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Journal articles on the topic 'Intuitionistic Fuzzy (1'

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Published: 3 June 2025

Last updated: 31 July 2025

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1

Nithya., A. "Operations on Intuitionisitc Fuzzy Soft Sets Based on First Zadeh's Logical Operators." International Journal of Trend in Scientific Research and Development 3, no. 1 (2018): 897–99. https://doi.org/10.31142/ijtsrd18986.

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In this paper, we have defined First Zadeh's intuitionistic fuzzy conjunction and intuitionistic fuzzy disjunction of two intuitionistic fuzzy soft sets. The author also defined some of their basic properties of intuitionistic fuzzy disjunction and conjunction with some examples. Nithya. A "Operations on Intuitionisitc Fuzzy Soft Sets Based on First Zadeh's Logical Operators" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-1 , December 2018, URL: https://www.ijtsrd.com/papers/ijtsrd18986.pdf

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Pratama, Dian. "STRUKTUR IMAGE DAN PRE-IMAGE HOMOMORFISMA PADA TRANSLASI RING FUZZY INTUITIONISTIK." Jurnal Ilmiah Matematika dan Pendidikan Matematika 11, no. 1 (2020): 59. http://dx.doi.org/10.20884/1.jmp.2020.12.1.1937.

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A set that is characterized by membership function and a non-membership function with the sum of both at intervals of 0 to 1 is called intuitionistik fuzzy set.. When it’s applied in ring’s theory, it will called intuitionistic fuzzy ring. In this research,if the topics is membership fuction and non-membership function then there are translates operator. This operator only changes the values of the membership and non-membership function while the properties are fixed. This journal discussed the structure of image ad pre-image homomorphism of translates on intuitionistic fuzzy rings. The result

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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

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Muhammad, Wedad Salman, Nada A. Laabi, and Asmaa Ali Zeyad. "On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces." European Journal of Theoretical and Applied Sciences 2, no. 1 (2024): 851–62. http://dx.doi.org/10.59324/ejtas.2024.2(1).75.

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The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intui

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Wedad, Salman Muhammad, A. Laabi Nada, and Ali Zeyad Asmaa. "On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces." European Journal of Theoretical and Applied Sciences 2, no. 1 (2024): 851–62. https://doi.org/10.59324/ejtas.2024.2(1).75.

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The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intui

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Pratama, Dian. "IMAGE DAN PRE-IMAGE TRANSLASI PADA GRUP FUZZY INTUITIONISTIK." Jurnal Ilmiah Matematika dan Pendidikan Matematika 8, no. 2 (2016): 41. http://dx.doi.org/10.20884/1.jmp.2016.8.2.2886.

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A intuitionistic fuzzy set in is set gives a membership function and a non-membership function (the complement of membership function) for each with the sum worth one. When it’s applied in group’s theory, it will called intuitionistic fuzzy group with conditions membership function is fuzzy subgroup and non-membership function is anti-fuzzy subgroup. In this research, the operator will be given a fuzzy set is called fuzzy translation operator. This operator is a mapping imposed on membership functions (fuzzy subset) to interval [ 0,1]. This research will discuss the properties homomorphism of

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S., Sivasangiri R. Balakumar and G. Saravanakumar. "e ⋆-connectedness in intuitionistic fuzzy topological spaces." Annals of Communications in Mathematics 4, no. 1 (2021): 26–34. https://doi.org/10.5281/zenodo.10048891.

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In this paper the concept of types of intuitionistic fuzzy e ?-connected and intuitionistic fuzzy e ?-extremally disconnected in intuitionistic fuzzy topological spaces are introduced and studied. Here we introduce the concepts of intuitionistic fuzzy e ?C5- connectedness, intuitionistic fuzzy e ?CS-connectedness, intuitionistic fuzzy e ?CM-connectedness, intuitionistic fuzzy e ?-strongly connectedness, intuitionistic fuzzy e ?-super connectedness, intuitionistic fuzzy e ?Ci-connectedness (i = 1, 2, 3, 4), and obtain several properties and some characterizations concerning connectedness in the

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Achik, S., I. Bakhadach, M. Oukessou, and S. Melliani. "Intuitionistic fuzzy Nakayama’s Lemma." Notes on Intuitionistic Fuzzy Sets 30, no. 4 (2024): 309–22. https://doi.org/10.7546/nifs.2024.30.4.309-322.

