$$\varvec{m}$$ m -Polar Fuzzy Labeling Graphs with Application

Akram, Muhammad; Adeel, Arooj

doi:10.1007/s11786-016-0277-x

Cited by 19 publications

(6 citation statements)

References 14 publications

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“…This kind of variable can well be represented by triangular or trapezoidal fuzzy numbers. For the study of linguistic variables, readers are referred to Zadeh (1975), Akram and Adeel (2016), Zhang et al (2017), and. Linguistic variables can be stated as various kinds of fuzzy numbers.…”

Section: Analysis Of Linguistic Variablesmentioning

confidence: 99%

Fuzzy Data Envelopment Analysis with Ordinal and Interval Data

Izadikhah

Roostaee

Emrouznejad

2021

Int. J. Unc. Fuzz. Knowl. Based Syst.

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In this paper, we reformulate the conventional DEA models as an imprecise DEA problem and propose a novel method for evaluating the DMUs when the inputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose, we convert all data into interval data. In order to convert each fuzzy number into interval data, we use the nearest weighted interval approximation of fuzzy numbers by applying the weighting function, and we convert each ordinal data into interval one. In this manner, we could convert all data into interval data. The presented models determine the interval efficiencies for DMUs. To rank DMUs based on their associated interval efficiencies, we first apply the Ω-index that is developed for ranking of interval numbers. Then, by introducing an ideal DMU, we rank efficient DMUs to present a complete ranking. Finally, we use one example to illustrate the process and one real application in health care to show the usefulness of the proposed approach. For this evaluation, we consider interval, ordinal, and fuzzy data alongside the precise data to evaluate 38 hospitals selected by OIG. The results reveal the capabilities of the presented method to deal with the imprecise data.

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Section: Analysis Of Linguistic Variablesmentioning

confidence: 99%

Fuzzy Data Envelopment Analysis with Ordinal and Interval Data

Izadikhah

Roostaee

Emrouznejad

2021

Int. J. Unc. Fuzz. Knowl. Based Syst.

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“… 2017 ), m -PF graph structures (Akram et al. 2016 ), faces and dual of m -PF graphs (Ghorai and Pal 2016a ), m -PF labeling graphs (Akram and Adeel 2016 ), fuzzy coloring of m -PF graphs (Mahapatra and Pal 2018 ), and applications of m -PF graphs in decision support systems (Akram and Sarwar 2017 ). The strength of connectedness between vertices has been recently studied in an m -PF graph (Mandal et al.…”

Section: Introductionmentioning

confidence: 99%

Connectivity indices of m-polar fuzzy network model, with an application to a product manufacturing problem

2022

Self Cite

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Connectivity is among the most essential concerns in graph theory and its applications. We consider this issue in a framework that stems from the combination of m-polar fuzzy set theory with graphs. We introduce two measurements of connectedness of m-polar fuzzy graphs that we call their connectivity and average connectivity indices. Examples are given, and the theoretical performance of these concepts is investigated. Particularly, we are concerned with the effect of deleting a vertex or an edge from an m-polar fuzzy graph, on its connectivity and average connectivity indices. We also establish bounding expressions for the connectivity index in complete m-polar fuzzy graphs, complete bipartite m-polar fuzzy graphs, and wheel m-polar fuzzy graphs. Moreover, we introduce some special types of vertices called m-polar fuzzy connectivity reducing vertices, m-polar fuzzy connectivity enhancing vertices, and m-polar fuzzy connectivity neutral vertices. Our theoretical contribution is applied to a product manufacturing problem that takes advantage of multi-polar uncertain information. The justification for our application is systematized using an algorithm. Finally, we compare the proposed method to existing methodologies to demonstrate its feasibility and applicability.

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“…Akram and Younas studied certain types of irregular m-polar fuzzy graphs in [12]. In 2016 Akram and Adeel studied on m-polar fuzzy labelling graphs [13] and Akram and Waseem introduced certain metrics in m-polar fuzzy graphs in [14]. Lately Prem Kumar studied on m-polar fuzzy graph representation of concept lattice [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Unify Steiner Weiner Distance for Some Class of m-Polar Fuzzy Graphs

Karbasioun

Ameri

2019

Fuzzy Information and Engineering

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Sometimes information in a network model is based on multi-agent, multi-attribute, multi-object, multi-polar information or uncertainty rather than a single bit. An m-polar fuzzy model is useful for such network models which gives more and more precision, flexibility, and comparability to the system as compared to the classical, fuzzy models. On the other, The Steiner tree problem in networks, and particularly in graphs, was formulated by Hakimi [25] and Levi [21] by definition minimal size connected tree sub graph that contains the vertices in S. Steiner trees have applications to multiprocessor computer networks. For example, it may be desired to connect a certain set of processors with a sub network that uses the fewest communication links. In this paper, we extend Steiner distance SW k (G) for m-polar fuzzy graphs and give this parameter for Join, composition and Cartesian product of two m-polar fuzzy graphs.

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$$\varvec{m}$$ m -Polar Fuzzy Labeling Graphs with Application

Cited by 19 publications

References 14 publications

Fuzzy Data Envelopment Analysis with Ordinal and Interval Data

Fuzzy Data Envelopment Analysis with Ordinal and Interval Data

Connectivity indices of m-polar fuzzy network model, with an application to a product manufacturing problem

Unify Steiner Weiner Distance for Some Class of m-Polar Fuzzy Graphs

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