A novel linguistic approach for multi-granular information fusion and decision-making using risk-based linguistic D numbers
Introduction
Granular computing paradigms were developed to enable decision-makers to have more flexibility and accuracy in dealing with different kinds of uncertain information. One of the frameworks applied among granular computing models is fuzzy sets. Fuzzy information granules consist of fuzzy sets or linguistic terms that are sufficiently interpretable [1]. In many decision-making problems, the probabilities differ with regard to various linguistic information [2]. Therefore, the concept of probabilistic linguistic expressions was proposed to deal with such situations. Several research studies have aimed to combine, compute, and analyze these probabilistic-based models, such as probabilistic linguistic term sets (PLTSs) [3], distribution assessment [4], probabilistic hesitant fuzzy sets [5], probabilistic interval-valued intuitionistic hesitant fuzzy sets [6], evidential reasoning [7], and linguistic D numbers [8].
When adopting multi-granular fuzzy information, it is crucial to know how credible the data is. In many decision-making and engineering problems, especially in the case of forecasting and decision-making for future events, the data analyzed contains some percentage of errors and risk [9]. These errors are caused by several factors, such as predicted/unpredicted effective factors, which result in a situation where knowledge of the present cannot be generalized in a confident and reliable way to a future situation. These errors are recognized as risk factors [10]. Risk factors can be considered as effective factors that cause variations in evaluated values and main values [11]. In order to model the reliability of multi-granular data obtained from different sources, a large number of studies have been conducted in which the reliabilities of different sources have been obtained by using dynamic reliability measures [12] or prior knowledge [13]. However, these methods are not suitable for risk modeling of data, since they only report on how reliable the source of the data is, and do not model variations in the data due to possible future-based risk factors. In addition, their reliability and credibility are commonly pessimistically estimated. Based on these approaches, unreliability likely worsens any data obtained, which is not necessarily the case in reality. Risk factors affect the information, i.e., ending up with an overestimation or underestimation [13], as compared to the actual value. Therefore, in order to account for the entire set of available data and reach to a robust solution, both overestimated (optimistic) and underestimated (pessimistic) outputs – which lead to local ignorance or interval uncertainty [14] – should be considered simultaneously. Thus, it is more rational to use interval-valued multi-granular models. A few studies have been proposed to model different risk evaluation scenarios, within which risk modeling has been conducted in two ways: (I) by considering the pessimistic-optimistic range of an evaluation due to risk factors [10]; and (II) by supposing a range indicating the degree of belief in an assessment [15]. However, there are cases where the risk factors pose risks to the evaluation and its belief simultaneously; it can be seen from the literature that no study has been carried out which considers the variations of assessment and belief due to risk factors simultaneously, especially when the data are in the form of linguistic terms.
D numbers were initially proposed to overcome some issues with the Dempster-Shafer theory (DST) [16]. There are strong hypotheses and hard constraints that limit the further development and application of DST in working with incomplete and fuzzy data. In DST, the elements are required to be mutually exclusive in the frame of discernment (FOD). Another constraint of the DST is that the sum of basic probabilities of a mass function is required to be equal to one, a condition that is called the completeness constraint [17]. Incompleteness of beliefs might occur due to a variety of reasons, including time pressure or lack of data or knowledge [18]. The linguistic D numbers approach can model incompleteness of beliefs, and does not involve the completeness constraint of the mass function, as compared to the classical DST [15]. Moreover, unlike other methods, it does not use the normalizing approach for dealing with incompleteness. Another characteristic of D numbers, as compared to the other multi-granular methods like distribution assessment, evidential reasoning, and DST, is that the aggregation set can be different from the basic set. This attribute gives more flexibility to the D numbers to model the variability of elements to capture risks and errors of the basic set itself. Therefore, different types of risk modeling can be considered, including pessimistic and optimistic modes of elements and beliefs.
The current study aims at developing a comprehensive framework based on linguistic D numbers, the so-called risk-based linguistic D numbers, to consider various risk scenarios by modeling intervals of pessimistic and optimistic modes of incomplete and probabilistic multi-granular linguistic information. For this purpose, firstly, the D numbers are extended to an interval-valued structure, then the pessimistic and optimistic modes of linguistic data are considered by proposing risk-based linguistic D numbers.
