A projection method for multiple attribute group decision making with probabilistic linguistic term sets

A simple combined projection method for conservative decision-making

Machine learning and artificial intelligence based techniques have brought great convenience to human life but along with a series of algorithmic “black box”, discrimination and ethical issues. One of the solutions is to integrate human and machine like the expert evaluation based research of multi-attribute decision-making where “human brain intelligence” is used for the support of “artificial intelligence”. In this article, we proposed a new and effective method to evaluate and rank alternatives in multi-attribute decision-making. Different from many existing approaches, this proposed method employs both the projection lengths and the projection angles of alternatives to make decisions. It supports psychological desirableness of decision makers and uses a Relu function to further enhance the output qualities. This proposed method is very simple to construct and applicable for much wider situations than the existing similar methods.

Bidirectional projection method for multi-attribute group decision making under probabilistic uncertain linguistic environment

The financial products selection in the financial services sector is a traditional multi-attribute group decision making (MAGDM) problem. Probabilistic uncertain linguistic sets (PULTSs) could be used to evaluate the financial products with uncertain linguistic terms and corresponding weights (probabilistic). The bidirectional projection (BP) method could take the bidirectional projection values into account. In this paper, we develop an integration model of information entropy and BP method under PULTSs. First of all, utilizing information entropy derives the priority weights of attributes. Next, utilizing the BP method of the PULTSs to obtain the final ranking of the alternatives. To depict the BP method, the formative vectors of two alternatives are defined, and a weighted vector model and inner product are improved under the PULTSs. In addition, through giving the case of financial products selection and some existing MAGDM methods for comparative analysis, it is proved that the method is practical and effective. The proposed approach also contributes to the effective selection of appropriate options in other decision-making matters.

Entropy-Based GLDS Method for Social Capital Selection of a PPP Project with q-Rung Orthopair Fuzzy Information

The social capital selection of a public–private-partnership (PPP) project could be regarded as a classical multiple attribute group decision-making (MAGDM) issue. In this paper, based on the traditional gained and lost dominance score (GLDS) method, the q-rung orthopair fuzzy entropy-based GLDS method was used to solve MAGDM problems. First, some basic theories related to the q-rung orthopair fuzzy sets (q-ROFSs) are briefly reviewed. Then, to fuse the q-rung orthopair fuzzy information effectively, the q-rung orthopair fuzzy Hamacher weighting average (q-ROFHWA) operator and q-rung orthopair fuzzy Hamacher weighting geometric (q-ROFHWG) operator based on the Hamacher operation laws are proposed. Moreover, to determine the attribute weights, the q-rung orthopair fuzzy entropy (q-ROFE) is proposed and some significant merits of it are discussed. Next, based on the q-ROFHWA operator, q-ROFE, and the traditional GLDS method, a MAGDM model with q-rung orthopair fuzzy information is built. In the end, a numerical example for social capital selection of PPP projects is provided to testify the proposed method and deliver a comparative analysis.

A Probabilistic Linguistic Multiple Attribute Decision Making Based on a New Correlation Coefficient Method and its Application in Hospital Assessment

The probabilistic linguistic term set (PLTS) is a newly emerging mathematical tool for handling uncertainties. It is considered a useful extension of linguistic term sets associated with probability information and can improve the effectiveness of multiple attribute decision making (MADM). This paper proposes a new PLTS correlation coefficient and addresses its usefulness in MADM problems. For achieving this aim, some new concepts of mean, variance, and covariance of the PLTS are first proposed. Moreover, a novel PLTS Pearson correlation coefficient is defined to overcome the shortcomings of the existing methods, whose significant feature is that it lies in the interval [−1,1], which makes it more effective in reflecting the negative and positive correlation between PLTSs. A weighted PLTS Pearson correlation coefficient is further defined to consider the importance of attribute weights and expand the scope of application. Then, a relative PLTS closeness coefficient is constructed based on the developed Pearson correlation coefficient, and based on which, a Pearson correlation-based TOPSIS (technique for order of preference by similarity to ideal solution) approach for MADM problems is developed. Finally, the effectiveness as well as the applicability of the developed method are illustrated through numerical examples and comparative analysis.