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Journal ArticleDOI

Morphism of bipolar intuitionistic fuzzy graphs

TL;DR: This paper defined bipolar intuitionistic fuzzy sets, bipolar intuitionist fuzzy relations, isomorphism of these graphs, and discussed some of their properties.
Abstract: In this paper, we define bipolar intuitionistic fuzzy sets, bipolar intuitionistic fuzzy relations, bipolar intuitionistic fuzzy graphs, isomorphism of these graphs and we discussed some of their properties
Citations
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Posted Content
01 Jan 2017-viXra
TL;DR: In this paper, the concept of bipolar single neutrosophic graphs was introduced, which is a generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, and bipolar intuitionistic graph.
Abstract: In this paper, we first define the concept of bipolar single neutrosophic graphs as the generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, single valued neutrosophic graphs and bipolar intuitionistic fuzzy graphs.

112 citations

Journal ArticleDOI
TL;DR: This research proposes some novel similarity measures for bipolar and interval-valued bipolar neutrosophic set such as the cosine similarity measures and weighted cosine similarities measures and applied the proposed measures of similarity for diagnosing bipolar disorder diseases.

110 citations


Cites background from "Morphism of bipolar intuitionistic ..."

  • ...Because of BFS’s potentiality, many authors have studied bipolar fuzzy models on algebraic structures such as the concepts of bipolar fuzzy relations [31], m-polar fuzzy set [34], bipolar fuzzy groups, fuzzy d-ideals of groups under (T-S) norm [35], bipolar valued fuzzy sub-semigroup, bipolar valued fuzzy bi-ideal, and bipolar valued fuzzy ideal [36], bipolar fuzzy sets in sub-semirings [37], and others [38-40, 52-57]....

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Journal ArticleDOI
01 Jul 2018
TL;DR: This article describes how an application of bipolar intuitionistic fuzzy soft set provides into a decision-making problem and a general algorithm to solve this decision making problem.
Abstract: This article describes how recently, a paper by D. Ezhilmaran and K. Sankar called Morphism of bipolar intuitionistic fuzzy graphs, has introduced bipolar intuitionistic fuzzy sets and morphism of bipolar intuitionistic fuzzy graphs. By using this concept, the authors of this article have combined a bipolar intuitionistic fuzzy set and a soft set. They introduce the notion of bipolar intuitionistic fuzzy soft set and study their basic properties. Also, presented in this article are the basic operations on bipolar intuitionistic fuzzy soft sets, extended unions, and the intersection of two bipolar intuitionistic fuzzy soft sets. An application of bipolar intuitionistic fuzzy soft set provides into a decision-making problem and a general algorithm to solve this decision making problem.

43 citations

Journal ArticleDOI
22 Jun 2018-Symmetry
TL;DR: In this paper, a modified Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with maximizing deviation method based on the single-valued neutrosophic set (SVNS) model is presented.
Abstract: A single-valued neutrosophic set (SVNS) is a special case of a neutrosophic set which is characterized by a truth, indeterminacy, and falsity membership function, each of which lies in the standard interval of [0, 1]. This paper presents a modified Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with maximizing deviation method based on the single-valued neutrosophic set (SVNS) model. An integrated weight measure approach that takes into consideration both the objective and subjective weights of the attributes is used. The maximizing deviation method is used to compute the objective weight of the attributes, and the non-linear weighted comprehensive method is used to determine the combined weights for each attributes. The use of the maximizing deviation method allows our proposed method to handle situations in which information pertaining to the weight coefficients of the attributes are completely unknown or only partially known. The proposed method is then applied to a multi-attribute decision-making (MADM) problem. Lastly, a comprehensive comparative studies is presented, in which the performance of our proposed algorithm is compared and contrasted with other recent approaches involving SVNSs in literature.

36 citations

Posted Content
01 Aug 2018-viXra
TL;DR: A modified Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with maximizing deviation method based on the single-valued neutrosophic set (SVNS) model is presented.
Abstract: A single-valued neutrosophic set (SVNS) is a special case of a neutrosophic set which is characterized by a truth, indeterminacy, and falsity membership function, each of which lies in the standard interval of [0, 1]. This paper presents a modified Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with maximizing deviation method based on the single-valued neutrosophic set (SVNS) model.