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Drawing upon Atanassov's pioneering work on intuitionistic fuzzy sets [1], this paper presents the concept of intuitionistic fuzzy Nakayama's Lemma, offering a natural extension to Rajesh Kumar et al.'s fuzzy Nakayama's Lemma [8]. Additionally, we define the intuitionistic fuzzy Jacobson radical and explore the product of an intuitionistic fuzzy ideal and intuitionistic fuzzy submodule. Finally, we conclude by introducing the sum of two intuitionistic fuzzy submodules.

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Chaudhary, Priti, and Tanuj Kumar. "Intuitionistic fuzzy inventory model with quadratic demand rate, time-dependent holding cost and shortages." Journal of Physics: Conference Series 2223, no. 1 (2022): 012003. http://dx.doi.org/10.1088/1742-6596/2223/1/012003.

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Abstract In the present work, we studied an inventory model under quadratic demand rate, linearly time-dependent holding cost, constant deterioration rate and allowed shortages. Intuitionistic fuzzy set (IFS) theory is an efficient tool to reduce the uncertainty that occurs due to hesitation, so we studied the considered model under intuitionistic fuzzy set theory. Further, the model is transformed into an intuitionistic fuzzy inventory model by taking the decision variables as triangular intuitionistic fuzzy numbers. To optimize the best inventory policy under the intuitionistic fuzzy environ

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Hidayahningrum, Syafitri, Noor Hidayat та Marjono Marjono. "An η-Intuitionistic Fuzzy Rings Structure". JTAM (Jurnal Teori dan Aplikasi Matematika) 7, № 1 (2023): 231. http://dx.doi.org/10.31764/jtam.v7i1.11833.

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In this article, we present the structure of η-intuitionistic fuzzy ring. An η-intuitionistic fuzzy ring is a structure which is built with combinating the definition of fuzzy ring, intuitionistic fuzzy set, and η-intuitionistic fuzzy set. The η-intuitionistic fuzzy set is characterized by any value η∈[0,1], where the degree of membership μ_(A^η ) (k) is obtained based on the averaging operator of the degree of membership μ_A (k) and the value of η∈[0,1]. While the degree of non membership ν_(A^η ) (k) is obtained based on the averaging operator of the degree of non membership ν_A (k) and the

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Sharma, P. K., and Chandni. "Categorical properties of intuitionistic fuzzy groups." Notes on Intuitionistic Fuzzy Sets 27, no. 4 (2021): 55–70. http://dx.doi.org/10.7546/nifs.2021.27.4.55-70.

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The category theory deals with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and acting as a unifying notion. In this paper, we study the relationship between the category of groups and the category of intuitionistic fuzzy groups. We prove that the category of groups is a subcategory of category of intuitionistic fuzzy groups and that it is not an Abelian category. We establish a function β : Hom(A, B) → [0; 1] × [0; 1] on the set of all intuitionistic fuz

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Pratama, Dian. "OPERATOR ⊞A and ⊠A ON INTUITIONISTIC FUZZY RING." Jurnal Ilmiah Matematika dan Pendidikan Matematika 12, no. 1 (2020): 35. http://dx.doi.org/10.20884/1.jmp.2020.12.1.2613.

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Intuitionistic fuzzy sets is a sets that are characterized by membership and non-membership function which sum is less than one. When applied to ring theory, it will called intuitionistic fuzzy rings. The fuzzy set operator is a mapping between the membership function and the interval [0,1]. In this study, we will describe properties of operator and in intuitionistic fuzzy rings. The characteristics that will be studied include the structure of and if A is an intuitive and fuzzy ring and vice versa.

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HUNG, WEN-LIANG. "USING STATISTICAL VIEWPOINT IN DEVELOPING CORRELATION OF INTUITIONISTIC FUZZY SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 09, no. 04 (2001): 509–16. http://dx.doi.org/10.1142/s0218488501000910.

