Linguistic group decision making with induced aggregation operators and probabilistic information

Extended Multicriteria Group Decision Making with a Novel Aggregation Operator for Emergency Material Supplier Selection

How to ensure the normal production of industries in an uncertain emergency environment has aroused a lot of concern in society. Selecting the best emergency material suppliers using the multicriteria group decision making (MCGDM) method will ensure the normal production of industries in this environment. However, there are few studies in emergency environments that consider the impact of the decision order of decision makers (DMs) on the decision results. Therefore, in order to fill the research gap, we propose an extended MCGDM method, whose main steps include the following: Firstly, the DMs give their assessment of all alternatives. Secondly, we take the AHP method and entropy weight method to weight the criteria and the DMs. Thirdly, we take the intuitionistic fuzzy hybrid priority weight average (IFHPWA) operator we proposed to aggregate evaluation information and take the TOPSIS method to rank all the alternatives. Finally, the proposed method is applied in a case to prove its practicability and effectiveness. The proposed method considers the influence of the decision order of the DMs on the decision results, which improves the accuracy and efficiency of decision-making results.

Entropy and probability based Fuzzy Induced Ordered Weighted Averaging operator

The traditional Ordered Weighting Average (OWA) operator is suitable for aggregating numerical attributes. However, this method fails when the attribute values are given in a linguistic form. In this paper, a novel aggregating method named Entropy and Probability based Fuzzy Induced Ordered Weighted Averaging (EPFIOWA) is proposed for Gaussian-fuzzy-number-based linguistic attributes. A method is first designed to obtain a reasonable weighting vector based on probability distribution and maximal entropy. Such optimal weighting vectors can be obtained under any given level of optimism, and the symmetric properties of the proposed model are proven. The linguistic attributes of EPFIOWA are represented by Gaussian fuzzy numbers because of their concise form and good operational properties. In particular, the arithmetic operations and distance measures of Gaussian fuzzy numbers required by EPFIOWA are given systematically. A novel method to obtain the order-inducing variables of linguistic attribute values is proposed in the EPFIOWA operators by calculating the distances between any Gaussian fuzzy number and a set of ordered grades. Finally, two numerical examples are used to illustrate the proposed approach, with evaluation results consistent with the observed situation.

Onsite/offsite social commerce adoption for SMEs using fuzzy linguistic decision making in complex framework

There has been a growing social commerce adoption trend among SMEs for few years. However, it is often a challenging strategic task for SMEs to choose the right type of social commerce. SMEs usually have a limited budget, technical skills and resources and want to maximise productivity with those limited resources. There is much literature that discusses the social commerce adoption strategy for SMEs. However, there is no work to enable SMEs to choose social commerce-onsite/offsite or hybrid strategy. Moreover, very few studies allow the decision-makers to handle uncertain, complex nonlinear relationships of social commerce adoption factors. The paper proposes a fuzzy linguistic multi-criteria group decision-making in a complex framework for onsite, offsite social commerce adoption to address the problem. The proposed approach uses a novel hybrid approach by combining FAHP, FOWA and selection criteria of the technological-organisation-environment (TOE) framework. Unlike previous methods, the proposed approach uses the decision maker's attitudinal characteristics and recommends intelligently using the OWA operator. The approach further demonstrates the decision behaviour of the decision-makers with Fuzzy Minimum (FMin), Fuzzy Maximum (FMax), Laplace criteria, Hurwicz criteria, FWA, FOWA and FPOWA. The framework enables the SMEs to choose the right type of social commerce considering TOE factors that help them build a stronger relationship with current and potential customers. The approach's applicability is demonstrated using a case study of three SMEs seeking to adopt a social commerce type. The analysis results indicate the proposed approach's effectiveness in handling uncertain, complex nonlinear decisions in social commerce adoption.

A Novel Approach for Multiplicative Linguistic Group Decision Making Based on Symmetrical Linguistic Chi-Square Deviation and VIKOR Method

Most linguistic-based approaches to multi-attribute group decision making (MAGDM) use symmetric, uniformly distributed sets of additive linguistic terms to express the opinions of decision makers. However, in reality, there are also some problems that require the use of asymmetric, uneven, i.e., non-equilibrium, multiplicative linguistic term sets to express the evaluation. The purpose of this paper is to propose a new approach to MAGDM under multiplicative linguistic information. The aggregation of linguistic data is an important component in MAGDM. To solve this problem, we define a chi-square for measuring the difference between multiplicative linguistic term sets. Furthermore, the linguistic generalized weighted logarithm multiple averaging (LGWLMA) operator and linguistic generalized ordered weighted logarithm multiple averaging (LGOWLMA) operator are proposed based on chi-square deviation. On the basis of the proposed two operators, we develop a novel approach to GDM with multiplicative linguistic term sets. Finally, the evaluation of transport logistics enterprises is developed to illustrate the validity and practicality of the proposed approach.

Pythagorean Membership Grade Aggregation Operators: Application in Financial knowledge

This paper presents the Pythagorean membership grade induced ordered weighted moving average (PMGIOWMA) operator with some particular cases and theorems. The main advantage of this new operator is that can include the knowledge, expectation, and aptitude of the decision maker into the Pythagorean membership function by using a weighting vector and induced variables. An application in financial knowledge based on a survey conducted in 13 provinces in Boyacá, Colombia, is presented.

