The arithmetic of discrete Z-numbers

Aliev, R. A.; Alizadeh, Akif A.; Huseynov, Oleg H.

doi:10.1016/j.ins.2014.08.024

Cited by 250 publications

(90 citation statements)

References 23 publications

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“…A Z-number has two components, Z ¼ ðA; BÞ; used to explain a value of a random variable X, where A is an estimation of a value of X and B is a measure of confidence of A [38]. For example, suppose a researcher gives the prediction of a condition of economy as follows [1]: Prediction of a condition of economy for the next year = (sturdy growth, sure). This forecast can be expressed as a Z-number evaluation, where X is the variable state of economy, A is a fuzzy number applied to explain the constraint "sturdy growth" and B is a fuzzy number to describe the degree of certainty of A.…”

Section: Definition 1 (Linguistic Variables)mentioning

confidence: 99%

“…A result is concluded by aggregating the fuzzy criteria weights and fuzzy rating of alternatives (1). The preferences of experts of the alternative i under the criterion j can be calculated using (2).…”

Section: Promethee and Fuzzy Prometheementioning

confidence: 99%

“…It is essential to state that transforming Z-numbers into conventional fuzzy numbers leads to loss of information. However, According to Aliev et al [1] the key benefit of this method is low computational complexity, which allows for an extensive range of its use.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Multi-criteria Group Decision-Making Approach for Facility Location Selection Using PROMETHEE Under a Fuzzy Environment

Tavakkoli–Moghaddam

Sotoudeh-Anvari

Siadat

2015

Lecture Notes in Business Information Processing

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Abstract. This paper presents a Z-PROMETHEE with Z-numbers as a new representation of vague information for a facility location selection (FLS) problem. The selection of a facility location, which is a kind of a multi-criteria decision making (MCDM) problem, should be considered from a strategic point of view. In a real-world situation, MCDM problems are generally under uncertainty. In order to overcome such a problem, fuzzy sets can be applied with the PROMETHEE to allow experts to combine inadequate information into the decision method. However, the fuzzy PROMETHEE also has some defects. The main problem is that the certainty of information is not taking into account. For explanation of real-life information, fuzziness and degree of the certainty of information are indispensable. In the proposed method, Z-numbers are used to evaluate the weights of the criteria. Hence, in comparison with the fuzzy model, the PROMETHEE with a Z-number (i.e., Z-PROMETHEE) can symbolize real life problems more realistically.

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Section: Definition 1 (Linguistic Variables)mentioning

confidence: 99%

Section: Promethee and Fuzzy Prometheementioning

confidence: 99%

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A Multi-criteria Group Decision-Making Approach for Facility Location Selection Using PROMETHEE Under a Fuzzy Environment

Tavakkoli–Moghaddam

Sotoudeh-Anvari

Siadat

2015

Lecture Notes in Business Information Processing

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show abstract

“…Z‐number combined with constraint and reliability is proposed by Zadeh, which is an increasingly hot topic in the research field of fuzzy set . Z‐number is a good framework to express the thinking and knowledge of human flexibly .…”

Section: Introductionmentioning

confidence: 99%

Generating Z-number based on OWA weights using maximum entropy

Kang

Deng

Hewage

et al. 2018

Int. J. Intell. Syst.

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In the application of Z‐number, how to generate Z‐number is a significant and open issue. In this paper, we proposed a method of generating Z‐number based on the OWA weights using maximum entropy considering the attitude (preference) of the decision maker. Some numerical examples are used to illustrate the effectiveness of the proposed method. Results show that the attitude (preference) of the decision maker can give an optimal possibility distribution of the reliability for Z‐number using maximum entropy.

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“…Aliev, Alizadeh, and Huseynov study the arithmetics of discrete Z ‐numbers in Ref. . After that H‐difference of discrete Z ‐numbers is proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

On Ranking of Continuous Z-Numbers with Generalized Centroids and Optimization Problems Based onZ-Numbers

Qiu

Xing

Dong

2017

Int. J. Intell. Syst.

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In this paper, we introduce the addition and g-difference of continuous Z-numbers at first. Then, we define a new partial order to rank the Z-numbers with generalized centroids. The g-derivative of Z-number function based on g-difference is proposed. It is well known that convexity plays a vital role in optimization problems; consequently, we present the convexity of Z-number function. Furthermore, we provide the optimality conditions for optimization problems based on Z-numbers. Finally, the validity of the discussion is illustrated by an example. C 2017 Wiley Periodicals, Inc.

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The arithmetic of discrete Z-numbers

Cited by 250 publications

References 23 publications

A Multi-criteria Group Decision-Making Approach for Facility Location Selection Using PROMETHEE Under a Fuzzy Environment

A Multi-criteria Group Decision-Making Approach for Facility Location Selection Using PROMETHEE Under a Fuzzy Environment

Generating Z-number based on OWA weights using maximum entropy

On Ranking of Continuous Z-Numbers with Generalized Centroids and Optimization Problems Based onZ-Numbers

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