ali, Ahmad Bin Azim, Ahmad ALoqaily, and Nabil Mlaiki. "Averaging aggregation operators under the environment of <i>q</i>-rung orthopair picture fuzzy soft sets and their applications in MADM problems." AIMS Mathematics 8, no. 4 (2023): 9027–53. http://dx.doi.org/10.3934/math.2023452.
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<abstract><p><italic>q</italic>-Rung orthopair fuzzy soft set handles the uncertainties and vagueness by membership and non-membership degree with attributes, here is no information about the neutral degree so to cover this gap and get a generalized structure, we present hybrid of picture fuzzy set and <italic>q</italic>-rung orthopair fuzzy soft set and initiate the notion of <italic>q</italic>-rung orthopair picture fuzzy soft set, which is characterized by positive, neutral and negative membership degree with attributes. The main contribution of this article is to investigate the basic operations and some averaging aggregation operators like <italic>q</italic>-rung orthopair picture fuzzy soft weighted averaging operator and <italic>q</italic>-rung orthopair picture fuzzy soft order weighted averaging operator under the environment of <italic>q</italic>-rung orthopair picture fuzzy soft set. Moreover, some fundamental properties and results of these aggregation operators are studied, and based on these proposed operators we presented a stepwise algorithm for MADM by taking the problem related to medical diagnosis under the environment of <italic>q</italic>-rung orthopair picture fuzzy soft set and finally, for the superiority we presented comparison analysis of proposed operators with existing operators.</p></abstract>
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Abu Bakar, Nashirah, Sofian Rosbi, and Azizi Abu Bakar. "Evaluation of Students Performance using Fuzzy Set Theory in Online Learning of Islamic Finance Course." International Journal of Interactive Mobile Technologies (iJIM) 15, no. 07 (2021): 202. http://dx.doi.org/10.3991/ijim.v15i07.20191.
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<p class="0abstract"><strong>Abstract—</strong>The objective of this study is to evaluate student performance using fuzzy set theory in Islamic Finance online course. This study focuses on selecting best individual among 30 students that registered for Islamic Bank Management course. The variables that involved in this study are online quiz marks, online assignment marks and online self-learning time. The outcome of the fuzzy set analysis was compared with final examination data. The methodology of this study involving converting real data to fuzzy set, intersection calculation, decision analysis using maximizing approach. Result of fuzzy set shows the best individual score is 0.9. This student selected as best candidate for student performance in online learning with considering three variables namely online quizzes, online assignment and online self-learning hour. The comparison with final examination marks shows a good agreement with fuzzy set theory that concluded best individual from fuzzy set theory exhibits highest performance during final examination. The main finding of this study can help educators to predict the best performer in online learning class. In the same time, finding of this study can act as guideline to advise students in achieving their desired grade for online learning course.</p>
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Al-Sharoa, Doaa. "(α1, 2, β1, 2)-complex intuitionistic fuzzy subgroups and its algebraic structure". AIMS Mathematics 8, № 4 (2023): 8082–116. http://dx.doi.org/10.3934/math.2023409.
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<abstract> <p>A complex intuitionistic fuzzy set is a generalization framework to characterize several applications in decision making, pattern recognition, engineering, and other fields. This set is considered more fitting and coverable to Intuitionistic Fuzzy Sets (IDS) and complex fuzzy sets. In this paper, the abstraction of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$) complex intuitionistic fuzzy sets and (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups were introduced regarding to the concept of complex intuitionistic fuzzy sets. Besides, we show that (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroup is a general form of every complex intuitionistic fuzzy subgroup. Also, each of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy normal subgroups and cosets are defined and studied their relationship in the sense of the commutator of groups and the conjugate classes of group, respectively. Furthermore, some theorems connected the (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroup of the classical quotient group and the set of all (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy cosets were studied and proved. Additionally, we expand the index and Lagrange's theorem to be suitable under (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups.</p> </abstract>
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Zeng, Wenyi, Rong Ma, Deqing Li, Qian Yin, Zeshui Xu, and Ahmed Mostafa Khalil. "Novel operations of weighted hesitant fuzzy sets and their group decision making application." AIMS Mathematics 7, no. 8 (2022): 14117–38. http://dx.doi.org/10.3934/math.2022778.
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<abstract><p>Weighted hesitant fuzzy set (WHFS) is an extension of hesitant fuzzy set (HFS), in which the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. In this paper, we redefine the union and intersection operations of weighted hesitant fuzzy elements (WHFEs), investigate their operation properties, and propose the variance function of the weighted hesitant fuzzy element (WHFE) to compare WHFEs. Furthermore, we develop two aggregation operators such as weighted hesitant fuzzy ordered weighted averaging (WHFOWA) and weighted hesitant fuzzy ordered weighted geometric (WHFOWG) operators to aggregate weighted hesitant fuzzy information, and present multiple-attribute group decision making algorithm under weighted hesitant fuzzy environment. Finally, four numerical examples are used to illustrate the effectiveness of our proposed aggregation operators.</p></abstract>
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Ashraf, Shahzaib, Huzaira Razzaque, Muhammad Naeem, and Thongchai Botmart. "Spherical q-linear Diophantine fuzzy aggregation information: Application in decision support systems." AIMS Mathematics 8, no. 3 (2023): 6651–81. http://dx.doi.org/10.3934/math.2023337.
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<abstract><p>The main goal of this article is to reveal a new generalized version of the q-linear Diophantine fuzzy set (q-LDFS) named spherical q-linear Diophantine fuzzy set (Sq-LDFS). The existing concepts of intuitionistic fuzzy set (IFS), q-rung orthopair fuzzy set (q-OFS), linear Diophantine fuzzy set (LDFS), and spherical fuzzy set have a wide range of applications in decision-making problems, but they all have strict limitations in terms of membership degree, non-membership degree, and uncertainty degree. We moot the article of the spherical q-linear Diophantine fuzzy set (Sq-LDFS) with control factors to alleviate these limitations. A Spherical q-linear Diophantine fuzzy number structure is independent of the selection of the membership grades because of its control parameters in three membership grades. An Sq-LDFS with a parameter estimation process can be extremely useful for modeling uncertainty in decision-making (DM). By using control factors, Sq-LDFS may classify a physical system. We highlight some of the downsides of q-LDFSs. By using algebraic norms, we offer some novel operational laws for Sq-LDFSs. We also introduced the weighted average and weighted geometric aggregation operators and their fundamental laws and properties. Furthermore, we proposed the algorithms for a multicriteria decision-making approach with graphical representation. Moreover, a numerical illustration of using the proposed methodology for Sq-LDF data for emergency decision-making is presented. Finally, a comparative analysis is presented to examine the efficacy of our proposed approach.</p></abstract>
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A.M, Ayisha Fenoon, and Francina Shalini A. "Interval Valued Pythagorean (p, q, r) – Spherical Fuzzy Set and their Aggregation Operators." International Journal of Humanities and Sciences 1, no. 2 (2024): 18–32. https://doi.org/10.34256/ijohs123.
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This research paper introduces the Aggregation Operators for Interval Valued Pythagorean (p, q, r) Spherical Fuzzy Set (IVPpqrSFSs) which is an extension of Spherical fuzzy set. IVPpqrSFSs helps us to handle uncertain & unclear information making it useful for real life decision making problems. The Arithmetic and Geometric Aggregation Operators are defined and their properties are explained.
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Ayub, Saba, Muhammad Shabir, Muhammad Riaz, Waqas Mahmood, Darko Bozanic, and Dragan Marinkovic. "Linear Diophantine Fuzzy Rough Sets: A New Rough Set Approach with Decision Making." Symmetry 14, no. 3 (2022): 525. http://dx.doi.org/10.3390/sym14030525.
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In this article, a new hybrid model named linear Diophantine fuzzy rough set (LDFRS) is proposed to magnify the notion of rough set (RS) and linear Diophantine fuzzy set (LDFS). Concerning the proposed model of LDFRS, it is more efficient to discuss the fuzziness and roughness in terms of linear Diophantine fuzzy approximation spaces (LDFA spaces); it plays a vital role in information analysis, data analysis, and computational intelligence. The concept of (<p,p′>,<q,q′>)-indiscernibility of a linear Diophantine fuzzy relation (LDF relation) is used for the construction of an LDFRS. Certain properties of LDFA spaces are explored and related results are developed. Moreover, a decision-making technique is developed for modeling uncertainties in decision-making (DM) problems and a practical application of fuzziness and roughness of the proposed model is established for medical diagnosis.