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Journal articles on the topic 'Fuzzy analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 March 2023

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1

Ma, Zhen Ming. "Some Types of Generalized Fuzzyn-Fold Filters in Residuated Lattices." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/736872.

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Fuzzy filters and their generalized types have been extensively studied in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzyn-fold filters such as generalized fuzzyn-fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters.

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2

Ameer, Eskandar, Hassen Aydi, and Muhammad Arshad. "On Fuzzy Fixed Points and an Application to Ordinary Fuzzy Differential Equations." Journal of Function Spaces 2020 (November 12, 2020): 1–12. http://dx.doi.org/10.1155/2020/8835751.

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The aim of this paper is to obtain the common fuzz fixed points of α -fuzzy mappings satisfying generalized almost Y , Λ -contraction in complete metric spaces. Our results are extensions and improvements of the several well-known recent and classical results in literature. We give an example for supporting these results. As an application, we apply our obtained results to study the existence of a solution for a second order nonlinear boundary value problem.

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3

Ameen, Zanyar A., Tareq M. Al-shami, A. A. Azzam, and Abdelwaheb Mhemdi. "A Novel Fuzzy Structure: Infra-Fuzzy Topological Spaces." Journal of Function Spaces 2022 (April 7, 2022): 1–11. http://dx.doi.org/10.1155/2022/9778069.

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Obtaining a weaker condition that preserves some inspired topological properties is always desirable. As a result, we introduce the concept of infra-fuzzy topology, which is a subset family that degrades the concept of fuzzy topology by omitting the condition of closedness under arbitrary unions. Fundamental properties of infra-fuzzy topological spaces are investigated, including infra-fuzzy open and infra-fuzzy closed sets, infra-fuzzy interior and infra-fuzzy closure operators, and the infra-fuzzy boundary of a fuzzy set. It is not possible to expect the latter concepts to have properties identical to those in ordinary fuzzy topological spaces. More precisely, the infra-fuzzy interior of a set need not be infra-fuzzy open, and the infra-fuzzy closure and boundary of a set may not be infra-fuzzy closed. Then, employing infra-fuzzy neighborhood systems, infra-fuzzy Q-neighborhood systems, the basis of infra-fuzzy topology, and infra-fuzzy relative topology, we propose several approaches for generating infra-fuzzy topologies. Finally, we define the notions of continuity, openness, closedness, and homeomorphism of mappings in the context of infra fuzziness and investigate some of their properties and characterizations. We show that the usual characterization of earlier notions in the infra-fuzzy structure is incorrect. We demonstrate that the family of all infra-fuzzy homeomorphisms on an infra-fuzzy topological space forms a group under mappings composition. We finish this work by proving that each infra-fuzzy homeomorphism between two infra-fuzzy topological spaces produces an isomorphism on groups of infra-fuzzy homeomorphisms of the corresponding spaces.

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4

Byrne, Peter. "Fuzzy analysis." Journal of Property Valuation and Investment 13, no. 3 (August 1995): 22–41. http://dx.doi.org/10.1108/14635789510088591.

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5

Madhuri, V., Omar Bazighifan, Ali Hasan Ali, and A. El-Mesady. "On Fuzzy F ∗ -Simply Connected Spaces in Fuzzy F ∗ -Homotopy." Journal of Function Spaces 2022 (April 28, 2022): 1–6. http://dx.doi.org/10.1155/2022/9926963.

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In this paper, the notions of fuzzy F ∗ -simply connected spaces and fuzzy F ∗ -structure homeomorphisms are introduced, and further fuzzy F ∗ -structure homeomorphism between fuzzy F ∗ -path-connected spaces are studied. Also, it is shown that every fuzzy F ∗ -structure subspace of fuzzy F ∗ -simply connected space is fuzzy F ∗ -simply connected subspace. Further, the concepts of fuzzy F ∗ -contractible spaces and fuzzy F ∗ -retracts are introduced, and it is proved that every fuzzy F ∗ -contractible space is fuzzy F ∗ -simply connected.

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6

Pedrycz, Witold. "From fuzzy data analysis and fuzzy regression to granular fuzzy data analysis." Fuzzy Sets and Systems 274 (September 2015): 12–17. http://dx.doi.org/10.1016/j.fss.2014.04.017.

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7

Papageorgiou, Nikolaos S. "Fuzzy topology and fuzzy multifunctions." Journal of Mathematical Analysis and Applications 109, no. 2 (August 1985): 397–425. http://dx.doi.org/10.1016/0022-247x(85)90159-3.

