Search Results (5)

Complex picture fuzzy sets are the updated version of the complex intuitionistic fuzzy sets. A complex picture fuzzy set covers three major grades such as membership, abstinence, and falsity with a prominent characteristic in which the sum of the triplet will be contained in the unit interval. In this scenario, we derive the power aggregation operators based on the Aczel–Alsina operational laws for managing the complex picture of fuzzy values. These complex picture fuzzy power aggregation operators are complex picture fuzzy Aczel–Alsina power averaging, complex picture fuzzy Aczel–Alsina weighted power averaging, complex picture fuzzy Aczel–Alsina power geometric, and complex picture fuzzy Aczel–Alsina weighted power geometric operators. We also investigate their theoretical properties. To justify these complex picture fuzzy power aggregation operators, we illustrate a procedure of a decision-making technique in the presence of complex picture fuzzy values and derive an algorithm to evaluate some multi-attribute decision-making problems. Finally, a practical example is examined to illustrate the decision-making procedure under the consideration of derived operators, and their performance is compared with that of various operators to show the supremacy and validity of the proposed approaches. Full article

A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods. Full article

The complex t-spherical fuzzy set (Ct-SFS) is a potent tool for representing fuzziness and uncertainty compared to the picture fuzzy sets and spherical fuzzy sets. It plays a key role in modeling problems that require two-dimensional data. The present study purposes the aggregation technique of Ct-SFSs with the aid of Aczel–-Alsina (AA) operations. We first introduce certain novel AA operations of Ct-SFSs, such as the AA sum, AA product, AA scalar multiplication, and AA scalar power. Subsequently, we propound a series of complex t-spherical fuzzy averaging and geometric aggregation operators to efficiently aggregate complex t-spherical fuzzy data. In addition, we explore the different characteristics of these operators, discuss certain peculiar cases, and prove their fundamental results. Thereafter, we utilize these operators and propose entropy measures to frame a methodology for dealing with complex t-spherical fuzzy decision-making problems with unknown criteria weight data. Finally, we provide a case study about vehicle model selection to illustrate the presented method’s applicability followed by a parameter analysis and comparative study. Full article

Aggregation operators (AOs) are utilized to overcome the influence of uncertain and vague information in different fuzzy environments. A multi-attribute decision-making (MADM) technique plays a vital role in several fields of different environments such as networking analysis, risk assessment, cognitive science, recommender systems, signal processing, and many more domains in ambiguous circumstances. In this article, we elaborated the notion of Aczel–Alsina t-norm (TNM) and t-conorm (TCNM) under the system of complex Pythagorean fuzzy (CPyF) sets (CPyFSs). Some basic operational laws of Aczel–Alsina TNM and TCNM are established including Aczel–Alsina sum, product, scalar multiplication, and power operations based on CPyFSs. We established several AOs of CPyFSs such as CPyF Aczel–Alsina weighted average (CPyFAAWA), and CPyF Aczel–Alsina weighted geometric (CPyFAAWG) operators. The proposed CPyFAAWA and CPyFAAWG operators are symmetric in nature and satisfy the properties of idempotency, monotonicity, boundedness and commutativity. To solve an MADM technique, we established an illustrative example to select a suitable candidate for a vacant post in a multinational company. To see the advantages of our proposed AOs, we compared the results of existing AOs with the results of newly established AOs. Full article

A contribution of this article is to introduce new q-rung Orthopair fuzzy (q-ROF) aggregation operators (AOs) as the consequence of Aczel–Alsina (AA) t-norm (TN) (AATN) and t-conorm (TCN) (AATCN) and their specific advantages in handling real-world problems. In the beginning, we introduce a few new q-ROF numbers (q-ROFNs) operations, including sum, product, scalar product, and power operations based on AATN and AATCN. At that point, we construct a few q-ROF AOs such as q-ROF Aczel–Alsina weighted averaging (q-ROFAAWA) and q-ROF Aczel–Alsina weighted geometric (q-ROFAAWG) operators. It is illustrated that suggested AOs have the features of monotonicity, boundedness, idempotency, and commutativity. Then, to address multi-attribute decision-making (MADM) challenges, we develop new strategies based on these operators. To demonstrate the compatibility and performance of our suggested approach, we offer an example of construction material selection. The outcome demonstrates the new technique’s applicability and viability. Finally, we comprehensively compare current procedures with the proposed approach. Full article