On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights

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Pavlacka O.; Pavlackova M.

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Journal Paper

Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2021 | Volume:18 | Issue:4 Page(s): 1-17

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Information Journal Paper

Title

On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights

Author(s)

Pavlacka O. | Pavlackova M. | Issue Writer Certificate

Keywords

Aggregation operatorQ2

fuzzy numbersQ2

normalized fuzzy weightsQ2

fuzzy probabilitiesQ2

fuzzy weighted aver-ageQ2

Abstract

Weighted average with normalized weights is a widely used Aggregation operator that takes into account the varying degrees of importance of the numbers in a data set. It possesses some important properties, like monotonicity, continuity, additivity, etc., that play an important role in practical applications. The inputs of the aggregation as well as the normalized weights are usually not known precisely. In such a case, their values can be expressed by fuzzy numbers, and the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights needs to be employed in the model. The aim of the paper is to reveal whether and in which way the properties of the weighted average operator can be observed also for its fuzzy extension. It is shown that it possesses three conditions characteristic for Aggregation operators { identity, monotonicity and boundary conditions, and besides that, also compensation, idempotency, stability for linear transformation, 1-lipschitzianity, and continuity. Furthermore, it is proved that it preserves strict monotonicity in case of positive fuzzy weights, and symmetry in case of equal fuzzy weights, although it does not coincide with the fuzzy arithmetic mean operator in such a case. One of the most valuable result of the study is the fact that in contrast to the crisp weighted average operator, it is not additive. The importance of the obtained results is discussed and illustrated by several illustrative examples.

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APA: Copy

Pavlacka, O., & Pavlackova, M.. (2021). On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights. IRANIAN JOURNAL OF FUZZY SYSTEMS, 18(4 ), 1-17. SID. https://sid.ir/paper/412587/en

Vancouver: Copy

Pavlacka O., Pavlackova M.. On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2021;18(4 ):1-17. Available from: https://sid.ir/paper/412587/en

IEEE: Copy

O. Pavlacka, and M. Pavlackova, “On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 18, no. 4 , pp. 1–17, 2021, [Online]. Available: https://sid.ir/paper/412587/en

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