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In this paper, we propose a method to calculate the correlation coefficient of intuitionistic fuzzy sets by means of mathematical statistics. This value obtained from our formula tell us not only the strength of relationship between the intuitionistic fuzzy sets, but also whether the intuitionistic fuzzy sets are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the proposed method to interval-valued intuitionistic fuzzy sets. The value of the correlation coefficient between interval-value

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Bhavadharani, R., and R. Irene Hepzibah. "IFM/IFEk/1 Queuing Model with Erlang Service under Heptagonal and Octagonal Intuitionistic Fuzzy Numbers." Indian Journal Of Science And Technology 17, no. 46 (2024): 4895–906. https://doi.org/10.17485/ijst/v17i46.3094.

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Objectives: This research identifies the steps involved in determining the membership and non-membership functions of significant State execution proportions in Erlang services and models α-cut operations. Additionally, we applied the DSW Algorithmic Rule to intuitionistic fuzzy heptagonal and octagonal numbers. In this case, the inter-entry rate is Poisson and exponential, both of which have an intuitionistic Erlang nature. The main objective of this research is to evaluate the performance of a single server queuing model in terms of fuzzy and intuitionistic queuing theory. Fuzzy and intuitio

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R, Bhavadharani, and Irene Hepzibah R. "IFM/IFEk/1 Queuing Model with Erlang Service under Heptagonal and Octagonal Intuitionistic Fuzzy Numbers." Indian Journal of Science and Technology 17, no. 46 (2024): 4895–906. https://doi.org/10.17485/IJST/v17i46.3094.

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Abstract <strong>Objectives:</strong> This research identifies the steps involved in determining the membership and non-membership functions of significant State execution proportions in Erlang services and models α-cut operations. Additionally, we applied the DSW Algorithmic Rule to intuitionistic fuzzy heptagonal and octagonal numbers. In this case, the inter-entry rate is Poisson and exponential, both of which have an intuitionistic Erlang nature. The main objective of this research is to evaluate the performance of a single server queuing model in terms of fuzzy and intuitionist

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Saleem, Kholoud W., Abir K. Salib, and Abrahim A. A.Tentush. "SEMIGROUPS IN TERMS OF INTUITIONISTIC FUZZY BI-IDEALS." EPH - International Journal of Applied Science 7, no. 1 (2021): 23–30. http://dx.doi.org/10.53555/eijas.v7i1.73.

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Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory. The concept of 'intuitionistic fuzzy set' (IFS) was introduced by Atanassov as a generalization of the concept fuzzy set by gives both a degree of membership and the degree of non-membership. As for fuzzy sets, the degree of membership is a real number between 0 and 1. This is also the case for the degree of non-membership, and further the sum of these two degrees is not greater than 1. Since fuzzy bi-ideal play a

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R., Srinivasan, and Rajesh K. "A NOTE ON PROPERTIES OF TEMPORAL INTUITIONISTIC FUZZY SETS OF SECOND TYPE." International Journal of Multidisciplinary Research and Modern Education 2, no. 2 (2016): 378–83. https://doi.org/10.5281/zenodo.174317.

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<em>Fuzzy Sets are generalized from the notion of classical (crisp) sets (Zadeh1965) [6]. A fuzzy subset A of E can be characterized with a membership function µ<sub>A</sub>: E → [0, 1]. Krassimir T. Atanassov further generalized fuzzy sets into Intuitionistic Fuzzy Sets (IFSs) in which non- membership function ν<sub>A </sub>: E → [0, 1] is also considered [1]. Further he extended IFSs into Temporal Intuitionistic Fuzzy Sets (TIFSs) in which time- moments are also taken into consideration. TIFSs are useful in time-based mathematical modeling. In this paper the present authors further introduce

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R., Srinivasan, and Rajesh K. "A NOTE ON PROPERTIES OF TEMPORAL INTUITIONISTIC FUZZY SETS OF SECOND TYPE." International Journal of Multidisciplinary Research and Modern Education 2, no. 2 (2016): 378–83. https://doi.org/10.5281/zenodo.204775.