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8

Prevot, M. "Fuzzy goals under fuzzy constraints." Journal of Mathematical Analysis and Applications 118, no. 1 (August 1986): 180–93. http://dx.doi.org/10.1016/0022-247x(86)90302-1.

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9

Watada, Junzo, Hideo Tanaka, and Kiyoji Asai. "Fuzzy discriminant analysis in fuzzy groups." Fuzzy Sets and Systems 19, no. 3 (July 1986): 261–71. http://dx.doi.org/10.1016/0165-0114(86)90055-2.

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10

Alaoui, Mohammed Kbiri, F. M. Alharbi, and Shamsullah Zaland. "Novel Analysis of Fuzzy Physical Models by Generalized Fractional Fuzzy Operators." Journal of Function Spaces 2022 (January 5, 2022): 1–12. http://dx.doi.org/10.1155/2022/2504031.

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The present article correlates with a fuzzy hybrid technique combined with an iterative transformation technique identified as the fuzzy new iterative transform method. With the help of Atangana-Baleanu under generalized Hukuhara differentiability, we demonstrate the consistency of this method by achieving fuzzy fractional gas dynamics equations with fuzzy initial conditions. The achieved series solution was determined and contacted the estimated value of the suggested equation. To confirm our technique, three problems have been presented, and the results were estimated in fuzzy type. The lower and upper portions of the fuzzy solution in all three examples were simulated using two distinct fractional orders between 0 and 1. Because the exponential function is present, the fractional operator is nonsingular and global. It provides all forms of fuzzy solutions occurring between 0 and 1 at any fractional-order because it globalizes the dynamical behavior of the given equation. Because the fuzzy number provides the solution in fuzzy form, with upper and lower branches, fuzziness is also incorporated in the unknown quantity. It is essential to mention that the projected methodology to fuzziness is to confirm the superiority and efficiency of constructing numerical results to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

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11

de Glas, Michel. "Fuzzy σ-fields and fuzzy measures." Journal of Mathematical Analysis and Applications 124, no. 1 (May 1987): 281–89. http://dx.doi.org/10.1016/0022-247x(87)90039-4.

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12

Friedler, Louis M. "Fuzzy closed and fuzzy perfect mappings." Journal of Mathematical Analysis and Applications 125, no. 2 (August 1987): 451–60. http://dx.doi.org/10.1016/0022-247x(87)90100-4.

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13

Theodorou, Yiannis, and Philippos Alevizos. "The fuzzy eigenvalue problem of fuzzy correspondence analysis." Journal of Interdisciplinary Mathematics 9, no. 1 (February 2006): 115–37. http://dx.doi.org/10.1080/09720502.2006.10700431.

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14

Al-shami, Tareq M., Hariwan Z. Ibrahim, A. A. Azzam, and Ahmed I. EL-Maghrabi. "SR-Fuzzy Sets and Their Weighted Aggregated Operators in Application to Decision-Making." Journal of Function Spaces 2022 (March 11, 2022): 1–14. http://dx.doi.org/10.1155/2022/3653225.

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An intuitionistic fuzzy set is one of the efficient generalizations of a fuzzy set for dealing with vagueness/uncertainties in information. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called square-root fuzzy sets (briefly, SR-Fuzzy sets) and contrast SR-Fuzzy sets with intuitionistic fuzzy sets and Pythagorean fuzzy sets. We discover the essential set of operations for the SR-Fuzzy sets along with their several properties. In addition, we define a score function for the ranking of SR-Fuzzy sets. To study multiattribute decision-making problems, we introduce four new weighted aggregated operators, namely, SR-Fuzzy weighted average (SR-FWA) operator, SR-Fuzzy weighted geometric (SR-FWG) operator, SR-Fuzzy weighted power average (SR-FWPA) operator, and SR-Fuzzy weighted power geometric (SR-FWPG) operator over SR-Fuzzy sets. We apply these operators to select the top-rank university and show how we can choose the best option by comparing the aggregate outputs through score values.

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15

Bhunia, Supriya, Ganesh Ghorai, Marwan Amin Kutbi, Muhammad Gulzar, and Md Ashraful Alam. "On the Algebraic Characteristics of Fuzzy Sub e-Groups." Journal of Function Spaces 2021 (October 20, 2021): 1–7. http://dx.doi.org/10.1155/2021/5253346.

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Fuzzy set is a modern tool for depicting uncertainty. This paper introduces the concept of fuzzy sub e-group as an extension of fuzzy subgroup. The concepts of identity and inverse are generalized in fuzzy sub e-groups. Every fuzzy subgroup is proven to be a fuzzy sub e-group, but the converse is not true. Various properties of fuzzy sub e-groups are established. Moreover, the concepts of proper fuzzy sub e-group and super fuzzy sub e-group are discussed. Further, the concepts of fuzzy e-coset and normal fuzzy sub e-group are presented. Finally, we describe the effect of e-group homomorphism on normal fuzzy sub e-groups.

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16

OGURA, Yukio. "Stochastic Fuzzy Analysis." Journal of Japan Society for Fuzzy Theory and Systems 10, no. 6 (1998): 1012–19. http://dx.doi.org/10.3156/jfuzzy.10.6_1012.

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17

ISHIBUCHI, Hisao. "Fuzzy Regression Analysis." Journal of Japan Society for Fuzzy Theory and Systems 4, no. 1 (1992): 52–60. http://dx.doi.org/10.3156/jfuzzy.4.1_52.

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18

Yoon, Jin Hee. "Fuzzy Mediation Analysis." International Journal of Fuzzy Systems 22, no. 1 (December 10, 2019): 338–49. http://dx.doi.org/10.1007/s40815-019-00727-6.

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19

Peters, Robert M., Stanley A. Shanies, and John C. Peters. "Fuzzy Cluster Analysis." Japanese Circulation Journal 62, no. 10 (1998): 750–54. http://dx.doi.org/10.1253/jcj.62.750.

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20

Buckley, J. J. "Fuzzy hierarchical analysis." Fuzzy Sets and Systems 17, no. 3 (December 1985): 233–47. http://dx.doi.org/10.1016/0165-0114(85)90090-9.

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21

Watanabe, Norio. "Fuzzy theories and statistics—fuzzy data analysis." Communications in Statistics: Case Studies, Data Analysis and Applications 7, no. 4 (October 2, 2021): 561–72. http://dx.doi.org/10.1080/23737484.2021.1991854.

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22

Bashir, Shahida, Muhammad Aslam, Rabia Mazhar, and Junaid Asghar. "Rough Fuzzy Ideals Induced by Set-Valued Homomorphism in Ternary Semigroups." Journal of Function Spaces 2022 (May 26, 2022): 1–8. http://dx.doi.org/10.1155/2022/6247354.

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The main objective of this paper is to characterize rough approximations of fuzzy ideals in ternary semigroups. Rough fuzzy ideals are used to deal with vague and incomplete information in decision-making problems. In this research, approximations for fuzzy prime ideals in ternary semigroups are studied. It is proved that generalized lower approximations and generalized upper approximations of ∈ , ∈ ∨ q -fuzzy prime (resp., semiprime) ideals of ternary semigroups are ∈ , ∈ ∨ q -fuzzy prime (resp., semiprime) ideals. For this, the concept of SSVH (strong set-valued homomorphism) and SVH (set-valued homomorphism) is used. Also, it is shown by examples that the lower approximations of fuzzy subsemigroups and fuzzy ideals are not fuzzy subsemigroups and fuzzy ideals, respectively, for SVH.

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23

SEO, Fumiko. "Fuzzy Decision Analysis and Fuzzy Utility Evaluation." Journal of Japan Society for Fuzzy Theory and Systems 11, no. 5 (1999): 721–33. http://dx.doi.org/10.3156/jfuzzy.11.5_17.

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24

UESU, Hiroaki. "Sociometry Analysis Applying Fuzzy Node Fuzzy Graph." Journal of Japan Society for Fuzzy Theory and Systems 14, no. 3 (2002): 299–309. http://dx.doi.org/10.3156/jfuzzy.14.3_299.

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25

Ismagilov, Ilyas Idrisovich, and Ghena Alsaied. "Fuzzy Regression Analysis using Trapezoidal Fuzzy Numbers." Industrial Engineering & Management Systems 19, no. 4 (December 31, 2020): 896–900. http://dx.doi.org/10.7232/iems.2020.19.4.896.

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26

Yongting, Cen. "Fuzzy quality and analysis on fuzzy probability." Fuzzy Sets and Systems 83, no. 2 (October 1996): 283–90. http://dx.doi.org/10.1016/0165-0114(95)00383-5.

