Enhancing ELECTRE I Method with Complex Spherical Fuzzy Information

This article is concerned to delineate the strategic approach of ELiminating Et Choice Translating REality (ELECTRE) method for multi-attribute group decision-making (MAGDM) in terms of complex spherical fuzzy sets. The feasible, well-suited, and marvelous structure of complex spherical fuzzy set compliments the decision-making efficiency and ranking calibre of ELECTRE I approach to present a beneficial and supreme aptitude strategy for MAGDM. Beside the proposed methodology, a few non-fundamental properties of complex spherical fuzzy weighted averaging (CSFWA) operator inclusive of shift invariance, homogenous, linearity, and additive property are also explored. The proposed procedure validates the individual opinions into an acceptable form by the dint of CSFWA operator and the aggregated opinions are further analyzed by the proposed complex spherical fuzzy- ELECTRE I (CSF-ELECTRE I) method. Within the consideration of proposed methodology, normalized Euclidean distances of complex spherical fuzzy numbers are also contemplated. In CSF-ELECTRE I method, the score, accuracy, and refusal degrees determine the concordance and discordance sets for each pair of alternatives to calculate the concordance and discordance indices, respectively. Based on aggregated outranking matrix, a decision graph is constructed to attain the ELECTREcally outranked solutions and the best alternative. This article provides supplementary approach at the final step to profess a linear ranking order of the alternatives. The versatility and feasibility of the presented method are embellished with two case studies from the business and IT field. Moreover, to ratify the intensity and aptitude of the presented methodology, we provide a comparative study with complex spherical fuzzy-TOPSIS method.

Decision-Making Analysis Based on Hesitant Fuzzy N-Soft ELECTRE-I Approach

For the formal expression of uncertain data, hesitant fuzzy set theory has established itself as a distinguished model because it has a broad use in multi-attribute decision-making problems. With the incorporation of features from N -soft sets, a useful framework referred to as hesitant fuzzy N -soft sets has acquired an even greater appeal. This model integrates and associates the hesitant environment with information regarding the existence of grades or star ratings. In this research article, we introduce a multi-attribute decision-making technique known as hesitant fuzzy N -soft ELECTRE-I, which computes the decision-maker assessments in an adjustable and formative manner. The proposed method also improves the robustness and accuracy of the decisions relying on grades or star ratings. Thus it lays a bedrock for subsequent analyses and applications. We justify the relevance and convenience of the proposed technique by testing it in actually existing scenarios. Finally, we give a comparison of this novel methodology with the HFNS-TOPSIS method.

Evaluating Sustainable Conceptual Designs Using an AHP-Based ELECTRE I Method

Evaluating sustainable conceptual designs is a crucial part of the development of new products in various sectors because it contributes to the survival and prosperity of companies. Such designs must be compatible with a product’s functional requirements and be sustainable in economic, environmental, and social terms. Various criteria, some qualitative and others quantitative, are considered when evaluating sustainable conceptual designs; some criteria may also have sub-criteria, and these criteria and sub-criteria may differ in importance. How to effectively evaluate various criteria and sub-criteria and weight them are the major research problem. This study developed an analytic hierarchy process (AHP)-based ELECTRE I method to resolve the evaluation problem; the method entails a two-level hierarchical structure to depict the relationships between the major criteria and sub-criteria and their corresponding weights, with weights obtained through an AHP. Furthermore, an extension based on the addition of net concordance value and net adjusted discordance value is proposed for ranking alternative designs; this extension yields more distinguishable results than the method of [Nijkamp and Van Delft Multi-Criteria Analysis and Regional Decision-Making, Vol. 8 (Springer Science & Business Media, 1977)], and the proposed extension in the ELECTRE I method captures more information in the modified summation matrix when aggregating values in the concordance matrix and the modified discordance matrix, representing an advantage over the method of [Zhang et al. Virtual network embedding using node multiple metrics based on simplified ELECTRE method, IEEE Access 6 (2018) 37314–37327]. In addition, to demonstrate the feasibility of the proposed method, the example of the evaluation and selection of sustainable conceptual designs in the furniture manufacturing industry is presented. Finally, a numerical comparison is made to show the advantages of the proposed method.