Improved Knowledge Measures for q-Rung Orthopair Fuzzy Sets

The q-rung orthopair fuzzy set (qROFS) defined by Yager is a generalization of Atanassov intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFSs). In this paper, we define the knowledge measure for qROFS by using the cosine inverse function. The information precision and information content are two facets of knowledge measure. Both facets of knowledge measure are considered. The properties of knowledge measure and their graphical explanations are discussed. An application of the knowledge measure in multi-attribute group decision-making (MAGDM) problem under the confidence level approach is given. A numerical example of the selection of renewable energy sources is discussed

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

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

Fuzzy decision making method based on CoCoSo with critic for financial risk evaluation

The financial risk evaluation is critically vital for enterprises to identify the potential financial risks, provide decision basis for financial risk management, and prevent and reduce risk losses. In the case of considering financial risk assessment, the basic problems that arise are related to strong fuzziness, ambiguity and inaccuracy. q-rung orthopair fuzzy set (q-ROFS), portrayed by the degrees of membership and non-membership, is a more resultful tool to seize fuzziness. In this article, the novel q-rung orthopair fuzzy score function is given for dealing the comparison problem. Later, the and operations are explored and their interesting properties are discussed. Then, the objective weights are calculated by CRITIC (Criteria Importance Through Inter-criteria Correlation). Moreover, we present combined weights that reflects both subjective preference and objective preference. In addition, the q-rung orthopair fuzzy MCDM (multi-criteria decision making) algorithm based on CoCoSo (Combined Compromise Solution) is presented. Finally, the feasibility of algorithm is stated by a financial risk evaluation example with corresponding sensitivity analysis. The salient features of the proposed algorithm are that they have no counter-intuitive case and have a stronger capacity in differentiating the best alternative. First published online 03 March 202

Algorithms for probabilistic uncertain linguistic multiple attribute group decision making based on the GRA and CRITIC method: application to location planning of electric vehicle charging stations

Electric vehicles (EVs) could be regarded as one of the most innovative and high technologies all over the world to cope with the fossil fuel energy resource crisis and environmental pollution issues. As the initiatory task of EV charging station (EVCS) construction, site selection play an important part throughout the whole life cycle, which is deemed to be multiple attribute group decision making (MAGDM) problem involving many experts and many conflicting attributes. In this paper, a grey relational analysis (GRA) method is investigated to tackle the probabilistic uncertain linguistic MAGDM in which the attribute weights are completely unknown information. Firstly, the definition of the expected value is then employed to objectively derive the attribute weights based on the CRiteria Importance Through Intercriteria Correlation (CRITIC) method. Then, the optimal alternative is chosen by calculating largest relative relational degree from the probabilistic uncertain linguistic positive ideal solution (PULPIS) which considers both the largest grey relational coefficient from the PULPIS and the smallest grey relational coefficient from the probabilistic uncertain linguistic negative ideal solution (PULNIS). Finally, a numerical case for site selection of electric vehicle charging stations (EVCS) is designed to illustrate the proposed method. The result shows the approach is simple, effective and easy to calculate

A Decision Support System for Assessing and Prioritizing Sustainable Urban Transportation in Metaverse

Blockchain technology and metaverse advancements allow people to create virtual personalities and spend time online. Integrating public transportation into the metaverse could improve services and collect user data. This study introduces a hybrid decision-making framework for prioritizing sustainable public transportation in Metaverse under q-rung orthopair fuzzy set (q-ROFS) context. In this regard, firstly q-rung orthopair fuzzy (q-ROF) generalized Dombi weighted aggregation operators (AOs) and their characteristics are developed to aggregate the q-ROF information. Second, a q-ROF information-based method using the removal effects of criteria (MEREC) and stepwise weight assessment ratio analysis (SWARA) models are proposed to find the objective and subjective weights of criteria, respectively. Then, a combined weighting model is taken to determine the final weights of the criteria. Third, the weighted sum product (WISP) method is extended to q-ROFS context by considering the double normalization procedures, the proposed operators and integrated weighting model. This method has taken the advantages of two normalization processes and four utility measures that approve the effect of benefit and cost criteria by using weighted sum and weighted product models. Next, to demonstrate the practicality and effectiveness of the presented method, a case study of sustainable public transportation in metaverse is presented in the context of q-ROFSs. The findings of this study confirms that the proposed model can recommend more feasible performance while facing numerous influencing factors and input uncertainties, and thus, provides a wider range of application

Some New Correlation Coefficient Measures Based on Fermatean Fuzzy Sets using Decision Making Approach in Pattern Analysis and Supplier Selection

Fermatean fuzzy set (FFS) is an effective tool to depict expert reasoning information in the decision‐making process than fuzzy sets (FS), intuitionistic fuzzy sets (IFS), and Pythagorean fuzzy sets (PFS). Keeping in mind the importance of correlation coefficient and application in medical diagnosis, decision making and pattern recognition, several studies on correlation coefficient measures have been proposed in the literature. As there does not exist any study concerning correlation coefficient measures for FFS, in this communication, we propose novel entropy-correlation measures for Fermatean fuzzy sets and applied it decision making problems of pattern analysis and multi-criteria decision making for supplier selection. With the help of proposed correlation coefficient, we establish some weighted measures for FFS. Using numerical computations, we determine the efficacy of the suggested measures over other measures. The aim of this study is to propose a novel and efficient methodology for evaluation of supplier’s selection with uncertain information. Finally, we establish the comparative study of our developed measures over the existing correlation coefficient measures. The analysis showed that the suggested methodology is reliable, flexible, and consistent with the existing techniques