Isomorphic multiplicative transitivity for intuitionistic and interval-valued fuzzy preference relations and its application in deriving their priority vectors

Intuitionistic fuzzy preference relations (IFPRs) are used to deal with hesitation while interval-valued fuzzy preference relations (IVFPRs) are for uncertainty in multi-criteria decision making (MCDM). This article aims to explore the isomorphic multiplicative transitivity for IFPRs and IVFPRs, which builds the substantial relationship between hesitation and uncertainty in MCDM. To do that, the definition of the multiplicative transitivity property of IFPRs is established by combining the multiplication of intuitionistic fuzzy sets and Tanino's multiplicative transitivity property of fuzzy preference relations (FPRs). It is proved to be isomorphic to the multiplicative transitivity of IVFPRs derived via Zadeh's Extension Principle. The use of the multiplicative transitivity isomorphism is twofold: (1) to discover the substantial relationship between IFPRs and IVFPRs, which will bridge the gap between hesitation and uncertainty in MCDM problems; and (2) to strengthen the soundness of the multiplicative transitivity property of IFPRs and IVFPRs by supporting each other with two different reliable sources, respectively. Furthermore, based on the existing isomorphism, the concept of multiplicative consistency for IFPRs is defined through a strict mathematical process, and it is proved to satisfy the following several desirable properties: weak--transitivity, max-max--transitivity, and center-division--transitivity. A multiplicative consistency based multi-objective programming (MOP) model is investigated to derive the priority vector from an IFPR. This model has the advantage of not losing information as the priority vector representation coincides with that of the input information, which was not the case with existing methods where crisp priority vectors were derived as a consequence of modelling transitivity just for the intuitionistic membership function and not for the intuitionistic non-membership function. Finally, a numerical example concerning green supply selection is given to validate the efficiency and practicality of the proposed multiplicative consistency MOP model

A systematic review on multi-criteria group decision-making methods based on weights: analysis and classification scheme

Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts’ weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts’ weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts’ weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions.The first author acknowledges support from the Spanish Ministry of Universities [grant number FPU18/01471]. The second and third author wish to recognize their support from the Serra Hunter program. Finally, this work was supported by the Catalan agency AGAUR through its research group support program (2017SGR00227). This research is part of the R&D project IAQ4EDU, reference no. PID2020-117366RB-I00, funded by MCIN/AEI/10.13039/ 501100011033.Peer ReviewedPostprint (published version

Managing Incomplete Preference Relations in Decision Making: A Review and Future Trends

In decision making, situations where all experts are able to efficiently express their preferences over all the available options are the exception rather than the rule. Indeed, the above scenario requires all experts to possess a precise or sufficient level of knowledge of the whole problem to tackle, including the ability to discriminate the degree up to which some options are better than others. These assumptions can be seen unrealistic in many decision making situations, especially those involving a large number of alternatives to choose from and/or conflicting and dynamic sources of information. Some methodologies widely adopted in these situations are to discard or to rate more negatively those experts that provide preferences with missing values. However, incomplete information is not equivalent to low quality information, and consequently these methodologies could lead to biased or even bad solutions since useful information might not being taken properly into account in the decision process. Therefore, alternative approaches to manage incomplete preference relations that estimates the missing information in decision making are desirable and possible. This paper presents and analyses methods and processes developed on this area towards the estimation of missing preferences in decision making, and highlights some areas for future research

A social network based approach for consensus achievement in multiperson decision making

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Nowadays we are living the apogee of the Internet based technologies and consequently web 2.0 communities, where a large number of users interact in real time and share opinions and knowledge, is a generalized phenomenon. This type of social networks communities constitute a challenge scenario from the point of view of Group Decision Making approaches, because it involves a large number of agents coming from different backgrounds and/or with different level of knowledge and influence. In these type of scenarios there exists two main key issues that requires attention. Firstly, the large number of agents and their diverse background may lead to uncertainty and or inconsistency and so, it makes difficult to assess the quality of the information provided as well as to merge this information. Secondly, it is desirable, or even indispensable depending on the situation, to obtain a solution accepted by the majority of the members or at least to asses the existing level of agreement. In this contribution we address these two main issues by bringing together both decision Making approaches and opinion dynamics to develop a similarity-confidence-consistency based Social network that enables the agents to provide their opinions with the possibility of allocating uncertainty by means of the Intuitionistic fuzzy preference relations and at the same time interact with like-minded agents in order to achieve an agreement

A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information

Single-valued trapezoidal neutrosophic numbers (SVTNNs) have a strong capacity to depict uncertain, inconsistent, and incomplete information about decisionmaking problems. Preference relations represent a practical tool for presenting decision makers’ preference information regarding various alternatives

Hospitality brand management by a score-based q-rung orthopair fuzzy V.I.K.O.R. method integrated with the best worst method

Hospitality brand management is a primary concern in the hotel industry and the evaluation of brands can be considered as a decision- making problem with multiple criteria. The evaluation information of brands may be uncertain sometimes. The q-rung orthopair fuzzy set (q-R.O.F.S.), which represents the preference degree of a person from the positive and negative aspects, has turned out to be an efficient tool in depicting uncertainty and vagueness in the decision-making process. This article dedicates to presenting an integrated multiple criteria decision-making method with q-R.O.F.S.. Firstly, a score function of the q-R.O.F.S. is proposed to solve the deficiencies of two existing score functions. Then, a weight-determining method based on the additive consistency of the preference relation is developed. A decision-making method integrating the score function, the best worst method and the VIsekriterijumska optimizacija I KOmpromisno Resenje (V.I.K.O.R.) which means multiple criteria compromise optimisation in English) method is further proposed. Finally, a case study regarding the hospitality brand management is provided to show the applicability and validity of the proposed method.The work was supported by the National Natural Science Foundation of China (71771156, 71971145), the Scholarship from China Scholarship Council (No. 201906240161) and the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah (No. RG-10-611- 39, No. RG-7-135-38)

Hospitality brand management by a score-based q-rung ortho pair fuzzy V.I.K.O.R. method integrated with the best worst method

Hospitality brand management is a primary concern in the hotel industry and the evaluation of brands can be considered as a decision-making problem with multiple criteria. The evaluation information of brands may be uncertain sometimes. The q-rung orthopair fuzzy set (q-R.O.F.S.), which represents the preference degree of a person from the positive and negative aspects, has turned out to be an efficient tool in depicting uncertainty and vagueness in the decision-making process. This article dedicates to presenting an integrated multiple criteria decision-making method with q-R.O.F.S.. Firstly, a score function of the q-R.O.F.S. is proposed to solve the deficiencies of two existing score functions. Then, a weight-determining method based on the additive consistency of the preference relation is developed. A decision-making method integrating the score function, the best worst method and the VIsekriterijumska optimizacija I KOmpromisno Resenje (V.I.K.O.R.) which means multiple criteria compromise optimisation in English) method is further proposed. Finally, a case study regarding the hospitality brand management is provided to show the applicability and validity of the proposed method