A new soft likelihood function based on power ordered weighted average operator

Abstract

The likelihood function is widely used in data processing but the classical likelihood function is too strict to deal with data with extreme values in real applications.To address this issue, a soft likelihood function based on power ordered weighted average (POWA) operator for probability distribution is proposed. Compared with the existing soft likelihood functions, one of the main features of the proposed likelihood function is that the weighted mean is displayed by the geometric mean of the weighted probability products. As a result, the effect on final result caused by extreme data can be efficiently decreased. Numerical examples are used to illustrate the efficiency of the proposed soft likelihood function. K E Y W O R D S geometric mean, likelihood function, OWA operator, POWA operator, soft likelihood function | INTRODUCTIONDealing with uncertainty information plays an important role in real applications. 1-3 Many math tools, such as fuzzy sets, 4-6 rough sets, 7 Z-numbers, 8-11 belief structures, 12-14 D numbers 15-17 entropy function, 18,19 and evidence theory, 20-22 are presented to handle different types of uncertainty information. Among these tools, probability is heavily studied and is widely used in many applications, including decision making, 23-26 estimation, 27,28 and uncertain measurement. [29][30][31][32] One of the most used models in probability is the likelihood function, which is used when data are available to describe plausibility of a parameter value. [33][34][35] However, it is very strict in real applications since the original likelihood function made up with the probability product is too strict to show the compatibility probabilities for the different pieces of evidence since any piece of probabilities, which are low-value would greatly reduce the likelihood function.How to cite this article: Song Y, Deng Y. A new soft likelihood function based on power ordered weighted average operator. Int J Intell

A Fuzzy Interval Time-Series Energy and Financial Forecasting Model Using Network-Based Multiple Time-Frequency Spaces and the Induced-Ordered Weighted Averaging Aggregation Operation

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Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

“…To deal with uncertainty, many tools and models have been proposed [41][42][43][44], such as fuzzy sets [45,46], basic probability assignment [47,48], rough sets [49], ordered weighted average operator [50], entropy [51][52][53][54], game theory [55,56] and complex networks [57][58][59][60][61][62]. In this section, some relative definitions are briefly introduced, such as refined expected value [40], measure [63,64] and Choquet integral [65].…”

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“…Recently, Song et al 23 proposed a new soft‐likelihood function based on the POWA operator proposed by Yager. The proposed soft‐likelihood function is defined as follows.…”

“…Recently, Song et al 23 proposed a new soft-likelihood function based on the power ordered weighted average (POWA) operator proposed by Yager. 10 However, through analysis, we find that the method proposed by Song et al has the following two defects: (a) The weight of POWA cannot comprehensively reflect the correlation between probability and OWA operator.…”