The paper is organized as follows: a literature survey on risk modeling in evaluations and studies on D numbers is provided in Section 2. The concepts associated with additive linguistics term sets, DST, and D numbers are briefly described in Section 3. The interval-valued D numbers model is explained in Section 4. Risk-based linguistic D numbers methodology and the multi-attribute decision-making (MADM) framework corresponding to the risk-based linguistic D numbers are discussed in Section 5. An example of failure modes and effects analysis using the proposed risk-based linguistic D numbers model is presented in Section 6. A summary and discussion on the model proposed in the present work and recommendations for future research are presented in Section 7.
Section snippets
Literature review
Various research studies have been performed in the areas of risk modeling of evaluation risks and D numbers methodology, which are discussed briefly as follows.
Preliminaries
This section briefly describes the additive linguistic terms, DST and D numbers, which are prerequisites for modeling the proposed interval-valued and risk-based linguistic D numbers.
Interval-valued linguistic D numbers
In this section, we develop the interval-valued linguistic D numbers model. Let us first present the main definitions and computation steps of the interval-valued linguistic D numbers (IVLD numbers) method. In this regard, by assuming that the IVLD numbers belief values are expressed as intervals, we then have the following:
Definition 9 For a discrete linguistic set , where bsi ∈ S and bsi ≠ bsj if i ≠ j, the IVLD numbers, represented by IDS({bsi}), are defined as follows:
Risk-based linguistic D numbers and their application to MADM problems
This section aims at proposing a new concept called risk-based linguistic D numbers (RBLD numbers) for risk modeling of linguistic D numbers due to future-events risk factors, as well as a new MADM framework based on this novel concept. In this regard, the risk modeling of linguistic D numbers is investigated in two different schemes, i.e., risk modeling of the beliefs and risk modeling of linguistic elements. This section is structured as follows. Risk modeling of beliefs is investigated in
Case study
In order to evaluate the applicability of the proposed model, it was tested on the rotor blades of an industrial turbine, as detailed in this section. Being thin and subjected to excessive loading in tough working environments and rotating at high speed, the rotor blades of an industrial turbine are at a high risk of failure, making the so-called "failure mode and effects analysis" (FMEA) a required design solution for improving their safety and reliability [36]. Commonly used across various
Conclusion
In this study, an interval-valued linguistic D numbers method was developed for dealing with incomplete interval belief structures. Moreover, in order to avoid loss of output information and to improve the accuracy of the information, the risk modeling of linguistic D numbers and various possible scenarios were examined through a new concept called risk-based linguistic D numbers. In this new methodology, pessimistic-optimistic models were proposed for beliefs and the linguistic elements of the
Declarations of Competing Interest
none.
Compliance with ethical standards
This article does not contain any studies with human participants or animals performed by any of the authors.
CRediT authorship contribution statement
Hamidreza Seiti: Conceptualization, Methodology, Visualization, Writing - original draft, Writing - review & editing. Ashkan Hafezalkotob: Data curation, Writing - original draft, Writing - review & editing, Validation. Enrique Herrera-Viedma: Investigation, Methodology, Supervision.
Acknowledgments
This work was supported by Spanish Ministry of Science and Universities with FEDER funds in the National Spanish project TIN2016-75850-R and the support of the RUDN University Program 5-100 (Russian Federation).
References (50)
- et al.
Building consensus in group decision making with an allocation of information granularity
Fuzzy Sets Syst.
(2014) - et al.
Probabilistic linguistic term sets in multi-attribute group decision making
Inf. Sci.
(2016) - et al.
Extending a pessimistic–optimistic fuzzy information axiom based approach considering acceptable risk: application in the selection of maintenance strategy
Appl. Soft Comput. J.
(2018) - et al.
Developing pessimistic–optimistic risk-based methods for multi-sensor fusion: An interval-valued evidence theory approach
Appl. Soft Comput. J.
(2018) - et al.
Developing a novel risk-based MCDM approach based on D numbers and fuzzy information axiom and its applications in preventive maintenance planning
Appl. Soft Comput.
(2019) A novel multi-criteria decision making method for assessing health-care waste treatment technologies based on D numbers
Eng. Appl. Artif. Intell.
(2018)- et al.
A new multi criteria decision making approach for medical imaging systems considering risk factors
Appl. Soft Comput.
(2015) - et al.
Risk-based material selection process supported on information theory: a case study on industrial gas turbine
Appl. Soft Comput.
(2017) - et al.
Environmental impact assessment based on D numbers
Expert Syst. Appl.
(2014) - et al.
D number theory based game-theoretic framework in adversarial decision making under a fuzzy environment
Int. J. Approx. Reason.
(2019)