Applied Z-numbers

Patel, Purvag; Rahimi, Shahram; Khorasani, Elham S.

doi:10.1109/nafips-wconsc.2015.7284154

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…The Z-numbers in the decision making matrix are converted to crisp numbers and the author show the effectiveness of their method. Patel, Rahimi, & Khorasani (2015) provided an applied model of Z-numbers based on certain realistic assumptions regarding probability distributions. Aliev, Alizadeh, Huseynov (2015) proposed an arithmetic to discrete Z-numbers as addition, subtraction, multiplication, division, square root and other operations.…”

Section: Introductionmentioning

confidence: 99%

TODIM and TOPSIS with Z-numbers

Krohling

Pacheco

Santos

2019

Frontiers Inf Technol Electronic Eng

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In this paper, we present an approach that is able to handle with Z-numbers in the context of Multi-Criteria Decision Making (MCDM) problems. Z-numbers are composed of two parts, the first one is a restriction on the values that can be assumed, and the second part is the reliability of the information. As human beings we communicate with other people by means of natural language using sentences like: the journey time from home to university takes about half hour, very likely. Firstly, Z-numbers are converted to fuzzy numbers using a standard procedure. Next, the Z-TODIM and Z-TOPSIS are presented as a direct extension of the fuzzy TODIM and fuzzy TOPSIS, respectively. The proposed methods are applied to two case studies and compared with the standard approach using crisp values. Results obtained show the feasibility of the approach. In addition, a graphical interface was built to handle with both methods Z-TODIM and Z-TOPSIS allowing ease of use for user in other areas of knowledge.

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Section: Introductionmentioning

confidence: 99%

TODIM and TOPSIS with Z-numbers

Krohling

Pacheco

Santos

2019

Frontiers Inf Technol Electronic Eng

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A Review on Some Arithmetic Concepts of Z-Number and Its Application to Real-World Problems

Abdullahi

Ahmad

Ramachandran³

2020

Int. J. Info. Tech. Dec. Mak.

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Zadeh introduced the concept of Z-numbers in 2011 to deal with imprecise information. In this regard, many research works have been published in an attempt to introduce some basic theoretical concepts of Z-numbers to model real-world problems. To understand the current challenges when dealing with Z-numbers and the feasibility of using Z-number in solving real-world problems, a comprehensive review of the existing work on Z-number is paramount. This paper consists of an overview of existing literature on Z-number and identifies some of the key areas that are required for further improvement.

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A precise solution to the shortest path optimization problem in graphs using Z-numbers

Güner,

Orhan,

Allahviranloo

et al. 2024

MATH

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<p>Communication networks are exposed to internal or external risks that can affect all or part of the system. The most important components that form the infrastructure of these systems are routers, which act as nodes. In the field of graph theory, there are sophisticated techniques that can be used to optimize the path of a packet as it travels through various routers from its origin to its destination. A notable example of such an algorithm is Dijkstra's algorithm, which is designed to efficiently determine the shortest path. The algorithm works under the assumption that the system operates under ideal conditions. Real-time systems can perform better if risk factors and optimal conditions are taken into account. The relationship between the nodes can be expressed by various metrics such as distance, delay, and bandwidth. The aforementioned metrics facilitate the calculation of the optimal path, with the ultimate objective of achieving low-latency networks characterized by rapid response times. Round-trip time (RTT) can be employed as a metric for measuring enhancements in a range of latency types, including those associated with processing, transmission, queuing, and propagation. The use of Z-numbers was employed in this study to incorporate risk into the optimal path metric. RTT was the preferred metric and reliability was represented by fuzzy linguistic qualifiers. A comparison of several scenarios was shown using a numerical example of a communication network. It is expected that this study will have a significant impact on the evolution from models that consider only ideal conditions to real-time systems that include risks using Z-numbers.</p>

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Applied Z-numbers

Cited by 3 publications

References 13 publications

TODIM and TOPSIS with Z-numbers

TODIM and TOPSIS with Z-numbers

A Review on Some Arithmetic Concepts of Z-Number and Its Application to Real-World Problems

A precise solution to the shortest path optimization problem in graphs using Z-numbers

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