Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview

Talea, Mohamed; Bakali, Assia; Smarandache, Florentín; Nagarajan, D.; Lathamaheswari, M.; Parimala, M.

doi:10.1007/s40747-019-0098-z

Cited by 49 publications

(28 citation statements)

References 60 publications

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“…The critical path is always reflected among the schedule, project phases throughout the lifecycle. A few established works in critical and shortest path methods are recently developed in the neutrosophic arena [24][25][26][27][28].…”

Section: Relationship Between Any Two Cylindrical Neutrosophic Singlementioning

confidence: 99%

Cylindrical neutrosophic single‐valued number and its application in networking problem, multi‐criterion group decision‐making problem and graph theory

Chakraborty

Mondal

Alam

et al. 2020

CAAI trans. intell. technol.

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In this study, the authors envisage the neutrosophic number from various distinct rational perspectives and viewpoints to give it a look of a conundrum. They focused and analysed neutrosophic fuzzy numbers when indeterminacy and falsity functions are dependent on each other, which serves an indispensable role for the uncertainty concept. Additionally, the idea of cylindrical neutrosophic single-valued number is focused here, when the indeterminacy and falsity functions are dependent to each other using an influx of different logical and innovative graphical representation. They also developed the score and accuracy function for this particular cylindrical neutrosophic single-valued number and analysed some real-life problems like networking critical path model problem and minimal spanning tree problem of operation research field when the numbers are in cylindrical neutrosophic ambiance. They also introduced a multi-criterion group decision-making problem in this cylindrical neutrosophic domain. This noble thought will help us to solve a plethora of daily life problems in the neutrosophic arena.

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Section: Relationship Between Any Two Cylindrical Neutrosophic Singlementioning

confidence: 99%

Cylindrical neutrosophic single‐valued number and its application in networking problem, multi‐criterion group decision‐making problem and graph theory

Chakraborty

Mondal

Alam

et al. 2020

CAAI trans. intell. technol.

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“…Broumi et al [15] dealt with SPP using single valued neutrosophic graphs. Broumi et al [16] made an analysis on SPP under various environments. Broumi et al [17] solved SPP under interval valued trapezoidal and triangular neutrosophic setting.…”

Section: Literature Reviewmentioning

confidence: 99%

Intelligent algorithm for trapezoidal interval valued neutrosophic network analysis

Nagarajan

Lathamaheswari

Talea

et al. 2020

CAAI trans. intell. technol.

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The shortest path problem has been one of the most fundamental practical problems in network analysis. One of the good algorithms is Bellman-Ford, which has been applied in network, for the last some years. Due to complexity in the decision-making process, the decision makers face complications to express their view and judgment with an exact number for single valued membership degrees under neutrosophic environment. Though the interval number is a special situation of the neutrosophic, it did not solve the shortest path problems in an absolute manner. Hence, in this work, the authors have introduced the score function and accuracy function of trapezoidal interval valued neutrosophic numbers with their illustrative properties. These properties provide important theoretical base of the trapezoidal interval valued neutrosophic number. Also, they proposed an intelligent algorithm called trapezoidal interval valued neutrosophic version of Bellman's algorithm to solve neutrosophic shortest path problem in network analysis. Further, comparative analysis has been made with the existing algorithm.

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“…Moreover, the fuzzy-based modified particle swarm optimization algorithm [22] and elite artificial bees' colony algorithm [23] can be used for solving FSP problem. An overview of efficient algorithms for solving SP problems with various types of input data in junction with fuzzy, intuitionistic, vague, interval fuzzy, interval-valued intuitionistic fuzzy and neutrosophic sets can be found in Broumi et al [24].…”

Section: Introductionmentioning

confidence: 99%

Solving fuzzy multi-objective shortest path problem based on data envelopment analysis approach

Bagheri

Ebrahimnejad

Razavyan

et al. 2021

Complex Intell. Syst.

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The shortest path problem (SPP) is a special network structured linear programming problem that appears in a wide range of applications. Classical SPPs consider only one objective in the networks while some or all of the multiple, conflicting and incommensurate objectives such as optimization of cost, profit, time, distance, risk, and quality of service may arise together in real-world applications. These types of SPPs are known as the multi-objective shortest path problem (MOSPP) and can be solved with the existing various approaches. This paper develops a Data Envelopment Analysis (DEA)-based approach to solve the MOSPP with fuzzy parameters (FMOSPP) to account for real situations where input–output data include uncertainty of triangular membership form. This approach to make a connection between the MOSPP and DEA is more flexible to deal with real practical applications. To this end, each arc in a FMOSPP is considered as a decision-making unit with multiple fuzzy inputs and outputs. Then two fuzzy efficiency scores are obtained corresponding to each arc. These fuzzy efficiency scores are combined to define a unique fuzzy relative efficiency. Hence, the FMOSPP is converted into a single objective Fuzzy Shortest Path Problem (FSPP) that can be solved using existing FSPP algorithms.

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Shortest path problem in fuzzy, intuitionistic fuzzy and neutrosophic environment: an overview

Abstract: In the last decade, concealed by uncertain atmosphere, many algorithms have been studied deeply to workout the shortest path problem. In this paper, we compared the shortest path problem with various existing algorithms. Finally, we concluded the best algorithm for certain environment.

Cited by 49 publications

References 60 publications

Cylindrical neutrosophic single‐valued number and its application in networking problem, multi‐criterion group decision‐making problem and graph theory

Cylindrical neutrosophic single‐valued number and its application in networking problem, multi‐criterion group decision‐making problem and graph theory

Intelligent algorithm for trapezoidal interval valued neutrosophic network analysis

Solving fuzzy multi-objective shortest path problem based on data envelopment analysis approach

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