Some Novel Picture 2-Tuple Linguistic Maclaurin Symmetric Mean Operators and Their Application to Multiple Attribute Decision Making

When solving multiple attribute decision making (MADM) problems, the 2-tuple linguistic variable is an effective tool that can not only express complex cognitive information but also prevent loss of information in calculation. The picture fuzzy set (PFS) has three degrees and has more freedom to express cognitive information. In addition, Archimedean t-conorm and t-norm (ATT) can generalize most existing t-conorms and t-norms and Maclaurin symmetric mean (MSM) operators can catch the relationships among the multi-input parameters. Therefore, we investigate several novel aggregation operators, such as the picture 2-tuple linguistic MSM (2TLMSM) operator based on the ATT (ATT-P2TLMSM) and the picture 2-tuple linguistic generalized MSM (2TLGMSM) operator based on ATT (ATT-P2TLGMSM). Considering that the input parameters have different importance, we proposed picture 2-tuple linguistic weighted MSM (2TLWMSM) operators based on ATT (ATT-P2TLWMSM) and picture 2-tuple linguistic weighted generalized MSM (2TLWGMSM) operators based on ATT (ATT-P2TLWGMSM). Finally, a MADM method is introduced, and an expositive example is presented to explain the availability and applicability of the developed operators and methods.

Similarity Measures of Linguistic Cubic Hesitant Variables for Multiple Attribute Group Decision-Making

A linguistic cubic hesitant variable (LCHV) is a hybrid form of linguistic values in group decision-making environments. It is composed of an interval language variable and multiple single-valued language variables given by different decision-makers (DMs). Due to the uncertainty and hesitation of DMs, the numbers of language variables in different LCHVs are unequal. Thus, the least common multiple number (LCMN) extension method was adopted. Based on the included angle and distance of two LCHVs, we presented two cosine similarity measures and developed a multiple attribute group decision-making (MAGDM) approach. An example of engineer selection was used to implement the proposed LCHV MAGDM method and demonstrate the simplicity and feasibility of the proposed method. The sensitivity analysis of weight changes for the two measures showed that the similarity measure based on distance was more stable than the similarity measure based on included angle in this application.

Vector Similarity Measures of Q-Linguistic Neutrosophic Variable Sets and Their Multi-Attribute Decision Making Method

Since language is used for thinking and expressing habits of humans in real life, the linguistic evaluation for an objective thing is expressed easily in linguistic terms/values. However, existing linguistic concepts cannot describe linguistic arguments regarding an evaluated object in two-dimensional universal sets (TDUSs). To describe linguistic neutrosophic arguments in decision making problems regarding TDUSs, this study proposes a Q-linguistic neutrosophic variable set (Q-LNVS) for the first time, which depicts its truth, indeterminacy, and falsity linguistic values independently corresponding to TDUSs, and vector similarity measures of Q-LNVSs. Thereafter, a linguistic neutrosophic multi-attribute decision-making (MADM) approach by using the presented similarity measures, including the cosine, Dice, and Jaccard measures, is developed under Q-linguistic neutrosophic setting. Lastly, the applicability and effectiveness of the presented MADM approach is presented by an illustrative example under Q-linguistic neutrosophic setting.

Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables

Linguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human thinking and judgments of an evaluated object. Nonetheless, the hybrid information regarding both uncertain linguistic arguments and hesitant linguistic arguments cannot be expressed through the various existing linguistic concepts. To reasonably express it, this study presents a linguistic cubic hesitant variable (LCHV) based on the concepts of a linguistic cubic variable and a hesitant fuzzy set, its operational relations, and its linguistic score function for ranking LCHVs. Then, the objective extension method based on the least common multiple number/cardinality for LCHVs and the weighted aggregation operators of LCHVs are proposed to reasonably aggregate LCHV information because existing aggregation operators cannot aggregate LCHVs in which the number of their hesitant components may imply difference. Next, a multi-attribute decision-making (MADM) approach is proposed based on the weighted arithmetic averaging (WAA) and weighted geometric averaging (WGA) operators of LCHVs. Lastly, an illustrative example is provided to indicate the applicability of the proposed approaches.

Operations and Aggregation Methods of Single-Valued Linguistic Neutrosophic Interval Linguistic Numbers and Their Decision Making Method

To comprehensively describe uncertain/interval linguistic arguments and confident linguistic arguments in the decision making process by a linguistic form, this study first presents the concept of a single-valued linguistic neutrosophic interval linguistic number (SVLN-ILN), which is comprehensively composed of its uncertain/interval linguistic number (determinate linguistic argument part) and its single-valued linguistic neutrosophic number (confident linguistic argument part), and its basic operations. Then, the score function of SVLN-ILN based on the attitude index and confident degree/level is presented for ranking SVLN-ILNs. After that, SVLN-ILN weighted arithmetic averaging (SVLN-ILNWAA) and SVLN-ILN weighted geometric averaging (SVLN-ILNWGA) operators are proposed to aggregate SVLN-ILN information and their properties are investigated. Further, a multi-attribute decision-making (MADM) method based on the proposed SVLN-ILNWAA or SVLN-ILNWGA operator and the score function is established under consideration of decision makers’ preference attitudes (pessimist, moderate, and optimist). Lastly, an actual example is given to show the applicability of the established MADM approach with decision makers’ attitudes.

Approach to Multiple Attribute Group Decision Making Based on Hesitant Fuzzy Linguistic Aggregation Operators

Inspired by the nonlinear weighted average operator, this paper proposes several generalized power average operators to aggregate hesitant fuzzy linguistic decision information. It is worth noting that the new operators take both the location and date weight information and the relative closeness of the decision-making information into consideration, a characteristic that results in objectivity and fairness in a group decision making. Moreover, we demonstrate some useful properties of the operators and discuss their associations. A new approach based on the designed operators is then proposed for hesitant fuzzy linguistic multiple attribute group decision-making problems, in which the attribute weights are known or unknown. Finally, this paper demonstrates the efficiency and feasibility of the proposed method through a numerical example.