Operations on fuzzy numbers

Dubois, Didier; Prade, Henri

doi:10.1080/00207727808941724

Cited by 2,258 publications

(942 citation statements)

References 4 publications

Supporting

Mentioning

921

Contrasting

Unclassified

Order By: Relevance

“…Triangular fuzzy numbers are special classes of fuzzy numbers whose membership is defined by three real numbers, expressed as (l, m, u) (Dubois & Prade, 1978). The symbols (l, m, u) represent the minimum possible value, the possible value and the maximum possible value, respectively.…”

Section: Appendix Fahp-topsis Framework Fuzzy Analytic Hierarchy Procmentioning

confidence: 99%

An FAHP-TOPSIS framework for analysis of the employee productivity in the Serbian electrical power companies

Knežević

Mandić

Mitrović

et al. 2017

mng

View full text Add to dashboard Cite

The aim of this paper is to apply an integrated model, which combines methods of classical and fuzzy Multi-criteria decision making (MCDM) in selected six large equity companies from the Serbian energy sector. The data considered are retrieved from the official financial statements. Four main criteria were analyzed, identified by the previous researchers and pointing to the employees’ productivity: Operating income/Number of employees, Equity/Number of employees, Net income/Number of employees and Total assets/Number of employees. The contribution of this paper lies in the application of a hybrid model that integrates two MCDM methods: Fuzzy Analytic Hierarchy Process (FAHP) and Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) to analyse the employee productivity in selected D-Electrical power supply companies operating in Serbia. The FAHP is an effective method for mathematical representation of uncertain and imprecise evaluations made by humans, while the TOPSIS method is an efficient way to rank the alternatives. Results show that operating income is of highest importance for estimating employee productivity and decision making, while equity is of the weakest. Furthermore, the most productive operations in large enterprises from selected companies of the sector D-Electrical power supply are found in the company PC EPS Beograd, and the lowest are in the ED Center llc Kragujevac.

show abstract

Section: Appendix Fahp-topsis Framework Fuzzy Analytic Hierarchy Procmentioning

confidence: 99%

An FAHP-TOPSIS framework for analysis of the employee productivity in the Serbian electrical power companies

Knežević

Mandić

Mitrović

et al. 2017

mng

View full text Add to dashboard Cite

show abstract

“…Uncertainty is generated by statistical data's lack, experts' fuzzy statements, by action of various factors, etc. However, in the scientific literature [1][2][3][4][5][6][7][8][9][10] are considered basically trapezoidal and triangular approximations of fuzzy numbers. By means of these approximations it is impossible to represent fuzzy number with multimodal value, for example, "or 3 or 4 ".…”

Section: Introductionmentioning

confidence: 99%

Algorithm of Arithmetical Operations with Fuzzy Numerical Data

Bocharnikov¹,

Sveshnikov²

2007

SSRN Journal

View full text Add to dashboard Cite

In this article the theoretical generalization for representation of arithmetic operations with fuzzy numbers is considered. Fuzzy numbers are generalized by means of fuzzy measures. On the basis of this generalization the new algorithm of fuzzy arithmetic which uses a principle of entropy maximum is created. As example, the summation of two fuzzy numbers is considered. The algorithm is realized in the software "Fuzzy for Microsoft Excel".

show abstract

“…see, e.g., [1,8,16,17]. So, if we know how to solve our problem under interval uncertainty, we can also solve it under fuzzy uncertainty -e.g., by repeating the above interval computations for α = 0, 0.1, .…”

Section: Second Case Study: Fuzzy Computationsmentioning

confidence: 99%

No-Free-Lunch Result for Interval and Fuzzy Computing: When Bounds Are Unusually Good, Their Computation Is Unusually Slow

Ceberio

Kreinovich

2011

Advances in Soft Computing

View full text Add to dashboard Cite

Abstract.On several examples from interval and fuzzy computations and from related areas, we show that when the results of data processing are unusually good, their computation is unusually complex. This makes us think that there should be an analog of Heisenberg's uncertainty principle well known in quantum mechanics: when we an unusually beneficial situation in terms of results, it is not as perfect in terms of computations leading to these results. In short, nothing is perfect. First Case Study: Interval ComputationsNeed for data processing. In science and engineering, we want to understand how the world works, we want to predict the results of the world processes, and we want to design a way to control and change these processes so that the results will be most beneficial for the humankind.For example, in meteorology, we want to know the weather now, we want to predict the future weather, and -if, e.g., floods are expected, we want to develop strategies that would help us minimize the flood damage.Usually, we know the equations that describe how these systems change in time. Based on these equations, engineers and scientists have developed algorithms that enable them to predict the values of the desired quantities -and find the best values of the control parameters. As input, these algorithms take the current and past values of the corresponding quantities.For example, if we want to predict the trajectory of the spaceship, we need to find its current location and velocity, the current position of the Earth and of the celestial bodies, then we can use Newton's equations to find the future locations of the spaceship.In many situations -e.g., in weather prediction -the corresponding computations require a large amount of input data and a large amount of computations steps. Such computations (data processing) are the main reason why computers were invented in the first place -to be able to perform these computations in reasonable time.

show abstract

Operations on fuzzy numbers

Cited by 2,258 publications

References 4 publications

An FAHP-TOPSIS framework for analysis of the employee productivity in the Serbian electrical power companies

An FAHP-TOPSIS framework for analysis of the employee productivity in the Serbian electrical power companies

Algorithm of Arithmetical Operations with Fuzzy Numerical Data

No-Free-Lunch Result for Interval and Fuzzy Computing: When Bounds Are Unusually Good, Their Computation Is Unusually Slow

Contact Info

Product

Resources

About