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.

Group decision-making analysis with complex spherical fuzzy N-soft sets.

This paper develops the ELiminating Et Choice Translating REality (ELECTRE) method under the generalized environment of complex spherical fuzzy $ N $-soft sets ($ CSFN\mathcal{S}_{f}Ss $) that have distinctive and empirical edge of non-binary parametrization and also indeed overcome the limitations and flaws of existing ELECTRE I methods. We propose an innovatory decision-making technique, namely, $ CSFN\mathcal{S}_{f} $-ELECTRE I method where the data and information are in modern modes. The proposed $ CSFN\mathcal{S}_{f} $-ELECTRE I method enjoys all the distinct and modern attributes of uncertain information which mainly comprises of parameterizations, neutral perspective, multi-valuation and two-dimensional representations. We support the proposed work by a flowchart along with an algorithm and then utilize it to solve the MAGDM problem under $ CSFN\mathcal{S}_{f} $ environment. This novel technique employs the principles of $ CSFN\mathcal{S}_{f} $ concordance and $ CSFN\mathcal{S}_{f} $ discordance sets which are established on score and accuracy functions and engrossed to enjoin the most superior alternative. Ultimately, the decision graph and aggregated outranking Boolean matrix are formulated by merging the outcomes of $ CSFN\mathcal{S}_{f} $ concordance and $ CSFN\mathcal{S}_{f} $ discordance indices which are evaluated through score function and distance measures, respectively. Moreover, linear-ranking order is evaluated which provides linear ordering of decision alternatives. A prime MAGDM problem of poverty alleviation is addressed from socio-economic field that approve the flexibility of the intended approach. We perform a sustaining comparison with another approach (CSF-ELECTRE I approach) to assure the productivity and potency of the proposed methodology. We also provide an allegorical line graph of this comparison that demonstrate the admissibility of the resulting outcomes.

A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators.

In this article, we introduce the 2-tuple linguistic bipolar fuzzy set (2TLBFS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into bipolar fuzzy set. The 2TLBFS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the 2-tuple linguistic bipolar fuzzy weighted averaging (2TLBFWA) operator and the 2-tuple linguistic bipolar fuzzy weighted geometric (2TLBFWG) operator are presented to fuse the 2TLBF numbers (2TLBFNs). The Heronian mean (HM) operator, which can reflect the internal correlation between attributes and their influence on decision results, is integrated into the 2TLBF environment to analyze the effect of the correlation between decision factors on decision results. Initially, the generalized 2-tuple linguistic bipolar fuzzy Heronian mean (G2TLBFHM) operator and generalized 2-tuple linguistic bipolar fuzzy weighted Heronian mean (G2TLBFWHM) operator are proposed and properties are explained. Further, 2-tuple linguistic bipolar fuzzy geometric Heronian mean (2TLBFGHM) operator and 2-tuple linguistic bipolar weighted geometric Heronian mean (2TLBFWGHM) operator are proposed along with some of their desirable properties. Then, an approach to multi-attribute group decision-making (MAGDM) based on the proposed aggregation operators under the 2TLBF framework is developed. At last, a numerical illustration is provided for the selection of the best photovoltaic cell to demonstrate the use of the generated technique and exhibit its adequacy.