Extending a pessimistic–optimistic fuzzy information axiom based approach considering acceptable risk: Application in the selection of maintenance strategy

Seiti, Hamidreza; Hafezalkotob, Ashkan; Fattahi, Reza

doi:10.1016/j.asoc.2017.11.017

Cited by 50 publications

(21 citation statements)

References 35 publications

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“…Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.2 of 20 applications, such as strategy selection [30][31][32][33][34], decision-making [35][36][37][38][39], prediction [40][41][42], and fault diagnosis [43,44]. In addition, Zadeh presented a useful theory in 1965, the fuzzy set (FS) theory [45], which drives a big step forward in decision theory.…”

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confidence: 99%

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

2020

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As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

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confidence: 99%

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

2020

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“…Many methods are presented to update the status with collected information, including Beyasian updating rule, Dempster combination rule, negation, dynamic model such as DEMATEL, neural model, and so on . The likelihood function is first defined as the product of probabilities.…”

Section: Preliminariesmentioning

confidence: 99%

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

Song

Deng

2019

Int J Intell Syst

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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

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“…Several mathematical tools have been proposed to represent and deal with uncertain information, such as fuzzy set theory [26], intuitionistic fuzzy set [27][28][29], entropy [30][31][32], evidence theory [33,34], rough set [35], Z-numbers [36,37], R-numbers [38,39], probabilistic linguistic set [40,41], etc. [42][43][44]. Among them, Dempster-Shafer evidence theory, also named evidence theory, which can be regarded as the extension of the traditional Bayesian probability theory, has been widely used in many areas, such as data fusion [45,46], evaluation of nuclear safeguards [47], conflict management [48,49], uncertain measure [50], information quality evaluation [51], target recognition [52], fault diagnostics [53][54][55][56][57], reliability assessment [58][59][60][61], etc.…”

Section: Introductionmentioning

confidence: 99%

A New Evaluation Methodology for Quality Goals Extended by D Number Theory and FAHP

2020

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Evaluation of quality goals is an important issue in process management, which essentially is a multi-attribute decision-making (MADM) problem. The process of assessment inevitably involves uncertain information. The two crucial points in an MADM problem are to obtain weight of attributes and to handle uncertain information. D number theory is a new mathematical tool to deal with uncertain information, which is an extension of evidence theory. The fuzzy analytic hierarchy process (FAHP) provides a hierarchical way to model MADM problems, and the comparison analysis among attributes is applied to obtain the weight of attributes. FAHP uses a triangle fuzzy number rather than a crisp number to represent the evaluation information, which fully considers the hesitation to give a evaluation. Inspired by the features of D number theory and FAHP, a D-FAHP method is proposed to evaluate quality goals in this paper. Within the proposed method, FAHP is used to obtain the weight of each attribute, and the integration property of D number theory is carried out to fuse information. A numerical example is presented to demonstrate the effectiveness of the proposed method. Some necessary discussions are provided to illustrate the advantages of the proposed method.

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Extending a pessimistic–optimistic fuzzy information axiom based approach considering acceptable risk: Application in the selection of maintenance strategy

Cited by 50 publications

References 35 publications

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

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

A New Evaluation Methodology for Quality Goals Extended by D Number Theory and FAHP

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