A novel distance measure for probabilistic linguistic term sets with application to emergency decision-making

The probabilistic linguistic term sets can express not only the decision makers’ several possible linguistic assessment values, but also the weight of each linguistic assessment value, so they can preserve the original decision information and then have become an efficient tool for solving multi-criteria group decision making problems. To promote the wide applicability of probabilistic linguistic term sets in various fields, this chapter focuses on the distance measures for probabilistic linguistic term sets and their applications in multi-criteria group decision making. This chapter first defines the distance between two probabilistic linguistic term elements. Based on this, a variety of distance measures are proposed to calculate the distance between two probabilistic linguistic term sets. Then, these distance measures are further extended to compute the distance between two collections of probabilistic linguistic term sets by considering the weight information of each criterion. After that, the concept of the satisfaction degree of an alternative is given and utilized to rank the alternatives in multi-criteria group decision making. Finally, a real example is given to show the use of these distance measures and then compare the probabilistic linguistic term sets with hesitant fuzzy linguistic term sets.

In the face of multi-attribute decision problems in complex situations, most traditional multi-attribute group decision methods are based on the assumption that the decision maker is perfectly rational, while in the face of complex decision problems, the decision maker usually has the psychological characteristics of limited rationality and may use more than one linguistic term to describe the decision information when expressing the decision information To this end, this paper selects probabilistic language term sets to describe complex preference information. First, to address the problem that the current probabilistic linguistic term set correlation coefficient cannot appropriately measure the degree of correlation among probabilistic linguistic term sets, this paper proposes a new probabilistic linguistic term set correlation coefficient from three characteristic factors of probabilistic linguistic term sets: mean, variance, and length rate. To integrate the attribute index weights, probabilistic linguistic term set weighted mixed correlation coefficients are proposed. Second, this paper introduces the TODIM method, which can consider the psychological behavior of decision makers, and proposes a TODIM multi-attribute decision making method based on probabilistic linguistic term sets with mixed correlation coefficients. Finally, through an empirical analysis of four Internet listed companies in a new first-tier city in China, this study verifies the rationality and validity of the proposed method. The results show that the mixed correlation coefficient can comprehensively measure the correlation between probabilistic linguistic term sets, which provides an important method for future multi-attribute decision making problems.

Inclusion measures of probabilistic linguistic term sets and their application in classifying cities in the Economic Zone of Chengdu Plain

Wireless sensor networks as an emerging technology have garnered a lot of attention recently. With the development of wireless sensor networks, some problems such as data delay, information loss, and others have gradually appeared. In order to cope with these problems, evaluating the service quality in wireless sensor networks is crucial. However, how to evaluate the service quality in wireless sensor networks and especially how to accurately portray the preferences of a decision maker exactly are often difficult. To deal with this challenge, firstly, an evaluation system of attributes related to the service quality in wireless sensor networks is constructed based on the existing studies. Then, the probabilistic linguistic method including the definition of probabilistic linguistic term sets, the operators of probabilistic linguistic term sets, and the ranking order of probabilistic linguistic term sets are introduced. Probabilistic term sets used to denote the preferences of a decision maker are considered as more appropriate expressions than classical linguistic term sets, 2-tuple linguistic term sets, and portion linguistic term sets in the process of evaluating the service quality in wireless sensor networks. Finally, the probabilistic linguistic method is applied in the constructed service quality in wireless sensor networks so as to demonstrate its validity and applicability and further to help the decision maker find the problems in the service quality in wireless sensor networks and improve them.

Comparing probabilistic linguistic term sets (PLTSs) is quite essential in solving PLTS-expressed multi-attribute group decision-making problems (PLTS-MAGDM). Researchers have designed various comparison measures to obtain the rank of PLTSs. However, most of the existing PLTS comparison measures need additional tedious adjustments before conducting a specific computation. Besides, these measures do not adequately consider the effects of the semantics of the basic linguistic term set and the probabilistic distributions. This paper proposes a new preference degree for g-granularity probabilistic term sets (g-GPLTSs) to overcome the two shortcomings simultaneously by integrating the effect from basic linguistic terms and probabilistic distributions without any adjustment. Moreover, the g-GPLTS preference degree also shows the extended adaptability for comparing PLTSs with unbalanced semantics. Based on the newly proposed preference degree, we construct a useful min-conflict model to solve PLTS-MAGDM with a large number of experts expressing the three-way primary grading. Finally, an illustrative example concerning software supplier selections, followed by the comparative analysis, is presented to verify the feasibility and effectiveness of the proposed method.

