An approach to construct entropies on interval-valued intuitionistic fuzzy sets by their distance functions

Che, Renqing; Suo, Chunfeng; Li, Yongming

doi:10.1007/s00500-021-05713-5

Cited by 10 publications

(5 citation statements)

References 36 publications

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“…Then, the intuitionistic fuzzy set was proposed, which extended fuzzy sets to represent the rejection degree by the non-membership degree [9]. Then, an interval-valued intuitionistic fuzzy set was proposed, where both the membership and non-membership degree are represented by intervals [32]. To represent the reliability of the information, the Z-number was then proposed [6].…”

Section: Literature Reviewmentioning

confidence: 99%

A Clustering Multi-Criteria Decision-Making Method for Large-Scale Discrete and Continuous Uncertain Evaluation

Wang

Zhan

2022

Entropy

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In recent years, Dempster–Shafer (D–S) theory has been widely used in multi-criteria decision-making (MCDM) problems due to its excellent performance in dealing with discrete ambiguous decision alternative (DA) evaluations. In the general framework of D–S-theory-based MCDM problems, the preference of the DAs for each criterion is regarded as a mass function over the set of DAs based on subjective evaluations. Moreover, the multi-criteria preference aggregation is based on Dempster’s combination rule. Unfortunately, this an idea faces two difficulties in real-world applications: (i) D–S theory can only deal with discrete uncertain evaluations, but is powerless in the face of continuous uncertain evaluations. (ii) The generation of the mass function for each criterion relies on the empirical judgments of experts, making it time-consuming and laborious in terms of the MCDM problem for large-scale DAs. To the best of our knowledge, these two difficulties cannot be addressed with existing D–S-theory-based MCDM methods. To this end, this paper proposes a clustering MCDM method combining D–S theory with the analytic hierarchy process (AHP) and the Silhouette coefficient. By employing the probability distribution and the D–S theory to represent discrete and continuous ambiguous evaluations, respectively, determining the focal element set for the mass function of each criterion through the clustering method, assigning the mass values of each criterion through the AHP method, and aggregating preferences according to Dempster’s combination rule, we show that our method can indeed address these two difficulties in MCDM problems. Finally, an example is given and comparative analyses with related methods are conducted to illustrate our method’s rationality, effectiveness, and efficiency.

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Section: Literature Reviewmentioning

confidence: 99%

A Clustering Multi-Criteria Decision-Making Method for Large-Scale Discrete and Continuous Uncertain Evaluation

Wang

Zhan

2022

Entropy

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“…In the process of MATSM, di erent evaluators have di erent access to the information of the evaluation object and their own understanding and analytical ability of the information, so the attribute evaluation of di erent evaluation objects is di erent. To solve the attribute weight problem of two-sided matching in a multigranularity probabilistic linguistic term set environment, this paper uses the concept of multi-granularity probabilistic linguistic distance entropy [37] to solve the attribute weight by combining the distance between probabilistic linguistic terms and information entropy.…”

Section: Determination Of Attribute Weights Based On Multigranularity...mentioning

confidence: 99%

A Multi-attribute Two-Sided Matching Decision Method Based on Multi-granularity Probabilistic Linguistic MARCOS

Jing

2022

Mathematical Problems in Engineering

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With the complexity of the matching environment, individual differences in matching objects and the uncertainty of evaluation information should be considered. The probabilistic linguistic term set (PLTS) is a useful tool to describe the uncertainty and limited cognition of matching objects. Thus, this paper proposes a multi-attribute two-sided matching method based on multi-granularity probabilistic linguistic MARCOS. First, we use a probabilistic linguistic term set with different granularities to express the evaluation information of different matching objects. Then, a conversion function is used to unify different granularity probabilistic linguistic terms. Second, a linguistic scale function is introduced to improve the expectation function, deviation degree, and distance of PLTS. The processed probabilistic linguistic evaluation information is transformed into accurate utility values through the transformation function. The evaluation attribute weights are determined by PLTS distance entropy. Based on this, this paper proposes a multi-granularity probabilistic linguistic MARCOS method to obtain the two-sided satisfaction degree. Finally, an optimization model which aims to maximize the overall satisfaction degree of matching objects by considering the stable matching condition is then established and solved to determine the matching between matching objects. The multi-objective two-sided matching model is constructed with the objective of maximizing the two-sided satisfaction degree. A case study of the service outsourcing matching is presented to validate the proposed method. The comparative analyses and discussions are also provided to demonstrate its effectiveness and scientific character.

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“…The graphical estimates of cover all lots tested appear to have an average value of about 1.6. Consider the following sample given the results of the tests, in millions of revolutions, of 23 The maximum likelihood estimate of is 2.102, the estimate of from the equation is 81.99. The upper-level estimates were randomly generated using Weibull distribution with parameters alpha = 85.99 and beta = 2.259, keeping n = 23.…”

Section: Examplementioning

confidence: 99%

“…The decision about the membership of interval numbers is proposed by Atanassove [21] under fuzzy environments through the interval-valued intuitionistic fuzzy set (IVIFS). Wei et al [22] presented the concept of entropy measure for IVIFS in pattern identification and [23,24] generalized the entropy measures for the neutrosophic set environment. Deli [25] developed a method for (4) T(p) = F(v), the linear optimization of the single-valued neutrosophic set and discussed its sensitivity.…”

Section: Introductionmentioning

confidence: 99%

Neutrosophic entropy measures for the Weibull distribution: theory and applications

Sherwani

Arshad

Albassam

et al. 2021

Complex Intell. Syst.

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Entropy is a standard measure used to determine the uncertainty, randomness, or chaos of experimental outcomes and is quite popular in statistical distribution theory. Entropy methods available in the literature quantify the information of a random variable with exact numbers and lacks in dealing with the interval value data. An indeterminate state of an experiment generally generates the data in interval form. The indeterminacy property of interval-valued data makes it a neutrosophic form data. This research proposed some modified forms of entropy measures for an important lifetime distribution called Weibull distribution by considering the neutrosophic form of the data. The performance of the proposed methods is assessed via a simulation study and three real-life data applications. The simulation and real-life data examples suggested that the proposed methodologies of entropies for the Weibull distribution are more suitable when the random variable of the distribution is in an interval form and has indeterminacy or vagueness in it.

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An approach to construct entropies on interval-valued intuitionistic fuzzy sets by their distance functions

Cited by 10 publications

References 36 publications

A Clustering Multi-Criteria Decision-Making Method for Large-Scale Discrete and Continuous Uncertain Evaluation

A Clustering Multi-Criteria Decision-Making Method for Large-Scale Discrete and Continuous Uncertain Evaluation

A Multi-attribute Two-Sided Matching Decision Method Based on Multi-granularity Probabilistic Linguistic MARCOS

Neutrosophic entropy measures for the Weibull distribution: theory and applications

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