An enhanced VIKOR method for multi-criteria group decision-making with complex Fermatean fuzzy sets

Fermatean fuzzy Linguistic term set based on linguistic scale function with Dombi aggregation operator and their application to multi criteria group decision -making problem

The selection of an industrial location is a challenging multiple-criteria decision-making (MCDM) problem that depends on taking a variety of locations as well as incompatible and inconsistent criteria. This paper proposed a comprehensive framework for the strategic selection of industrial locations, considering both quantitative and qualitative aspects. Decision-makers (DMs) have to deal with ambiguous information throughout this process due to a complex decision environment or their insufficient knowledge. We present a new Fermatean Fuzzy (FF) Linguistic term set based on the Dombi aggregation operators (AOs). By combining the FF set with Linguistic variables, the FF Linguistic (FFL) set is an effective approach for thoroughly representing uncertain evaluation information. We establish a basic operational principles and certain aggregation operator under FFL information, such as the FF Linguistic Dombi weighted averaging (FFLDWA) operator FF Linguistic Dombi weighted geometric (FFLDWG) operator and some fundamental properties of these operators with appropriated elaboration. Based on these operators, a multi-criteria group decision-making technique is developed. Finally, we used a numerical example to compare the flexibility of the suggested technique with other existing methods. Thus, by knowing priorities industries, the best site can be selected.

Complex Fermatean fuzzy extended TOPSIS method and its applications in decision making

The fuzzy set has its own limitations due to the membership function only. The fuzzy set does not describe the negative aspects of an object. The Fermatean fuzzy set covers the negative aspects of an object. The complex Fermatean fuzzy set is the most effective tool for handling ambiguous and uncertain information. The aim of this research work is to develop new techniques for complex decision-making based on complex Fermatean fuzzy numbers. First, we construct different aggregation operators for complex Fermatean fuzzy numbers, using Einstein t-norms. We define a series of aggregation operators named complex Fermatean fuzzy Einstein weighted average aggregation (CFFEWAA), complex Fermatean fuzzy Einstein ordered weighted average aggregation (CFFEOWAA), and complex Fermatean fuzzy Einstein hybrid average aggregation (CFFEHAA). The fundamental properties of the proposed aggregation operators are discussed here. The proposed aggregation operators are applied to the decision-making technique with the help of the score functions. We also construct different algorithms based on different aggregation operators. The extended TOPSIS method is described for the decision-making problem. We apply the proposed extended TOPSIS method to MAGDM problem "selection of an English language instructor". We also compare the proposed models with the existing models.

Multi-attribute decision-making based on novel Fermatean fuzzy similarity measure and entropy measure

To deal with situations involving uncertainty, Fermatean fuzzy sets are more effective than Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. Applications for fuzzy similarity measures can be found in a wide range of fields, including clustering analysis, classification issues, medical diagnosis, etc. The computation of the weights of the criteria in a multi-criteria decision-making problem heavily relies on fuzzy entropy measurements. In this paper, we employ t-conorms to suggest various Fermatean fuzzy similarity measures. We have also discussed all of their interesting characteristics. Using the suggested similarity measurements, we have created some new entropy measures for Fermatean fuzzy sets. By using numerical comparison and linguistic hedging, we have established the superiority of the suggested similarity metrics and entropy measures over the existing measures in the Fermatean fuzzy environment. The usefulness of the proposed Fermatean fuzzy similarity measurements is shown by pattern analysis. Last but not least, a novel multi-attribute decision-making approach is described that tackles a significant flaw in the order preference by similarity to the ideal solution, a conventional approach to decision-making, in a Fermatean fuzzy environment.

Identifying Root Causes of Important Service Failures across Medical Examination Processes with Integration of 4M1E, ITLV, GRA, DEMATEL and FMEA

Medical examination plays an essential role in most medical treatment processes, and thus, the quality of service relevant to medical examination has great impact on patient satisfaction. The targeted hospital has long been faced with the problem that patient satisfaction of its medical examination department is below average. An assessment model, integrating 4M1E, ITLV, GRA, DEMATEL and FMEA, was developed in this study to identify the root causes of important service failures across medical examination processes, where (1) a cause-and-effect diagram was enhanced with 4M1E, identifying the list of failure modes relevant to service quality over the medical examination process with the 4M1E analysis framework, (2) FMEA experts were enabled to report their assessment results in their preferred ways by using the ITLV scheme, (3) causes of failure to failure modes with was figured out with DEMATEL, and (4) the evaluation results were improved by integrating GRA. Experimental results obtained by the proposed approach are compared with several benchmarks, and it was observed that (1) the results obtained by the proposed model are more suitable when FMEA experts prefer using different assessment languages versus other approaches; (2) the proposed model can figure out the key root causes according to their impact on overall failure modes.

A new method to determine the Fermatean fuzzy optimal solution of transportation problems

 Transportation Problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportation costs, are precisely known. However, due to uncertainty in practical applications, it is necessary to study TP in an uncertain environment. In this paper, we define the Trapezoidal Fermatean Fuzzy Number (TrFFN) and its arithmetic operations. Then we introduce a new approach to solve TP, where transportation cost, supply, and demand are treated as TrFFN, and we call it Fermatean Fuzzy TP (FFTP). We illustrate the feasibility and superiority of this method with two application examples, and compare the performance of this method with existing methods. Furthermore, the advantages of the proposed method over existing methods are described to address TP in uncertain environments.