Novel basic operational laws for linguistic terms, hesitant fuzzy linguistic term sets and probabilistic linguistic term sets

Distance measures are important in the framework of multi-criterion decision making with probabilistic linguistic term sets. However, few studies investigated the distance of probabilistic linguistic term sets from the perspective of probability distributions. Due to this fact, this paper originally proposes a probabilistic linguistic Kolmogorov-Smirnov distance measure to identify the gaps between probability distributions. As a basis of this distance measure, the cumulative probability distributions of probabilistic linguistic term sets are introduced. Then, a common basic scale is given to get the probabilistic linguistic Kolmogorov-Smirnov distance between the probabilistic linguistic term sets with different lengths. After that, a linear programming technique for multidimensional analysis of preferences is developed based on the probabilistic linguistic Kolmogorov-Smirnov distance. An illustration of the hospital service quality evaluation is solved by the proposed method, and a sensitivity analysis is done to demonstrate the reliability of the results.

Comparisons of probabilistic linguistic term sets for multi-criteria decision making

In today’s education industry, online teaching is increasingly becoming an important teaching way, and it is necessary to evaluate the quality of online teaching so as to improve the overall level of the education industry. The online teaching quality evaluation is a typical multi-attribute group decision-making (MAGDM) problem, and its evaluation index can be expressed by linguistic term sets (LTSs) by decision makers (DMs). Especially, multi-granularity probabilistic linguistic term sets (MGPLTSs) produced from many DMs are more suitable to express complex fuzzy evaluation information, and they can not only provide different linguistic term set for different DMs the give their preferences, but also reflect the importance of each linguistic term. Based on the advantages of MGPLTSs, in this paper, we propose a transformation function of MGPLTSs based on proportional 2-tuple fuzzy linguistic representation model. On this basis, the operational laws and comparison rules of MGPLTSs are given. Then, we develop a new Choquet integral operator for MGPLTSs, which considers the relationship among attributes and does not need to consider the process of normalizing the probabilistic linguistic term sets (PLTSs), and can effectively avoid the loss of evaluation information. At the same time, the properties of the proposed operator are also proved. Furthermore, we propose a new MAGDM method based on the new operator, and analyze the effectiveness of the proposed method by online teaching quality evaluation. Finally, by comparing with some existing methods, the advantages of the proposed method are shown.

Risk evaluation is a primary but important task for technological innovation projects and this task is a multiple criteria group decision-making (MCGDM) process with probabilistic uncertainty and fuzzy uncertainty. Compromise programming decision-making methods with probabilistic linguistic term sets (PLTSs) are more appropriate for risk evaluation of technological innovation projects. This paper proposes a new approach named improved probabilistic linguistic-vise kriterijumska optimizacija kompromisno resenje (PL-VIKOR) method with probabilistic linguistic term sets for risk evaluation of technological innovation projects. Firstly, by fully considering both the relationship between each alternative and the positive ideal solution and the relationship between each alternative and negative ideal solution, the improved PL-VIKOR method for dealing with MCGDM problems is developed to make up the deficiency of the traditional PL-VIKOR method. Then, the improved PL-VIKOR method is applied to solve a practical MCGDM problem with probabilistic linguistic term sets involving the risk evaluation of technologically innovative projects for venture capital. Finally, we make some comparative analyses between the improved PL-VIKOR method and some existing methods to analyze the advantages and disadvantages of the proposed method. The results reflect that the improved PL-VIKOR method is more reasonable when calculating the distance measure between two PLTSs, and it can make the risk evaluation of technological innovation project MCGDM with PLTSs more objective.

In recent years, the assessment of desirable renewable energy alternative has been an extremely important concern that could change the environment and economic growth. To tackle the circumstances, some authors have paid attention to selecting the desirable renewable energy option by employing the decision-making assessment and linguistic term sets. With a fast-growing interest in multi-criteria group decision-making (MCGDM) problems, researchers are tirelessly working towards new techniques for better decision-making. Decision makers (DMs) generally rate alternatives linguistically with different probabilities occurring for each term. Previous studies on linguistic decision-making have either ignored this idea or have used an only a single value for representing the weight of the linguistic term. Since expression of the complete probability distribution is hard and implicit hesitation exists, representation of weights of the linguistic terms using a single value becomes imprecise and unreasonable. To avoid this challenge, an interval-valued probabilistic linguistic term set (IVPLTS) is used, which is a generalization of (probabilistic linguistic term set) PLTS. Inspired by the usefulness of IVPLTS concept, we develop a decision framework for rational decision making. Initially, some operational laws and axioms are presented. Further, a novel aggregation operator known as interval-valued probabilistic linguistic simple weighted geometry (IVPLSWG) is developed for aggregating DMs’ preferences. Also, criteria weights are determined using the newly developed interval-valued probabilistic linguistic standard variance (IVPLSV) approach and alternatives are ranked using the extended VIKOR (VlseKriterijumskaOptimizacijaKompromisnoResenje) method under IVPLTS environment. Finally, a numerical example of renewable energy assessment is demonstrated to show the practicality of the developed decision framework. Also, the strengths and weaknesses of the developed decision framework are illustrated by comparison with existing ones.