29 citations

References
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Book
01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.

52,705 citations

Book
01 Jan 1969

16,023 citations

Book
01 Jan 1989
TL;DR: A survey of fundamental notions fuzzy set theory the model of natural language semantics and linguistic variables fuzzy logic decision and control fuzzy systems fuzzy algorithms and programming languages other applications general problems of fuzzy set theorists are surveyed.
Abstract: Survey of fundamental notions fuzzy set theory the model of natural language semantics and linguistic variables fuzzy logic decision and control fuzzy systems fuzzy algorithms and programming languages other applications general problems of fuzzy set theory.

491 citations

Book
26 Apr 2000
TL;DR: Fuzzy Subsets: Fuzzy Relations.- FuzzY Equivalence Relations.- Pattern Classification.- Similarity Relations.- References.- fuzzy Graphs: Paths and Connectedness.
Abstract: Fuzzy Subsets: Fuzzy Relations.- Fuzzy Equivalence Relations.- Pattern Classification.- Similarity Relations.- References.- Fuzzy Graphs: Paths and Connectedness. Bridges and Cut Vertices. Forests and Trees. Trees and Cycles. A Characterization of Fuzzy Trees. (Fuzzy) Cut Sets. (Fuzzy Chords, (Fuzzy) Cotrees, and (Fuzzy) Twigs. (Fuzzy) 1-Chain with Boundary 0, (Fuzzy) Coboundary, and (Fuzzy) Cocycles. (Fuzzy) Cycle Set and (Fuzzy) Cocycle Set.- Fuzzy Line Graphs.- Fuzzy Interval Graphs. Fuzzy Intersection Graphs. Fuzzy Interval Graphs. The Fulkerson and Gross Characterization. The Gilmore and Hoffman Characterization.- Operations on Fuzzy Graphs: Cartesian Product and Composition. Union and Join.- On Fuzzy Tree Definition.- References.- Applications of Fuzzy Graphs: Clusters.- Cluster Analysis. Cohesiveness. Slicing in Fuzzy Graphs.- Application to Cluster Analysis.- Fuzzy Intersection Equations. Existence of Solutions.- Fuzzy Graphs in Database Theory. Representation of Dependency Structure r(X,Y) by Fuzzy Graphs.- A Description of Strengthening and Weakening Members of a Group. Connectedness Criteria. Inclusive Connectedness Categories. Exclusive Connectedness Categories.- An Application of Fuzzy Graphs to the Problem Concerning Group Structure. Connectedness of a Fuzzy Graph. Weakening and Strenghtening Points of a Fuzzy Directed Graph.- References.- Fuzzy Hypergraphs: Fuzzy Hypergraphs.- Fuzzy Transversals of Fuzzy Hypergraphs. Properties of Tr(H). Construction of H3.- Coloring of Fuzzy Hypergraphs. beta-degree Coloring Procedures. Chromatic Values of Fuzzy Colorings.- Intersecting Fuzzy Hypergraphs. Characterization of Strongly Intersecting Hypergraphs. Simply Ordered Intersecting Hypergraphs. H-dominant Transversals.- Hebbian Structures.- Additional Applications.- References.

468 citations


"Morphism of bipolar intuitionistic ..." refers methods in this paper

  • ...Complement of fuzzy graphs were introduced by Mordeson and Nair[7]....

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  • ...[7] J.N. Mordeson, P.S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, second ed., Physica Verlag, Heidelberg, 1998, 2001....

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Journal ArticleDOI
TL;DR: It is shown that a fuzzy group can be associated with a fuzzy graph in a natural way and some properties of fuzzy graphs are considered and the notions of eccentricity and center are introduced.

399 citations


"Morphism of bipolar intuitionistic ..." refers background in this paper

  • ...Bhattacharya[5] in 1987 developed some remarks on fuzzy graphs, Mordeson and Peng[6] studied some operations on fuzzy graphs....

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