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<em>Fuzzy Sets are generalized from the notion of classical (crisp) sets (Zadeh1965) [6]. A fuzzy subset A of X can be characterized with a membership function µ<sub>A</sub>: X → [0, 1]. Krassimir T. Atanassov further generalized fuzzy sets into Intuitionistic Fuzzy Sets (IFSs) in which non- membership function ν<sub>A</sub>: X → [0, 1] is also considered [1]. Further he extended IFSs into Temporal Intuitionistic Fuzzy Sets (TIFSs) in which time- moments are also taken into consideration. TIFSs are useful in time-based mathematical modeling. In this paper, the present authors further introduce

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Ma, Rufei, Shousheng Liu, Zeshui Xu, and Qian Lei. "Series based on the new order in intuitionistic fuzzy environment." Journal of Intelligent & Fuzzy Systems 40, no. 1 (2021): 319–30. http://dx.doi.org/10.3233/jifs-191679.

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Intuitionistic fuzzy number (IFN) is an effective tool for dealing with the uncertain information, and it has been applied to various fields. According to IFNs, the intuitionistic fuzzy calculus has been developed, which can effectively integrate the continuous uncertain information. Series in intuitionistic fuzzy environment is a part of the intuitionistic fuzzy calculus theory, of which core idea is limit. However, the order used in the existing limit theory is not the one used in intuitionistic fuzzy calculus, causing the separation of the limit theory and intuitionistic fuzzy calculus. Thu

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DESCHRIJVER, GLAD, and ETIENNE E. KERRE. "CLASSES OF INTUITIONISTIC FUZZY T-NORMS SATISFYING THE RESIDUATION PRINCIPLE." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 06 (2003): 691–709. http://dx.doi.org/10.1142/s021848850300248x.

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Intuitionistic fuzzy sets constitute an extension of fuzzy sets: while fuzzy sets give a degree to which an element belongs to a set, intuitionistic fuzzy sets give both a membership degree and a non-membership degree. The only constraint on those two degrees is that the sum must be smaller than or equal to 1. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In the fuzzy case a t-norm satisfies the residuation principle if and only if it is left-continuous. Deschrijver, Cornelis and Kerre proved that for intuitionistic fu

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Khan, Vakeel, and Mohd Faisal. "Some topological properties of intuitionistic fuzzy quasi normed space." Filomat 38, no. 25 (2024): 8907–16. https://doi.org/10.2298/fil2425907k.

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We establish the concept of an intuitionistic fuzzy quasi-normed space and provide an illustrative example. Through our exploration, we ascertain that an intuitionistic fuzzy quasi-norm can indeed transition into an intuitionistic fuzzy norm. However, it is worth noting that not every topology that supports intuitionistic fuzzy quasi-norms can be classified as metrizable. We establish the definitions of open balls and sequence convergence within intuitionistic fuzzy quasi-normed spaces. Additionally, we introduce the concepts of left/right N-Cauchy sequences, both in the context of topologNy ?

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Singh, Surendra, and Tanuj Kumar. "An intuitionistic fuzzy inventory model with waste disposal using the triangular intuitionistic fuzzy numbers." Journal of Physics: Conference Series 2223, no. 1 (2022): 012004. http://dx.doi.org/10.1088/1742-6596/2223/1/012004.

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Abstract In the present study, we formulate an inventory model with waste disposal cost under the intuitionistic fuzzy environment. To optimize the best inventory policy under the intuitionistic fuzzy environment, the alpha-cut approach is used for the defuzzification of all intuitionistic fuzzy decision variables. This study aims to reduce the total inventory cost and adjust the waste outcomes during the production processes to keep a clean and green climate, which will be cost-effective for any organization, both environmentally and economically. A numerical example is presented regarding th

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B. K. Tripathy, S. P. Jena, and S. K. Ghosh. "An Intuitionistic fuzzy count and cardinality of Intuitionistic fuzzy sets." Malaya Journal of Matematik 1, no. 04 (2013): 123–33. http://dx.doi.org/10.26637/mjm104/014.

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The notion of Intuitonistic fuzzy sets was introduced by Atanassov [1] as an extension of the concept of fuzzy sets introduced by Zadeh such that it is applicable to more real life situations. In order to measure the cardinality of fuzzy sets several attempts have been made [4,6,8]. However, there are no such measures for intuitionistic fuzzy sets. In this paper we define the sigma count and relative sigma count for intuitionistic fuzzy sets and establish their properties. Also, we illustrate the genration of quantification rules.