Decision making is the key component of people’s daily life, from choosing a mobile phone to engaging in a war. To model the real world more accurately, probabilistic linguistic term sets (PLTSs) were proposed to manage a situation in which several possible linguistic terms along their corresponding probabilities are considered at the same time. Previously, in linguistic term sets, the probabilities of all linguistic term sets are considered to be equal which is unrealistic. In the process of decision making, due to the vagueness and complexity of real life, an expert usually hesitates and unable to express its opinion in a single term, thus making it difficult to reach a final agreement. To handle real life scenarios of a more complex nature, only membership linguistic decision making is unfruitful; thus, some mechanism is needed to express non-membership linguistic term set to deal with imprecise and uncertain information in more efficient manner. In this article, a novel notion called probabilistic hesitant intuitionistic linguistic term set (PHILTS) is designed, which is composed of membership PLTSs and non-membership PLTSs describing the opinions of decision makers (DMs). In the theme of PHILTS, the probabilities of membership linguistic terms and non-membership linguistic terms are considered to be independent. Then, basic operations, some governing operational laws, the aggregation operators, normalization process and comparison method are studied for PHILTSs. Thereafter, two practical decision making models: aggregation based model and the extended TOPSIS model for PHILTS are designed to classify the alternatives from the best to worst, as an application of PHILTS to multi-attribute group decision making. In the end, a practical problem of real life about the selection of the best alternative is solved to illustrate the applicability and effectiveness of our proposed set and models.

Probabilistic linguistic term sets (PLTSs) are an effective tool in keeping with the habits of decision makers (DMs). However, in multi-criteria group decision making (MCGDM) problems, it is necessary to deal with the information reliability problem because of the difference of the DMs’ knowledge backgrounds and knowledge structures. Therefore, this paper proposes a novel concept called probabilistic reliable linguistic term sets. Based on which, some basic operations, comparison laws, distance measures, similarity measures and aggregation operators are defined. After that, we propose the probabilistic reliable linguistic gained and lost dominance score method to cope with MCGDM problems, and we further apply the proposed method to solve an investment project selection problem about lucky bag machine. Finally, we make some comparative analyses to verify the effectiveness and highlight the strength of the proposed method compared with four methods, i.e., the aggregation-based method, the TOPSIS method under probabilistic reliable linguistic environment, the gained and lost dominance score (GLDS) method with probabilistic linguistic information and the GLDS method with hesitant linguistic information.

Multi-attribute group decision-making (MAGDM) is widely applied to various areas for solving real-life problems, including technology selection, credit assessment, strategic planning evaluation, supplier selection, etc. To describe the complex and imprecise cognition, it is more convenient to provide the decision-making information in linguistic terms rather than concrete numerical values. Thus, several linguistic models, such as the fuzzy linguistic approach (FLA), hesitant fuzzy linguistic term sets (HFLTSs), hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), and probabilistic linguistic term sets (PLTS) have been proposed successively. Due to the flexibility and comprehensiveness of PLTS, it has aroused growing concern. However, it also has a big limitation of requiring the membership degree to be 1 by default, and it does not consider the degree of non-membership and hesitancy of a linguistic variable. Therefore, the probabilistic hesitant intuitionistic fuzzy linguistic term sets (PHIFLTSs) have been presented to extend the PLTS by combining the membership and non-membership in symmetry to depict the evaluation of the experts. To overcome the existing shortcomings and enrich the methodology framework of PHIFLTSs, some novel operational laws are defined to extend the applicability and methodology of the PHIFLTSs in MAGDM. Furthermore, the distance and correlation measures for the PHIFLTSs are improved to make up the shortage of the current distance measures. In addition, the unbalanced linguistic terms are taken into account to represent the cognitive complex information of experts. At last, a MAGDM model based on the multiplicative multi-objective optimization by ratio analysis (MULTIMOORA) approach with the use of the developed novel operational laws and correlation measures is presented, which results in more accuracy and effectiveness. A real-word application example is presented to demonstrate the working of the proposed methodology. Moreover, a thorough comparison is done with related existing works in order to show the validity of this methodology.

This paper focuses on proposing a new decision framework under probabilistic linguistic term set (PLTS) for rational decision making. The PLTS concept is a generalization of hesitant fuzzy linguistic term set (HFLTS) which overcomes the limitation of HFLTS by associating occurring probability to each linguistic term. Initially, a new aggregation operator is presented for fusing decision makers’ (DMs) preferences. Following this, a new extension is put forward for statistical variance (SV) method under PLTS for criteria weight calculation and a new extension is presented for WASPAS (weighted arithmetic sum product assessment) method under PLTS context for ranking objects. The applicability of the proposed decision framework is demonstrated by using a numerical example and the strength and weakness of the proposal are investigated by comparison with other state-of-the-art methods.