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Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method.

The aim of this paper is to define some new operation laws for the trapezoidal linguistic cubic fuzzy number and Hamming distance. Furthermore, we define and use the trapezoidal linguistic cubic fuzzy TOPSIS method to solve the multi criteria decision making (MCDM) method. The new ranking method for trapezoidal linguistic cubic fuzzy numbers (TrLCFNs) are used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method.

Social norms play an important role in regulating the behavior of societies. They are behavioral standards that are considered acceptable in a group or society and violating them will result in sanction to violator. Both governments and various cultural communities use this social component to solve various problems in society. The use of norms leads to a large reduction in community spending to control harmful behaviors. Social norms have two important aspects of promulgating and sanctioning. They are promulgated by activists in the community and, after creation, are endorsed with a sanction. Norms can be used to promote a variety of different behaviors. Online social networks have established a new and influential platform for promulgating social norms. We first redefined the Rescorla-Wagner conditional learning model in the context of social norms with the help of a norm’s intrinsic properties, and extract the main coefficients in the Rescorla-Wagner model related to it. Based on this model, we extract a network structure related parameter (i.e. clustering coefficient) for any individual in the social network to promulgate the norm with the conditional learning method. In this paper, by using the intrinsic properties of norms, we use and tune the Rescorla-Wagner conditioning model in order to obtain a new model for social norm promulgation. Based on this, we define criteria for the amount of effort required to promulgate norms in social networks. We show that there is negative correlation between the amount of effort required by each node to promulgate a norm and the clustering coefficient of that node. This result can be used to devise effective algorithms for social norms evolution.

Pythagorean fuzzy set is one of the successful extensions of the intuitionistic fuzzy set for handling uncertainties in information. Under this environment, in this paper, we introduce the notion of Pythagorean fuzzy Einstein hybrid averaging (PFEHA) aggregation operator along with some of its properties, namely idempotency, boundedness, and monotonicity. PFEHA aggregation operator is the generalization of Pythagorean fuzzy Einstein weighted averaging aggregation operator and Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. The operator proposed in this paper provides more accurate and precise results as compared to the existing operators. Therefore, this method plays a vital role in real-world problems. Finally, we applied the proposed operator and method to multiple-attribute group decision making.

The selection of an appropriate third-party logistics (3PL) provider has become an inescapable option for shippers in today's business landscape, as the outsourcing of logistics activities continues to increase. Choosing the 3PL supplier that best meets their requirements is one of the most difficult difficulties that logistics consumers face. Effective decision-making (DM) is critical in dealing with such scenarios, allowing shippers to make well-informed decisions within a restricted timeframe. The importance of DM arises from the possible financial repercussions of poor decisions, which can result in significant financial losses. In this regard, we introduce p, q-spherical fuzzy set (p, q-SFS), a novel concept that extends the concept of T-spherical fuzzy sets (T-SFSs). p, q-SFS is a comprehensive representation tool for capturing imprecise information. The main contribution of this article is to define the basic operations and a series of averaging and geometric AOs under p, q-spherical fuzzy (p, q-SF) environment. In addition, we establish several fundamental properties of the proposed aggregation operators (AOs). Based on these AOs, we propose a stepwise algorithm for multi-criteria DM (MCDM) problems. Finally, a real-life case study involving the selection of a 3PL provider is shown to validate the applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

Motivated by the concept of type-2 fuzzy sets, we introduce a novel framework known as trapezoidal type-2 Pythagorean fuzzy sets (TRT-2-PFSs), an extension of triangular fuzzy sets. Basic operations like addition and scalar multiplication of two TRT-2-Pythagorean fuzzy numbers (TRT-2-PFNs) are defined. We also explore comparative analysis and distance measurements between two TRT-2-PFNs. A methodology for evaluating unknown weight vectors and criteria weights is proposed. Building upon TRT-2-PFSs, an extension of the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method is developed to address intricate decision-making challenges. Ultimately, the newly introduced TRT-2-PFS-based TODIM technique is employed to tackle multicriteria decision-making (MCDM) problems. [ABSTRACT FROM AUTHOR]

In this paper, we construct an extended version of the TOPSIS method by using cubic information, and provide a numerical application to verify and demonstrate the practicality of the method. A new extension of the gray relation analysis (GRA) method is introduced by using cubic information. We also propose the cubic fuzzy multi-attribute group decision-making model, and the relation between the cubic TOPSIS method and the cubic gray relation analysis (CGRA) method is introduced. Finally, the proposed method is used for selection in sol–gel synthesis of titanium carbide nanopowders. We analyzed the proposed method by using a numerical application to sol–gel synthesis of titanium carbide nanopowders.

On-demand resource provisioning and elasticity are two of the main characteristics of the cloud computing paradigm. As a result, the load on a cloud service provider (CSP) is not fixed and almost always a number of its physical resources are not used, called spare resources. As the CSPs typically don't want to be overprovisioned at any time, they procure physical resources in accordance to a pessimistic forecast of their loads and this leads to a large amount of spare resources most of the time. Some CSPs rent their spare resources with a lower price called the spot price, which varies over time with respect to the market or the internal state of the CSP. In this paper, we assume the spot price to be a function of the CSP's load. We introduce the concept of a parasite CSP, which rents spare resources from several CSPs simultaneously with spot prices and rents them to its customers with an on-demand price lower than the host CSPs' on-demand prices. We propose the overall architecture and interaction model of the parasite CSP. Mathematical analysis has been made to calculate the amount of spare resources of the host CSPs, the amount of resources that the parasite CSP can rent (its virtual capacity) as well as the probability of SLA violations. We evaluate our analysis over pricing data gathered from Amazon EC2 services. The results show that if the parasite CSP relies on several host CSPs, its virtual capacity can be considerable and the expected penalty due to SLA violation is acceptably low.