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The best‐worst method (BWM) is a multi‐criteria decision‐making (MCDM) approach for solving several types of real‐life decision‐making problems. The basic BWM determines the priority order by pairwise comparisons of the best and worst criteria. The strength of the preference assigned via numerical value for linguistic interpretations of relative comparisons ranges from 1 to 9, representing preferences among the criterion. However, the amount of strength is entirely dependent on the choice of the decision‐makers. Though expert's opinions may differ due to various reasons such as incomplete information, lack of knowledge, ambiguity in linguistic terms, and so forth. Therefore, it is highly likely that the expert may provide multiple viewpoints for the preferences values. Thus, this study proposes a novel extension of the BWM named the multi‐choice best‐worst method (MCBWM), dealing with the concept of multiple choices of preference relations to compare the criterion. The MCBWM overcomes the limitation of BWM, where the pairwise preferences in the comparisons are multi‐choice parameters rather than single parametric values. Multiple real‐world MCDM applications are illustrated in experimental studies to show the quality, performance, and applicability of our proposed MCBWM. A detailed comparative analysis of the proposed approach has been done with the well‐known existing decision‐making techniques and their optimal results are compared. The proposed method offers a new direction for the MCDM approaches for solving real‐life problems. [ABSTRACT FROM AUTHOR]

Distance measures are among the most studied phenomena for deciding the degree of belongingness between the two distinct objects. This paper presents a new distance measure among intuitionistic fuzzy sets (IFSs) using the generalized difference sequence spaces within p-summable intuitionistic fuzzy bounded variation (IFBV). The IFBV is a procedure used to approximate the arc-length of an intuitionistic fuzzy-valued function (IFVF) over the IFS, i.e. distance function of all data points of IFS distributed over the geometrical structure of IFBV with power p. The topological uniqueness in the proposed distance measure made it distinguishable, independent from the reflective relationship, and free from the reflective symmetry. All distance measure characteristics are satisfied, and various situations showing the inclusive relations within distance metrics are drawn. Moreover, the proposed distance measure is applied for multi-attribute decision-making approaches, namely the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and GRA (Grey Relational Analysis) techniques. An improved Intuitionistic Fuzzy TOPSIS (IFTOPSIS) and Trapezoidal Intuitionistic Fuzzy GRA (TrIFGRA) techniques are developed to demonstrate the superiority of proposed distance measure with several established ones. With suitable examples, we thoroughly illustrate the functioning of the IFTOPSIS and TrIFGRA decision-making procedures. Extensive comparisons with other popular distance measures are performed to check the effectiveness of our proposed distance measure. [ABSTRACT FROM AUTHOR]