The aim of this paper is to redefine the notion of spherical fuzzy soft sets as a more general concept to make them more functional for solving multi-criteria decision-making problems.We first define the set operations under the new spherical fuzzy soft set environment and obtain some fundamental properties of them.Then, we construct the spherical fuzzy soft Aggregation Operator which allows establishing a more efficient and useful method to solve the multi-criteria decision-making problems. We establish an algorithm for the decision-making process which is more useful, simple, and easier than the existing methods.After constructing the method for solving the decision-making problem, we give a numerical example based on linguistic terms to show that the validity of the proposed technique.Finally, we analyze the reliability of the results of this method with the help of the comparative studies by applying this to a real-time data set and using the existing methods.

Background: A medical device is any instrument, apparatus, implement, machine, appliance, software, material, which is intended material, to be utilized, either alone or in combination, for medical purpose. These devices should work precisely and the maintenance program of them has also a key role to achieve this goal. Many of the maintenance programs have not considered important functional parameters such as equipment type, risk factors, and expert opinion. Objective: The purpose of this study is to present a novel fuzzy method for medical device risk assessment. The obtained values for risk could be used to prioritize maintenance operations by considering allocation budget. Material and Methods: This experimental study aims to make a new application of Ordered-Weighted Average Operator in Aggregation of different parameters for calculating Risk Priority Number. This model is a fuzzy multi-criteria decision making approach based on risk maintenance framework for medical device prioritization. Results: A limited budget is one of the barrier in medical centers. The suggested framework presents a simple and reliable method to choose the best maintenance strategy for each kind of medical device by considering budget limitation. Based on obtained results from numerical model, defibrillators and surgical suction have respectively the highest and the lowest priority in mentioned example. Conclusion: Risk prioritization of medical devices is valuable because the medical centers can prioritize maintenance operations and thereby to establish preference of maintenance strategy. Implementation of our proposed maintenance program has many effective results in medical center budgets.

Aggregation Operators (AOs) have been studied by many scholars. As many AOs are proposed, there is still lacking approach to classify the categories of AO, and to select the appropriate AO within the AO candidates. In this research, each AO can be regarded as a cognitive style or individual difference. A Cognitive Style and Aggregation Operator (CSAO) model is pro- posed to analyze the mapping relationship between the Aggregation Operators and the cognitive styles represented by the decision attitudes. Four algorithms are proposed for CSAO: CSAO-1, CSAO-2 and two selection strategies on the basis of CSAO-1 and CSAO-2. The numerical examples illustrate how the choice of the Aggregation Operators on the basis of the decision attitudes can be determined by the selection strategies of CSAO-1 and CSAO-2. The CSAO model can be applied to decision making systems with the selection problems of the appropriate Aggregation Operators with consideration of the cognitive styles of the decision makers.

A cubic bipolar fuzzy number (CBFN) is extremely useful for conveying ambiguous data in real-world settings. The idea of a priority degree is used in an MCDM in which the parameters have a prioritization relationship. Aggregation Operators (AOs) are created by assigning non-negative real numbers called priority degrees to tight priority levels. As a result, "cubic bipolar fuzzy prioritized averaging Operator with priority degrees (CBFPDA)" and "cubic bipolar fuzzy prioritized geometric Operator with priority degrees (CBFPGD)" are presented as prioritized Operators with CBFNs. The proposed approaches results are compared to those of numerous other related studies. The existing method's properties are frequently compared to those of other current methods, emphasizing the superiority of the provided work over currently employed Operators. In addition, the impact of priority degrees on information fusion and object ranking is investigated. The discussion of a third party reverse logistic provider (3PRLP) optimization problem's practical implementation is a secondary goal. A numerical example is used to examine the effectiveness, superiority, and logic of the recommended way to refer about 3PRLP. Following the procedure of choosing the best strategy and rating the viable alternatives, a comparison analysis is performed.

Molodtsov initiated soft set theory that provided a general mathematical framework for handling with uncertainties in which we encounter the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as bipolar fuzzy set theory. The main object of this paper is to lay a foundation for providing a new application of bipolar fuzzy soft tool in considering many problems that contain uncertainties. In present study, Aggregation of bipolar fuzzy soft numbers have so far not yet been applied for ranking of alternatives in decision-making problems. To this propose, bipolar fuzzy soft weighted arithmetic averaging (BFSWAA) Operator, bipolar fuzzy soft weighted geometric averaging (BFSWGA) Operator have been used to compare two bipolar fuzzy soft numbers (BFSNs) for aggregating different bipolar fuzzy soft input arguments in bipolar fuzzy soft environment. Then, their related properties have been investigated. Finally, a practical example for selection of alternatives is given to demonstrate the utility and application of the proposed work.

The Schwarz inequality and Jensen’s one are fundamental in a Hilbert space. Regarding a sesquilinear map B(X, Y ) = Y*X as an Operatorvalued inner product, we discuss Operator versions for the above inequalities and give simple conditions that the equalities hold.

Based on the classical works of Clifford inducing partial order from semigroups, recently, Gupta and Jayaram explored the order $\sqsubseteq_{F}$ from an associative operation $F$ through \emph{local left identity} (\textbf{LLI}). Inspired by their works, we further present an order $\sqsubseteq^{*}_F$ obtained from non-commutative operation $F$ which has the \emph{local right identity} (\textbf{LRI}) since the non-commutativity of $F$ implies that the local left and right identity may be different for each element, which means that both orders may not coincide in the same domain. Firstly, we determine an equivalent characterization for two orders induced by non-commutative operation $F$. Secondly, we investigate both orders induced by semi-t-Operators and deeply study their properties. Finally, we characterize both orders obtained from semi-uninorm (resp. semi-nullnorm) under the condition that semi-uninorm (resp. semi-nullnorm) is locally continuous.