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27

Di Nola, Antonio, and Aldo G. S. Ventre. "On fuzzy integral inequalities and fuzzy expectation." Journal of Mathematical Analysis and Applications 125, no. 2 (August 1987): 589–99. http://dx.doi.org/10.1016/0022-247x(87)90108-9.

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28

Suzuki, Hisakichi. "On fuzzy measures defined by fuzzy integrals." Journal of Mathematical Analysis and Applications 132, no. 1 (May 1988): 87–101. http://dx.doi.org/10.1016/0022-247x(88)90045-5.

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29

Mursaleen, M., M. Balamurugan, K. Loganathan, and Kottakkaran Sooppy Nisar. "( ∈ , ∈ ∨ q ˘ )-Bipolar Fuzzy b -Ideals of BCK/BCI-Algebras." Journal of Function Spaces 2021 (February 10, 2021): 1–8. http://dx.doi.org/10.1155/2021/6615288.

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In this paper, the idea of ∈ , ∈ ∨ q ˘ -bipolar fuzzy b -ideals and an ∈ , ∈ ∨ q ˘ -bipolar fuzzy ideals of BCK / BCI -algebras is delivered, and their related properties are investigated with the aid of some examples. We also provide the connection between ∈ , ∈ ∨ q ˘ -bipolar fuzzy ideals and bipolar fuzzy ideals and ∈ , ∈ ∨ q ˘ -bipolar fuzzy b -ideals and bipolar fuzzy b -ideals by way of counterexamples.

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30

Kattan, Doha A., Maria Amin, and Abdul Bariq. "Certain Structure of Lagrange’s Theorem with the Application of Interval-Valued Intuitionistic Fuzzy Subgroups." Journal of Function Spaces 2022 (February 24, 2022): 1–9. http://dx.doi.org/10.1155/2022/3580711.

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This paper presents the concept of an interval-valued intuitionistic fuzzy subgroup defined on interval-valued intuitionistic fuzzy sets. We study some of the fundamental algebraic properties of interval-valued intuitionistic fuzzy cosets and interval-valued intuitionistic fuzzy normal subgroup of a given group. This idea is used to describe the interval-valued intuitionistic fuzzy order and index of interval-valued intuitionistic fuzzy subgroup. We have created numerous algebraic properties of interval-valued intuitionistic fuzzy order of an element. We also prove the interval-valued intuitionistic fuzzification of Lagrange’s theorem.

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31

Hussain, Aftab, Umar Ishtiaq, Khalil Ahmed, and Hamed Al-Sulami. "On Pentagonal Controlled Fuzzy Metric Spaces with an Application to Dynamic Market Equilibrium." Journal of Function Spaces 2022 (January 11, 2022): 1–8. http://dx.doi.org/10.1155/2022/5301293.

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In this manuscript, we coined pentagonal controlled fuzzy metric spaces and fuzzy controlled hexagonal metric space as generalizations of fuzzy triple controlled metric spaces and fuzzy extended hexagonal b-metric spaces. We use a control function in fuzzy controlled hexagonal metric space and introduce five noncomparable control functions in pentagonal controlled fuzzy metric spaces. In the scenario of pentagonal controlled fuzzy metric spaces, we prove the Banach fixed point theorem, which generalizes the Banach fixed point theorem for the aforementioned spaces. An example is offered to support our main point. We also presented an application to dynamic market equilibrium.

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32

Aljahdaly, Noufe H., Muhammad Naeem, and Noorolhuda Wyal. "Analysis of Fuzzy Kuramoto-Sivashinsky Equations under a Generalized Fuzzy Fractional Derivative Operator." Journal of Function Spaces 2022 (June 7, 2022): 1–11. http://dx.doi.org/10.1155/2022/9517158.

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This paper evaluates a semianalytical strategy combined with a novel fuzzy integral transformation and an iterative method inside the fuzziness concept known as the new iterative transform method. Additionally, we apply the abovementioned technique to the fractional fuzzy Kuramoto-Sivashinsky equations with g H -differentiability by employing various initial conditions. Numerous algebraic properties of the fuzzy fractional derivative Atangana-Baleanu operator are illustrated concerning the Shehu transformation to demonstrate their utility. Additionally, a general technique for Atangana-Baleanu fuzzy fractional derivatives is proposed in the sense of Caputo. It is important to note that the purpose of the suggested fuzziness technique is to establish the efficiency and accuracy of analytical solution to nonlinear fuzzy fractional partial differential equations that emerge in complex and physical structures.

