Application of Z-numbers in multi-criteria decision making

Xiao, Zhi-Quan

doi:10.1109/iccss.2014.6961822

Cited by 26 publications

(17 citation statements)

References 15 publications

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“…This case study proposed by Xiao (2014) consists in the evaluation of certain type of clothing by male customers. The alternatives are: like 1 A (very much), 2 A (like), 3 A (ordinary) and 4 A (dislike).…”

Section: Case Study 2 -Clothing Evaluationmentioning

confidence: 99%

“…The weights of criteria are crisp values. (Xiao, 2014). The Z-TODIM and Z-TOPSIS were applied to this problem after converting the Z-number to trapezoidal fuzzy numbers (Xiao, 2014).…”

Section: Case Study 2 -Clothing Evaluationmentioning

confidence: 99%

“…(Xiao, 2014). The Z-TODIM and Z-TOPSIS were applied to this problem after converting the Z-number to trapezoidal fuzzy numbers (Xiao, 2014). In table 9, we present the results obtained by Z-TODIM, Z-TOPSIS and those provided by Xiao (2014).…”

Section: Case Study 2 -Clothing Evaluationmentioning

confidence: 99%

“…An application to search the criteria's for the evaluation of best universities. Xiao (2014) proposed a method for fuzzy multi-criteria decision making with Znumbers, where the evaluation of each alternative with respect to each criterion is described as a Z-number. The Z-numbers in the decision making matrix are converted to crisp numbers and the author show the effectiveness of their method.…”

Section: Introductionmentioning

confidence: 99%

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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: Case Study 2 -Clothing Evaluationmentioning

confidence: 99%

“…The weights of criteria are crisp values. (Xiao, 2014). The Z-TODIM and Z-TOPSIS were applied to this problem after converting the Z-number to trapezoidal fuzzy numbers (Xiao, 2014).…”

Section: Case Study 2 -Clothing Evaluationmentioning

confidence: 99%

Section: Case Study 2 -Clothing Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

TODIM and TOPSIS with Z-numbers

Krohling

Pacheco

Santos

2019

Frontiers Inf Technol Electronic Eng

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“…Kang et al [21] solved the decision-making problem by converting Z-number to crisp numbers using the approach given in [22]. Xiao et al [23] converted Z-number to type-2 fuzzy set to solve multicriteria decision-making. Here, by calculating the centroid type-2 fuzzy sets, it is converted to the crisp numbers for decisionmaking.…”

Section: Introductionmentioning

confidence: 99%

Estimation of Food Security Risk Level UsingZ-Number-Based Fuzzy System

Abiyev

Uyar

İlhan

et al. 2018

Journal of Food Quality

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Fuzzy logic systems based on If-en rules are widely used for modelling of the systems characterizing imprecise and uncertain information. ese systems are basically based on type-1 fuzzy sets and allow handling the uncertain and imprecise information to some degree in the developed models. Zadeh extended the concept of fuzzy sets and proposed Z-number characterized by two components, constraint and reliability parameters, which are an ordered pair of fuzzy numbers. Here, the rst component is used to represent uncertain information, and the second component is used to evaluate the reliability or the con dence in truth. Znumber is an e ective approach to solving uncertain problems. In this paper, Z-number-based fuzzy system is proposed for estimation of food security risk level. To construct fuzzy If-en rules, the basic parameters cereal yield, cereal production, and economic growth a ecting food security are selected, and the relationship between these input parameters and risk level are determined through If-en fuzzy rules. e fuzzy interpolative reasoning is proposed for construction of inference mechanism of a Z-number-based fuzzy system. e designed system is tested using Turkey cereal data for assessing food security risk level and prediction periods of the food supply.

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Ranking of Z‐numbers based on value and ambiguity at levels of decision making

Chutia

2020

Int J Intell Syst

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The concept of Z-number, is very new in the literature, proposed by Zadeh in 2011. The Z-number Z A B = (,) is a pair of fuzzy numbers where the first component represents the restriction and the second component represents the certainty of the first component. Further, its application is evident in decision-making problems, risk assessment, linear programming problems, and so forth. Hence, under such circumstances ranking of Z-numbers need an utmost attention, as such, a few methods of ranking Z-numbers are proposed by various researcher. However, in many situations the existing methods depict drawbacks and limitations as discussed in this paper. Hence, a new method of ranking Z-numbers is essential for an appropriate decision-making. In this paper, a new method of ranking Z-numbers based on the concept of value and ambiguity at levels of decision-making have been proposed. The method seems to deliver a reasonable decision and proper ranking of Z-numbers of various types. A few numerical examples are discussed which show the out-performance of the proposed method.

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Application of Z-numbers in multi-criteria decision making

Cited by 26 publications

References 15 publications

TODIM and TOPSIS with Z-numbers

TODIM and TOPSIS with Z-numbers

Estimation of Food Security Risk Level UsingZ-Number-Based Fuzzy System

Ranking of Z‐numbers based on value and ambiguity at levels of decision making

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