On <i>m</i>-Polar Interval-valued Fuzzy Graph and its Application

Bera, Sanchari; Pal, Madhumangal

doi:10.1080/16168658.2020.1785993

Cited by 11 publications

(4 citation statements)

References 26 publications

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“…Some applications of m-polar fuzzy graphs for facilitating the decision-making process in a wide variety of studied domains are discussed in [31,34,35]. It is obvious that the presented methods and techniques have the potential to deal with multi-attribute, multicriteria, and multi-objective problems in uncertain and fuzzy environments.…”

Section: Lexicographic Productmentioning

confidence: 99%

M-Polar Fuzzy Graphs and Deep Learning for the Design of Analog Amplifiers

Ivanova

Durcheva

2023

Mathematics

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The design of analog circuits is a complex and repetitive process aimed at finding the best design variant. It is characterized by uncertainty and multivariate approaches. The designer has to make different choices to satisfy a predefined specification with required parameters. This paper proposes a method for facilitating the design of analog amplifiers based on m-polar fuzzy graphs theory and deep learning. M-polar fuzzy graphs are used because of their flexibility and the possibility to model different real-life multi-attribute problems. Deep learning is applied to solve a regression task and to predict the membership functions of the m-polar fuzzy graph vertices (the solutions), taking on the role of domain experts. The performance of the learner is high since the obtained errors are very small: Root Mean Squared Error is from 0.0032 to 0.0187, Absolute Error is from 0.022 to 0.098 and Relative Error is between 0.27% and 1.57%. The proposed method is verified through the design of three amplifiers: summing amplifier, subtracting amplifier, and summing/subtracting amplifier. The method can be used for improving the design process of electronic circuits with the possibility of automating some tasks.

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Section: Lexicographic Productmentioning

confidence: 99%

M-Polar Fuzzy Graphs and Deep Learning for the Design of Analog Amplifiers

Ivanova

Durcheva

2023

Mathematics

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“…Applying the idea of interval-valued k-polar fuzzy (IV k PF) sets to BCK/BCI-algebras, Muhiuddin and Al-Kadi extended the work of [22], proposed the concepts of IV k PF subalgebras and IV k PF (commutative) ideals in BCK(BCI)algebras, and investigated some essential properties [26]. Since that time, the notions of multi-polar hybrid FSs have been utilized in many scientific and technological fields, among which are graph theory [27][28][29][30], topology [31], matroid theory [32], decision-making [33,34] and so on. By extending the work of [22] and motivated by the previous works, the notion of C k P subalgebras and (closed) C k P ideals in BCK/BCI-algebras is presented by combining the concept of k PF subalgebras/(closed) ideals and cubic subalgebras/(closed) ideals, and characterizations of subalgebras and ideals according to the properties of C k P structures are given in this present work.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras

Al-Masarwah

Alshehri

2022

Mathematics

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Cubic multipolar structure with finite degree (briefly, cubic k-polar (CkP) structure) is a new hybrid extension of both k-polar fuzzy (kPF) structure and cubic structure in which CkP structure consists of two parts; the first one is an interval-valued k-polar fuzzy (IVkPF) structure acting as a membership grade extended from the interval P[0,1] to P[0,1]k (i.e., from interval-valued of real numbers to the k-tuple interval-valued of real numbers), and the second one is a kPF structure acting as a nonmembership grade extended from the interval [0,1] to [0,1]k (i.e., from real numbers to the k-tuple of real numbers). This approach is based on generalized cubic algebraic structures using polarity concepts and therefore the novelty of a CkP algebraic structure lies in its large range comparative to both kPF algebraic structure and cubic algebraic structure. The aim of this manuscript is to apply the theory of CkP structure on BCK/BCI-algebras. We originate the concepts of CkP subalgebras and (closed) CkP ideals. Moreover, some illustrative examples and dominant properties of these concepts are studied in detail. Characterizations of a CkP subalgebra/ideal are given, and the correspondence between CkP subalgebras and (closed) CkP ideals are discussed. In this regard, we provide a condition for a CkP subalgebra to be a CkP ideal in a BCK-algebra. In a BCI-algebra, we provide conditions for a CkP subalgebra to be a CkP ideal, and conditions for a CkP subalgebra to be a closed CkP ideal. We prove that, in weakly BCK-algebra, every CkP ideal is a closed CkP ideal. Finally, we establish the CkP extension property for a CkP ideal.

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“…Fuzzy sets are used to describe the uncertainty of things, and are widely used in fuzzy reasoning, fuzzy intelligent decision-making systems and other fields, and thus have received widespread attention (see Bera and Pal [1] and [2], Islam and Pal [3], Samanta1 et al [4], Amanathulla et al [5], Pal et al [6], Prabakaran et al [7], Bagherinia et al [8], Gonzalez et al [9], and Maldonado et al [10]). On the other hand, graphs are an effective tool to describe the structured data.…”

Section: Introductionmentioning

confidence: 99%

Domination of Bipolar Fuzzy Graphs in Various Settings

Gong

Hua

Gao

2021

Int J Comput Intell Syst

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Bipolar fuzzy sets are used to describe the positive and negative of the uncertainty of objects, and the bipolar fuzzy graphs are used to characterize the structural relationship between uncertain concepts in which the vertices and edges are assigned positive and negative membership function values to feature the opposite uncertainty elevation. The dominating set is the control set of vertices in the graph structure and it occupies a critical position in graph analysis. This paper mainly contributes to extending the concept of domination in the fuzzy graph to the bipolar frameworks and obtaining the related expanded concepts of a variety of bipolar fuzzy graphs. Meanwhile, the approaches to obtain the specific dominating sets are presented. Finally, a numeral example on city data in Yunnan Province is presented to explain the computing of domination in bipolar fuzzy graph in the specific application.

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On m-Polar Interval-valued Fuzzy Graph and its Application

Cited by 11 publications

References 26 publications

M-Polar Fuzzy Graphs and Deep Learning for the Design of Analog Amplifiers

M-Polar Fuzzy Graphs and Deep Learning for the Design of Analog Amplifiers

Algebraic Perspective of Cubic Multi-Polar Structures on BCK/BCI-Algebras

Domination of Bipolar Fuzzy Graphs in Various Settings

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