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33

Alleheb, Lubna Abdul Aziz, and Kholood Mohammad Alsager. "Certain Concepts of Q -Hesitant Fuzzy Ideals." Journal of Function Spaces 2022 (July 22, 2022): 1–8. http://dx.doi.org/10.1155/2022/7099148.

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The hesitant fuzzy set model has attracted the interest of scholars in various fields. The striking framework of hesitant fuzzy sets is keen to provide a larger domain of preference for fuzzy information modeling of deployment membership. Starting from the hybrid properties of hesitant fuzzy ideals (HFI), this paper constructs a new generalized hybrid structure Q -HFI. The concept of Q -hesitant fuzzy exchange ideal in B C K -algebra is considered. Lastly, Q -hesitant fuzzy exchange ideal features are described.

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34

Mufti, Zeeshan Saleem, Eiman Fatima, Rukhshanda Anjum, Fairouz Tchier, Qin Xin, and Md Moyazzem Hossain. "Computing First and Second Fuzzy Zagreb Indices of Linear and Multiacyclic Hydrocarbons." Journal of Function Spaces 2022 (March 22, 2022): 1–8. http://dx.doi.org/10.1155/2022/6281592.

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Fuzzy graph theory was invented by Rosenfeld. It is the extension of the work of L.A. Zadeh on fuzzy sets. Rosenfeld extracted the fuzzy-related concepts using the graph theoretic concepts. Topological indices for crisp theory have already been discussed in the literature but these days, topological index-related fuzzy graphs are much popular. Fuzzy graphs are being used as an application in different fields of sciences such as broadcast, communications, producing, social network, man-made reasoning, data hypothesis, and neural systems. In this paper, we have computed some fuzzy topological indices such as first and second Zagreb indices, Randic index, and harmonic index of fuzzy chemical graph named phenylene.

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35

Rana, Shweta. "Sentiment Analysis for Hindi Text using Fuzzy Logic." Indian Journal of Applied Research 4, no. 8 (October 1, 2011): 437–40. http://dx.doi.org/10.15373/2249555x/august2014/111.

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36

AL-Mafrji, Ahmad Abdullah Mohammed, and Ahmed Burhan Mohammed. "Analysis of Patients Data Using Fuzzy Expert System." Webology 19, no. 1 (January 20, 2022): 4027–34. http://dx.doi.org/10.14704/web/v19i1/web19265.

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Many problems are facing many developed and developing countries in the medical field, and the most important of these problems is the analysis and diagnosis of patient data for government and private hospitals. This is due to the lack of experience of medical staff, especially new ones, which affects the provision of correct medical services to patients. It is no secret that these countries are making great efforts to overcome these problems. The study focuses on the use of a fuzzy expert system to analyze patient data based on (age, type of review) to reach the result of the analysis (intensive care, medium care, no care) and this system helps to give advice and good analysis of patient data, which can increase the speed of gaining experience for new and inexperienced medical staff in this field.

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37

Tahernia, N. "Fuzzy-Logic Tree Approach for Seismic Hazard Analysis." International Journal of Engineering and Technology 6, no. 3 (2014): 182–85. http://dx.doi.org/10.7763/ijet.2014.v6.692.

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38

Faried, Nashat, Mohamed S. S. Ali, and Hanan H. Sakr. "On Fuzzy Soft Linear Operators in Fuzzy Soft Hilbert Spaces." Abstract and Applied Analysis 2020 (July 31, 2020): 1–13. http://dx.doi.org/10.1155/2020/5804957.

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Due to the difficulty of representing problem parameters fuzziness using the soft set theory, the fuzzy soft set is regarded to be more general and flexible than using the soft set. In this paper, we define the fuzzy soft linear operator T~ in the fuzzy soft Hilbert space H~ based on the definition of the fuzzy soft inner product space U~,·,·~ in terms of the fuzzy soft vector v~fGe modified in our work. Moreover, it is shown that ℂnA, ℝnA and ℓ2A are suitable examples of fuzzy soft Hilbert spaces and also some related examples, properties and results of fuzzy soft linear operators are introduced with proofs. In addition, we present the definition of the fuzzy soft orthogonal family and the fuzzy soft orthonormal family and introduce examples satisfying them. Furthermore, the fuzzy soft resolvent set, the fuzzy soft spectral radius, the fuzzy soft spectrum with its different types of fuzzy soft linear operators and the relations between those types are introduced. Moreover, the fuzzy soft right shift operator and the fuzzy soft left shift operator are defined with an example of each type on ℓ2A. In addition, it is proved, on ℓ2A, that the fuzzy soft point spectrum of fuzzy soft right shift operator has no fuzzy soft eigenvalues, the fuzzy soft residual spectrum of fuzzy soft right shift operator is equal to the fuzzy soft comparison spectrum of it and the fuzzy soft point spectrum of fuzzy soft left shift operator is the fuzzy soft open disk λ~<~1~. Finally, it is shown that the fuzzy soft Hilbert space is fuzzy soft self-dual in this generalized setting.