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Kim, Kyung Ho, and Young Bae Jun. "Intuitionistic fuzzy interior ideals of semigroups." International Journal of Mathematics and Mathematical Sciences 27, no. 5 (2001): 261–67. http://dx.doi.org/10.1155/s0161171201010778.

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We consider the intuitionistic fuzzification of the concept of interior ideals in a semigroupS, and investigate some properties of such ideals. For any homomorphismffrom a semigroupSto a semigroupT, ifB=(μB,γB)is an intuitionistic fuzzy interior ideal ofT, then the preimagef−1(B)=(f−1(μB),f−1(γB))ofBunderfis an intuitionistic fuzzy interior ideal ofS.

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Atanassov, Krassimir. "Type-1 Fuzzy Sets and Intuitionistic Fuzzy Sets." Algorithms 10, no. 3 (2017): 106. http://dx.doi.org/10.3390/a10030106.

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Sharma, P. K. "AN INVESTIGATION OF F-CLOSURE OF INTUITIONISTIC FUZZY SUBMODULES OF A MODULE." South East Asian Journal of Mathematics and Mathematical Sciences 19, no. 02 (2023): 261–72. http://dx.doi.org/10.56827/seajmms.2023.1902.19.

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In this paper, we introduce the notion of F-closure of intuitionistic fuzzy submodules of a module M. Our attempt is to investigate various characteristics of such an F-closure. If F is a non-empty set of intuitionistic fuzzy ideals of a commutative ring R and A is an intuitionistic fuzzy submodule of M, then the F-closure of A is denoted by ClM F (A). If F is weak closed under intersection, then (1) F-closure of A exhibits the submodule character, and (2) the intersection of F-closure of two intuitionistic fuzzy submodules equals the F-closure of intersection of the intuitionistic fuzzy submo

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Islam, Md Saiful, Md Sahadat Hossain, and Md Asaduzzaman. "Level Separation on Intuitionistic Fuzzy T1 Spaces." Journal of Bangladesh Academy of Sciences 42, no. 1 (2018): 73–85. http://dx.doi.org/10.3329/jbas.v42i1.37834.

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Intuitionistic fuzzy T1 spaces are defined and studied in this paper. Eight new notions of intuitionistic fuzzy T1 spaces are defined and some relationship among them has been investigated. Some relations between the defined notions and other given notions of intuitionistic fuzzy T1 spaces has also been investigated. Under some conditions it is observed that image and preimage preserve intuitionistic fuzzy T1 spaces. Hereditary and productive property of such spaces has been also investigated.Journal of Bangladesh Academy of Sciences, Vol. 42, No. 1, 73-85, 2018

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Riaz, Muhammad, Khadija Akmal, Yahya Almalki, and Daud Ahmad. "Cubic Intuitionistic Fuzzy Topology with Application to Uncertain Supply Chain Management." Mathematical Problems in Engineering 2022 (November 16, 2022): 1–22. http://dx.doi.org/10.1155/2022/9631579.

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The concept of the cubic intuitionistic fuzzy set is an effective hybrid model for modeling uncertainties with an intuitionistic fuzzy set and an interval-valued intuitionistic fuzzy set, simultaneously. The primary objective of this study is to develop a topological structure on cubic intuitionistic fuzzy sets with P-order and R-order as well as to define some fundamental characteristics and significant results with illustrations. Taking advantage of topological data analysis with cubic intuitionistic information, novel multicriteria group decision-making methods are developed for an uncertai

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Sirbiladze, Gia, and Otar Badagadze. "Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making." International Journal of Information Technology & Decision Making 16, no. 01 (2017): 245–79. http://dx.doi.org/10.1142/s0219622016500449.

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Associated Intuitionistic Fuzzy Probabilistic Averaging (As-IFPA) and Associated Intuitionistic Fuzzy Probabilistic Geometric (As-IFPG) operators based on the Choquet integral and an associated probability class of a fuzzy measure are constructed. Propositions on the correctness of the extensions are proved: (1) The As-IFPA (As-IFPG) operator for the fuzzy measure — capacity of order two coincides with the Intuitionistic Fuzzy Choquet Averaging (Intuitionistic Fuzzy Choquet Geometric) operator; (2) The As-IFPA (As-IFPG) operator coincides with the Intuitionistic Fuzzy Probabilistic Averaging (

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Dr., V. S. Subha. "ROUGH INTUITIONISTIC FUZZY IDEALS IN Γ - SEMIGROUPS". International Journal of Applied and Advanced Scientific Research (IJAASR) 1, № 1 (2016): 254–60. https://doi.org/10.5281/zenodo.3605043.

