A novel approach to multi-attribute group decision-making based on interval-valued intuitionistic fuzzy power Muirhead mean

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method

Unsymmetrical basic uncertain information with some decision-making methods

Motivated by a specific decision-making situation, this work proposes the concept and definition of unsymmetrical basic uncertain information which is a further generalization of basic uncertain information and can model uncertainties in some new decision-making situations. We show that unsymmetrical basic uncertain information in some sense can model linguistic hedges such as 'at least' and 'at most'. Formative weighted arithmetic means and induced aggregations are defined for the proposed concept. Rules-based decision making and semi-copula based integral for this concept with some numerical examples are also presented.The paper is supported by National Natural Science Foundation of China with grant nos. 72171182 and 71801175, Grant APVV-18-0052, Grant PID2019-108392GBI00, financed by MCIN/AEI/10.13039/501100011033

Performance Measure Using a Multi-Attribute Decision-Making Approach Based on Complex T-Spherical Fuzzy Power Aggregation Operators

Performance measurement has a vital role in almost every field of life especially when uncertainty is involved in processing information. The purpose of this research is to use the concept of power aggregation operators (PAOs) of complex T-spherical fuzzy sets (CTSFSs) to analyze the performance measures of software packages. In comparison to other studies, the main advantage of the PAOs of CTSFSs is its ability to feature four possible aspects of the information under uncertainty. In CTSFSs, each component has further two aspects denoted by their amplitude and phase terms and hence provides us a better ground to deal with practical problems. Another advantage of using PAOs for performance evaluation is the involvement of the relationship of the input arguments that play an essential role in aggregation. Other traditional aggregation operators (AOs) do not have such capabilities. We aim to develop complex T-spherical fuzzy (TSF) power weighted averaging and complex TSF power weighted geometric (CTSFPWG) operators and evaluated their validity using some tests. Ultimately, using the recommended operators, multi-attribute decision-making (MADM) algorithm is established for the performance evaluation of the software packages. With the help of a numerical example, we demonstrated the proposed MADM algorithm using complex uncertain information. The results show a positive impact by analyzing them after a comparative analysis where the results obtained using complex TSF PAOs seem to be more reliable than the results obtained using previously developed AOs. To see the effectiveness of the algorithm, the results are numerically compared using some existing approaches, and conclusions are drawn

Sine hyperbolic fractional orthotriple linear Diophantine fuzzy aggregation operator and its application in decision making

The idea of sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs), which allows more uncertainty than fractional orthotriple fuzzy sets (FOFSs) is noteworthy. The regularity and symmetry of the origin are maintained by the widely recognized sine hyperbolic function, which satisfies the experts' expectations for the properties of the multi-time process. Compared to fractional orthotriple linear Diophantine fuzzy sets, sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs) provide a significant idea for enabling more uncertainty. The objective of this research is to provide some reliable sine hyperbolic operational laws for FOLDFSs in order to sustain these properties and the significance of sinh-FOLDFSs. Both the accuracy and score functions for the sinh-FOLDFSs are defined. We define a group of averaging and geometric aggregation operators on the basis of algebraic t-norm and t-conorm operations. The basic characteristics of the defined operators are studied. Using the specified aggregation operators, a group decision-making method for solving real-life decision-making problem is proposed. To verify the validity of the proposed method, we compare our method with other existing methods

Distributed Linguistic Representations in Decision Making: Taxonomy, Key Elements and Applications, and Challenges in Data Science and Explainable Artificial Intelligence

Distributed linguistic representations are powerful tools for modelling the uncertainty and complexity of preference information in linguistic decision making. To provide a comprehensive perspective on the development of distributed linguistic representations in decision making, we present the taxonomy of existing distributed linguistic representations. Then, we review the key elements and applications of distributed linguistic information processing in decision making, including the distance measurement, aggregation methods, distributed linguistic preference relations, and distributed linguistic multiple attribute decision making models. Next, we provide a discussion on ongoing challenges and future research directions from the perspective of data science and explainable artificial intelligence.National Natural Science Foundation of China (NSFC) 71971039 71421001,71910107002,71771037,71874023 71871149Sichuan University sksyl201705 2018hhs-5

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc