Probabilistic Hesitant Fuzzy Taxonomy Method Based on Best–Worst-Method (BWM) and Indifference Threshold-Based Attribute Ratio Analysis (ITARA) for Multi-attributes Decision-Making

The probabilistic hesitant elements (PHFEs) are a beneficial augmentation to the hesitant fuzzy element (HFE), which is intended to give decision-makers more flexibility in expressing their biases while using hesitant fuzzy information. To extrapolate a more accurate interpretation of the decision documentation, it is sufficient to standardize the organization of the elements in PHFEs without introducing fictional elements. Several processes for unifying and arranging components in PHFEs have been proposed so far, but most of them result in various disadvantages that are critically explored in this paper. The primary objective of this research is to recommend a PHFE unification procedure that avoids the deficiencies of operational practices while maintaining the inherent properties of PHFE probabilities. The prevailing study advances the hypothesis of permutation on PHFEs by suggesting a new sort of PHFS division and subtraction compared with the existing unification procedure. Eventually, the proposed PHFE-unification process will be used in this study, an innovative PHFEs based on the Weighted Aggregated Sum Product Assessment Method-Analytic Hierarchy Process (WASPAS-AHP) perspective for selecting flexible packaging bags after the prohibition on single-use plastics. As a result, we have included the PHFEs-WASPAS in our selection of the most effective fuzzy environment for bio-plastic bags. The ranking results for the suggested PHFEs-MCDM techniques surpassed the existing AHP methods in the research study by providing the best solution. Our solutions offer the best bio-plastic bag alternative strategy for mitigating environmental impacts. 

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An innovative probabilistic hesitant fuzzy set MCDM perspective for selecting flexible packaging bags after the prohibition on single-use plastics

The probabilistic hesitant fuzzy element (PHFE) is a worthwhile extension of hesitant fuzzy element (HFE) which is a means of allowing the decision makers more flexibility in expressing their preferences by the use of hesitant information in practical decision making process. To derive a more realistic expression of decision information, it is necessary to unify the arrangement of elements in PHFEs without imposing artificial elements. Up to now, several processes concerning the unification and arrangement of elements in PHFEs have been proposed, and while, most suffer from different drawbacks being critically discussed in the present study. The main aim of this study is to propose a PHFE unification process which does not have the shortcomings of existing processes, and does not change the inherent characteristic of PHFE probabilities. Based on the proposed unification process, the current study seeks to extend the theory of arithmetic operations on PHFEs by proposing and developing novel types of PHFS division and subtraction. Finally, the proposed PHFE unification process is applied to a number of multiple criteria decision-making (MCDM) problems for illustrating its vast range of applicability.

An innovative unification process for probabilistic hesitant fuzzy elements and its application to decision making

The consensus of randomness and ambiguity exists in real world problems. To depict fuzziness, randomness and statistical ambiguity in a single framework, we develop an interactive approach to MCDM method, in which assessment of alternative over attributes are provided by probabilistic hesitant fuzzy elements (PHFEs). This method provides a tool to the decision makers for reasonable ranking of alternatives. The core intention of this paper is to define a series of novel distance and similarity measures and score function for PHFEs. To demonstrate the effectiveness of developed model, a real case study is taken as an example. To completely describe statistical and non-statistical uncertainty, suitable probability distribution function is associated with each element of constructed HFSs. The proposed method is more superior to other MCDM methods, because of introducing probabilistic information in HFEs, which can be helpful to ensure the integrality and accurateness of hesitant fuzzy information.

Novel Distance and Similarity Measures for Probabilistic Hesitant Fuzzy Set and Its Applications in Stock Selection Problems

Compared with the general fuzzy decision making, the calculation process under the probabilistic hesitant fuzzy environment involves two new issues that need further consideration, namely quantitative element probability and qualitative element preference. The contributions of this study are to address them in the same modeling framework. For the quantitative element probability, also element occurrence probability, we propose an optimization method by developing the probabilistic hesitant fuzzy envelopment rate and introducing six behavior strategies. This method deals with two complex scenarios, namely, the occurrence probabilities are completely unknown or partially missing. For the qualitative element preference given by decision makers, we design a fusion technique and propose the probabilistic hesitant fuzzy element preference fusion (PHFEF) model based on the above optimization method. Thus, the PHFEF model is used to address the above issues in the same modeling framework. To apply the above models, we further provide a step-by-step decision-making process to reasonably use the PHFEF model in the probabilistic hesitant fuzzy environment. Finally, an illustrative example is used to show the feasibility and further comparisons are given to present the rationality of the proposed methods. 

Occurrence probability derivation considering different behavior strategies and decision making under the probabilistic hesitant fuzzy environment

An outranking method for multicriteria decision making with probabilistic hesitant information

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An outranking method for multicriteria decision making with probabilistic hesitant information