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In this paper we apply the concept of rough intuitionistic fuzzy set in ᴦ-semigoup and discuss some of its properties. We introduce the notion of rough intuitionistic fuzzy left (right, two-sided,bi-,(1,2)-) ideals in ᴦ-semigoup and give some properties of such ideals.

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Islam, R., M. S. Hossain, and M. F. Hoque. "A study on intuitionistic L-fuzzy T₁ spaces." Notes on Intuitionistic Fuzzy Sets 26, no. 3 (2020): 33–42. http://dx.doi.org/10.7546/nifs.2020.26.3.33-42.

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The paper yields some new conjectures of intuitionistic lattice fuzzy ''T''<sub>1</sub> spaces underlying to the concepts of intuitionistic fuzzy topological spaces. These conjectures convey some appreciable and intriguing properties as “Good extension” and “Hereditary” properties. Despite these, all suppositions sustain under one-one, onto, and continuous mapping.

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Atanassov, Krassimir, Eulalia Szmidt, Janusz Kacprzyk, and Nora Angelova. "Intuitionistic fuzzy implications revisited. Part 1." Notes on Intuitionistic Fuzzy Sets 25, no. 3 (2019): 71–78. http://dx.doi.org/10.7546/nifs.2019.25.3.71-78.

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Alkouri, Abd Ulazeez M., and Abdul Razak Salleh. "Complex Atanassov's Intuitionistic Fuzzy Relation." Abstract and Applied Analysis 2013 (2013): 1–18. http://dx.doi.org/10.1155/2013/287382.

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This paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) problems, in complex Atanassov's intuitionistic fuzzy realm. A new structure of relation between two CAIFSs, called complex Atanassov's intuitionistic fuzzy relation (CAIFR), is obtained. This relation is formally generalised from a conventional Atanassov's intuitionistic fuzzy relation, based on complex A

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Dr., M. Mary Jansi Rani, and Sudhalakshmi P. "INTUITIONISTIC M-FUZZY IDEALS OF SEMIGROUPS." International Journal of Computational Research and Development 2, no. 2 (2017): 47–49. https://doi.org/10.5281/zenodo.848247.

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Rajasekar, M., and T. S. Thilagavathi. "Intuitionistic Fuzzy Regular Grammars." Journal of Physics: Conference Series 1850, no. 1 (2021): 012099. http://dx.doi.org/10.1088/1742-6596/1850/1/012099.

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Biswas, Amit, Moumita Chiney, and Syamal Kumar Samanta. "Intuitionistic Type-2 Fuzzy Normed Linear Space and Some of Its Basic Properties." Mathematics 12, no. 14 (2024): 2176. http://dx.doi.org/10.3390/math12142176.

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An intuitionistic fuzzy set is a more generalised tool than a fuzzy set for handling unpredictability as, in an intuitionistic fuzzy set, there is scope for considering a grade of non-membership, independent of the grade of membership, only satisfying the condition that their sum is less or equal to 1. The motivation of this paper is to introduce the notion of intuitionistic type-2 fuzzy normed linear space (IT2FNLS). Here, to each vector x, we assign two fuzzy real number valued grades, one for its norm and the other for the negation of its norm. A theorem of the decomposition of the intuitio

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R. Amutha,. "An operations and relations on the Cartesian Product of Interval Valued Intuitionistic Fuzzy Matrices." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 50–62. https://doi.org/10.52783/cana.v32.3837.

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In this paper, we study an operations and relations on the cartesian product over interval valued intuitionistic fuzzy matrices are introduced and its some properties are explored. We prove some equality based on the operation and the relation over interval valued intuitionistic fuzzy matrices. Finally, we introducing some cartesian formulas 1, 2, 3, 4, 5 in cartesian product of interval valued intuitionistic fuzzy matrices.