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39

Alshammari, Mohammad, Wael W. Mohammed, and Mohammed Yar. "Novel Analysis of Fuzzy Fractional Klein-Gordon Model via Semianalytical Method." Journal of Function Spaces 2022 (May 16, 2022): 1–9. http://dx.doi.org/10.1155/2022/4020269.

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The current article discusses the new fuzzy iterative transform method, a hybrid methodology based on fuzzy logic and an iterative transformation technique. We demonstrate the consistency of our technique by employing the Caputo derivative under generalized Hukuhara differentiability to construct fractional fuzzy Klein-Gordon equations with the initial fuzzy condition. The series produced result was calculated and compared to the exact result’s recommended equations. Two problems were used to verify our method, with the results approximated in fuzzy form. The upper and lower half of the fuzzy results were approximated in each of the two examples using two distinct fractional orders between zero and one. Because it globalizes the dynamical behavior of the specified equation, it produces all forms of fuzzy results at any fractional order between 0 and 1. Since fuzzy numbers offer their results in a fuzzy form with lower and upper branches, the unknown amount also adds fuzziness. It is crucial to emphasize that the suggested fuzziness method is intended to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations found in complex and physical structures.

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40

Razzaque, Asima, and Abdul Razaq. "On q -Rung Orthopair Fuzzy Subgroups." Journal of Function Spaces 2022 (June 6, 2022): 1–9. http://dx.doi.org/10.1155/2022/8196638.

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The q -rung orthopair fuzzy environment is an innovative tool to handle uncertain situations in various decision-making problems. In this work, we characterize the idea of a q -rung orthopair fuzzy subgroup and examine various algebraic attributes of this newly defined notion. We also present q -rung orthopair fuzzy coset and q -rung orthopair fuzzy normal subgroup along with relevant fundamental theorems. Moreover, we introduce the concept of q -rung orthopair fuzzy level subgroup and proved related results. At the end, we explore the consequence of group homomorphism on the q -rung orthopair fuzzy subgroup.

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41

Anjum, R., F. Sarfraz, N. Kausar, Y. U. Gaba, H. Aydi, M. Munir, and Salahuddin. "Some Studies in Hemirings by the Falling Fuzzy k -Ideals." Journal of Function Spaces 2021 (August 3, 2021): 1–10. http://dx.doi.org/10.1155/2021/6874456.

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In this article, we establish the idea of falling fuzzy k -ideals in hemirings through the falling shadow theory and fuzzy sets. We shall express the relations between fuzzy k -ideals and falling fuzzy k -ideals in hemirings. In particular, we shall establish different characterizations of k -hemiregular hemirings in the perfect positive correlation and independent probability space by means of falling fuzzy k -ideals.

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42

de Prada Vicente, M. A., and M. Saralegui Aranguren. "Fuzzy filters." Journal of Mathematical Analysis and Applications 129, no. 2 (February 1988): 560–68. http://dx.doi.org/10.1016/0022-247x(88)90271-5.

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43

Mesiar, R. "Fuzzy Observables." Journal of Mathematical Analysis and Applications 174, no. 1 (March 1993): 178–93. http://dx.doi.org/10.1006/jmaa.1993.1109.

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44

Rao, S. P., and Q. G. Li. "Fuzzy -Continuous Posets." Abstract and Applied Analysis 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/607934.

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The aim of this paper is to generalize fuzzy continuous posets. The concept of fuzzy subset system on fuzzy posets is introduced; some elementary definitions such as fuzzy -continuous posets and fuzzy -algebraic posets are given. Furthermore, we try to find some natural classes of fuzzy -continuous maps under which the images of such fuzzy algebraic structures can be preserved; we also think about fuzzy -continuous closure operators in alternative ways. An extension theorem is presented for extending a fuzzy monotone map defined on the -compact elements to a fuzzy -continuous map defined on the whole set.