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Akram, Muhammad, Amna Habib, Farwa Ilyas, and Jawaria Dar. "Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making." Mathematical and Computational Applications 23, no. 3 (2018): 42. http://dx.doi.org/10.3390/mca23030042.

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The purpose of this research study is to present some new operations, including rejection, symmetric difference, residue product, and maximal product of Pythagorean fuzzy graphs (PFGs), and to explore some of their properties. This research article introduces certain notions, including intuitionistic fuzzy graphs of 3-type (IFGs3T), intuitionistic fuzzy graphs of 4-type (IFGs4T), and intuitionistic fuzzy graphs of n-type (IFGsnT), and proves that every IFG(n−1)T is an IFGnT (for n ≥ 2). Moreover, this study discusses the application of Pythagorean fuzzy graphs in decision making.

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39

Pérez-Cañedo, Boris, José Luis Verdegay та Eduardo René Concepción-Morales. "An ε-Constraint Method for Multiobjective Linear Programming in Intuitionistic Fuzzy Environment". International Journal of Intelligent Systems 2023 (12 квітня 2023): 1–14. http://dx.doi.org/10.1155/2023/9677396.

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Effective decision-making requires well-founded optimization models and algorithms tolerant of real-world uncertainties. In the mid-1980s, intuitionistic fuzzy set theory emerged as another mathematical framework to deal with the uncertainty of subjective judgments and allowed to represent hesitancy in a decision-making problem. Nowadays, intuitionistic fuzzy multiobjective linear programming (IFMOLP) problems are a topic of extensive research, for which a considerable number of solution approaches are being developed. Among the available solution approaches, ranking function-based approaches

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40

Abhishek Kumar Yadav and Dr. R. N. Singh. "Study of Fuzzy Closure and Fuzzy Point." International Journal of Scientific Research in Science and Technology 11, no. 4 (2024): 636–40. https://doi.org/10.32628/ijsrst241151218.

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Three years after Zadeh introduced the notion of a fuzzy set in his seminal paper in 1965, the first paper of fuzzy topology, introduced by Chang, appeared in 1968. Atanassov introduced and studied the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Coker came out with the concept called “intuitionistic fuzzy topological spaces”. Tong introduced and investigated strong forms of open sets called strong regular open, θ-open, and δ-open sets, respectively. In this present paper, we studied fuzzy closure and fuzzy point [1-5].

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41

HUNG, WEN-LIANG. "PARTIAL CORRELATION COEFFICIENTS OF INTUITIONISTIC FUZZY SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, no. 01 (2002): 105–12. http://dx.doi.org/10.1142/s0218488502001351.

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In many applications, partial correlation for three or more intuitionistic fuzzy sets are very important, but Hung [12] do not discuss this problem. In this paper, we propose a method to calculate the partial correlation of intuitionistic fuzzy sets by means of multivariate correlation model. In order to fit into normal framework, we use empirical logit transform (see Agresti [1] and Johnson and Wichern [13]) for the degree of membership of intuitionistic fuzzy set to achive this.

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42

Akter, Mousumi, Kaniz Fatema, and Sahadat Hossain. "Implementation of intuitionistic fuzzy soft set theoretic scheme in decision making." Journal of Bangladesh Academy of Sciences 47, no. 1 (2023): 109–17. http://dx.doi.org/10.3329/jbas.v47i1.63349.

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Fuzzy soft set theory is becoming more and more important for coming up with coherent and logical answers to numerous real-world issues that are riddled with uncertainty, imprecision, and vagueness. The intuitionistic fuzzy soft set was investigated theoretically later on. Wherever uncertainty resulting from ambiguity manifests in more sophisticated ways, the combination of intuitionistic fuzzy set and intuitionistic fuzzy soft set is more efficient from an implementational standpoint. In this paper, the motivation of our work is to establish a new methodology to select an object from an inexa

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43

Mehra, Seema. "Common Fixed Points of Weakly Compatible Mappings in ~-Chainable Intuitionistic Fuzzy Metric Spaces." International Journal of Engineering & Technology 1, no. 1 (2012): 14. http://dx.doi.org/10.14419/ijet.v1i1.24.

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The aim of this paper is to introduce the notion of~-chainable intuitionistic fuzzy metric spaces and prove a common fixed point theorem for four weakly compatible mappings in this newly defined space. Our result is intuitionistic fuzzy version of Cho and Jung's [1] and Mukherjee's [9] results in ~-chainable fuzzy metric space.

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44

Atanassov, Krassimir. "Intuitionistic fuzzy modal operators of second type over interval-valued intuitionistic fuzzy sets. Part 1." Notes on Intuitionistic Fuzzy Sets 24, no. 2 (2018): 8–17. http://dx.doi.org/10.7546/nifs.2018.24.2.8-17.

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45

Riečan, Beloslav, and Dagmar Markechová. "Rényi Entropy and Rényi Divergence in the Intuitionistic Fuzzy Case." Tatra Mountains Mathematical Publications 72, no. 1 (2018): 77–105. http://dx.doi.org/10.2478/tmmp-2018-0023.

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Abstract Our objective in this paper is to define and study the Rényi entropy and the Rényi divergence in the intuitionistic fuzzy case. We define the Rényi entropy of order of intuitionistic fuzzy experiments (which are modeled by IF-partitions) and its conditional version and we examine their properties. It is shown that the suggested concepts are consistent, in the case of the limit of q going to 1, with the Shannon entropy of IF-partitions. In addition, we introduce and study the concept of Rényi divergence in the intuitionistic fuzzy case. Specifically, relationships between the Rényi div

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46

Kumar, P. Senthil. "A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems." International Journal of Operations Research and Information Systems 9, no. 3 (2018): 90–122. http://dx.doi.org/10.4018/ijoris.2018070105.

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This article describes how in solving real-life solid transportation problems (STPs) we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation, many authors have suggested the intuitionistic fuzzy (IF) representation for the data. In this article, the author tried to categorise the STP under uncertain environment. He formulates the intuitionistic fuzzy solid transportation problem (IFSTP) and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The STP has uncertaint

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47

Kumar, Vijay, та M. Mursaleen. "On (λ,µ)-statistical convergence of double sequences on intuitionistic fuzzy normed spaces". Filomat 25, № 2 (2011): 109–20. http://dx.doi.org/10.2298/fil1102109k.

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In this paper, we define (?, ?)- statistical convergence and (?, ?)-statistical Cauchy double sequences on intuitionistic fuzzy normed spaces (IFNS in short), where ? = (?n ) and ? = (?m) be two non-decreasing sequences of positive real numbers such that each tending to ? and ?n+1 ? ?n + 1, ?1 = 1; ?m+1 ? ?m + 1, ?1 = 1. We display example that shows our method of convergence is more general for double sequences in intuitionistic fuzzy normed spaces.

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48

Liu, Peng, Yingkui Gu, and Shancheng Ao. "Reliability analysis of diesel engine cooling system based on improved Bayesian network." Journal of Physics: Conference Series 2761, no. 1 (2024): 012025. http://dx.doi.org/10.1088/1742-6596/2761/1/012025.

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Abstract For the benefit of solving the problem of absoluteness of conditional probability distribution and difficulty in obtaining basic event probability in Bayesian networks, this paper studies the reliability of diesel engine cooling systems through leakage noise or gate intuitionistic fuzzy Bayesian network. Firstly, the leakage noise or gate is introduced into the intuitionistic fuzzy Bayesian network, which makes the results more realistic. Secondly, prior probability in the Bayesian network is obtained based on the similarity aggregation method of triangular intuitionistic fuzzy number

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49

Nazra, Admi, Syafruddin, Riri Lestari, and Gandung Catur Wicaksono. "Hesitant intuitionistic fuzzy soft sets." Journal of Physics: Conference Series 890 (September 2017): 012118. http://dx.doi.org/10.1088/1742-6596/890/1/012118.

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Wang, Hong, and Hong Juan Zhang. "Attribute Reduction of Intuitionistic Fuzzy Concept Lattices." Applied Mechanics and Materials 713-715 (January 2015): 1649–54. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1649.

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In this paper, we turn intuitionistic fuzzy information systems into 0-1 formal contexts by using dominance relation. A pair of operators is defined to get the formal concept lattices in the intuitionistic fuzzy information systems. Furthermore, some properties and attribute reduction based on discernibility matrices is investigated.

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