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45

Furqan, Salman, Hüseyin Işık, and Naeem Saleem. "Fuzzy Triple Controlled Metric Spaces and Related Fixed Point Results." Journal of Function Spaces 2021 (May 20, 2021): 1–8. http://dx.doi.org/10.1155/2021/9936992.

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In this study, we introduce fuzzy triple controlled metric space that generalizes certain fuzzy metric spaces, like fuzzy rectangular metric space, fuzzy rectangular b -metric space, fuzzy b -metric space, and extended fuzzy b -metric space. We use f , g , h , three noncomparable functions as follows: m q μ , η , t + s + w ≥ m q μ , ν , t / f μ , ν ∗ m q ν , ξ , s / g ν , ξ ∗ m q ξ , η , w / h ξ , η . We prove Banach fixed point theorem in the settings of fuzzy triple controlled metric space that generalizes Banach fixed point theorem for aforementioned spaces. An example is presented to support our main results. We also apply our technique to the uniqueness for the solution of an integral equation.

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46

Alesemi, Meshari, Naveed Iqbal, and Noorolhuda Wyal. "Novel Evaluation of Fuzzy Fractional Helmholtz Equations." Journal of Function Spaces 2022 (April 29, 2022): 1–8. http://dx.doi.org/10.1155/2022/8165019.

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The current article discusses the fuzzy new iterative transform approach, which is a combination of a fuzzy hybrid methodology and an iterative transformation technique. We establish the consistence of our strategy by obtaining fractional fuzzy Helmholtz equations with the initial fuzzy condition using the Caputo derivative under generalized Hukuhara differentiability. The series obtained result was calculated and compared to the proposed equations of the actual result. Three challenges were provided to validate our method, and the outcomes were approximated in fuzzy form. In each of the three examples, the upper and bottom halves of the fuzzy solution were approximated utilizing two various fractional order between 0 and 1. Due to the fact that it globalizes the dynamical behavior of the specified equation, it produces all forms of fuzzy results at any fractional order between 0 and 1. Due to the fact that the fuzzy numbers presents the result in a lower and upper branches fuzzy type, the unknown quantity incorporates fuzziness as well. It is critical to emphasize that the purpose of the proposed fuzziness approach is to demonstrate the efficiency and superiority of numerical solutions to nonlinear fractional fuzzy partial differential equations that arise in complex and physical structures.

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47

Shao, Yabin, and Huanhuan Zhang. "Fuzzy Integral Equations and Strong Fuzzy Henstock Integrals." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/932696.

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48

Dumitrescu, D. "Fuzzy Measures and the Entropy of Fuzzy Partitions." Journal of Mathematical Analysis and Applications 176, no. 2 (July 1993): 359–73. http://dx.doi.org/10.1006/jmaa.1993.1220.

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49

Liu, Baoding, and Augustine O. Esogbue. "Fuzzy Criterion Set and Fuzzy Criterion Dynamic Programming." Journal of Mathematical Analysis and Applications 199, no. 1 (April 1996): 293–311. http://dx.doi.org/10.1006/jmaa.1996.0142.

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50

Muhiuddin, G., N. Alam, S. Obeidat, N. M. Khan, H. N. Zaidi, S. A. K. Kirmani, A. Altaleb, and J. M. Aqib. "Fuzzy Set Theoretic Approach to Generalized Ideals in BCK/BCI-Algebras." Journal of Function Spaces 2022 (April 4, 2022): 1–8. http://dx.doi.org/10.1155/2022/5462248.

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This paper deals with the study of generalizations of fuzzy subalgebras and fuzzy ideals in BCK/BCI-algebras. In fact, the notions of ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy subalgebras, ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy ideals, and ∈ ∨ κ ~ ∗ , q κ ~ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy ideals in BCK/BCI-algebras are introduced. Some examples are provided to demonstrate the logic of the concepts used in this paper. Moreover, some characterizations of these notions are discussed. In addition, the concept of ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy commutative ideals is introduced, and several significant characteristics are discussed. It is shown that for a BCK-algebra A , every ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -commutative ideal of a BCK-algebra is an ∈ , ∈ ∨ κ ~ ∗ , q κ ~ -fuzzy ideal, but the converse does not hold in general; a counter example is constructed.

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