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The concept of continuous function-valued $q$-rung orthopair fuzzy set (CFV${}_q$ROFS) represents an innovative framework within fuzzy set theory, where the assessment of an element’s membership and nonmembership degrees is accomplished through continuous functions. This paper introduces a novel entropy measure for CFV${}_q$ROFS, employing the Riemann integral. Furthermore, it outlines a theoretical framework for constructing a similarity measure based on entropy and presents a distance measure. The newly introduced entropy measure is used for weighting criteria and measuring the distance of the alternatives in decision-making processes. To illustrate the practical utility of these concepts, an extended Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is proposed and is employed to tackle a real-world problem previously addressed in the literature. The outcomes of this extended TOPSIS are compared with those given in existing studies, and a sensitivity analysis is performed concerning the variable $q$.

The Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) are pivotal methods in multi-criteria decision-making, addressing causal relationships among criteria and ranking alternatives, respectively. This paper introduces a novel approach, integrating DEMATEL and TOPSIS under the framework of single-valued neutrosophic set (SVNS) to handle indeterminacy in decision-making. Applied to a knowledge management strategy case, the method utilizes eight criteria and four alternatives derived from the literature. The process involves DEMATEL for expert weight determination and direct-relation matrix creation through linguistic variable influence. Subsequently, TOPSIS is employed to rank alternatives based on distance measures. The combined method identifies the ‘Human Resource Department’ as the most crucial in knowledge management strategy. This integrated approach facilitates organizations in pinpointing vital criteria and alternatives for effective knowledge management. Comparative analyses with existing methods are also presented.

The main objective of this paper is to introduce the novel concept of spherical linguistic fuzzy number. The spherical linguistic fuzzy number contains linguistic term, positive, neutral and negative membership degrees with the conditions that the square sum of its membership degrees is less than or equal to $1$. Then, we discuss some basic operational rules of SLFNs and define a generalized distance measure between two SLFNs. Here, we define two newly aggregation operators, namely, SLFNWA operator and SLFNWG operator. Furthermore, we demonstrate an MCGDM technique using the defined aggregation operator, which has been applied to solve a real-life numerical problem. Finally, rigorous sensitivity analysis and comparative study are given to check the effectiveness, utility and rationality of the proposed operational law and multi-criteria group decision-making technique.

In this paper, we use a technique for order preference called TOPSIS, to determine the ranking of importance of certain subfactors of causal factors of political stability. We introduce the use of intuitionistc fuzzy sets in the analysis.

We propose an approach for multi-attribute group decision-making (MAGDM) problems under neutrosophic information, where the preference values of alternatives over the attributes and the importance of attributes are expressed in terms of single-valued neutrosophic sets. Firstly, we develop a nonlinear programming approach based on Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to determine relative closeness intervals of alternatives. Secondly, we aggregate closeness intervals to find out the ranking order of all alternatives by computing their optimal membership degrees based on the ranking method of interval numbers. Finally, we provide an illustrative example to show the effectiveness of the proposed approach.

The corona virus disease 2019 (COVID-19) has emerged as a fatal virus. This deadly virus has taken the whole world into clutches and many people have embraced death due to this invincible bug. The death toll is rising with every tick of time. The aspiration behind this article is to discover the preventive measure that should be taken to cope with this intangible enemy. We study the prime notions of novel sort of topology accredited Pythagorean $m$-polar fuzzy topology along with its prime attributes. We slightly amend the well-acknowledged multi-criteria decision analysis tool TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) to befit the proposed multi-criteria group decision making (MCGDM) problem of exploring the most effective method for curing from COVID-19 employing the proposed model.

The aim of this paper is to introduce the notion of m-polar spherical fuzzy set (mPSFS) as a hybrid model of spherical fuzzy set (SFS) and m-polar fuzzy set (mPFS). The proposed model named as mPSFS is an efficient model to address multi-polarity in a spherical fuzzy environment. That is, an mPSFS assigns $m$ number of ordered triple of three independent grades (membership degree, neutral-membership degree and non-membership degree) against each alternative in the universe of discourse. The existing models, namely, mPFS and SFS, are the special cases of suggested hybrid mPSFS. In order to ensure the novelty of this robust extension, various operations on the m-polar spherical fuzzy sets (mPSFSs) are introduced with some brief illustrations to understand these concepts. A robust multi-criteria decision-making (MCDM) method is established by using new score function and accuracy function for m-polar spherical fuzzy numbers (mPSFNS). Additionally, the extensions of technique of order preference by similarity to ideal solution (TOPSIS) and gray relationship analysis (GRA) towards m-polar spherical fuzzy environment are proposed. Moreover, an application to nephrotic syndrome which may lead to kidney damage is analyzed by extensions TOPSIS and GRA. The proposed techniques and their algorithms provide a fruitful diagnosis procedure in the treatment of nephrotic syndrome. Lastly, we give a comparison analysis of the suggested models with some existing models as well.

Bipolar disorder ($𝔹𝔻$) is a neurodegenerative disease that consists of two main manifestations: mania and depression. In the clinical diagnosis of $𝔹𝔻$, there are two primary components. First and foremost is itself $𝔹𝔻$ which is often wrongly diagnosed as unipolar depression in clinical finding. This is so because in clinical diagnosis the first factor is often neglected due to its approach towards positivity. As a result, the element of bipolarity dies down, and the condition worsens. The second disadvantage is that $𝔹𝔻$ is frequently misdiagnosed due to comparable indications and symptoms. To overcome these diagnosis issues, a cubic bipolar fuzzy set (CBFS) which comprises both bipolar fuzzy set (BFS) and interval-valued bipolar fuzzy set (IVBFS) is very helpful for clinical diagnosis of $𝔹𝔻$. A CBFS has the ability to handle bipolarity with suitable closed intervals to express positive and negative grades to build a solid numerical demonstrating interaction to analyze this disorder effectively. For these objectives, the algorithms of technique for the order of preference by similarity to positive ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE-I) for multi-criteria decision-making (MCDM) based on CBF information are developed. The application of proposed algorithms is presented for clinical diagnosis of $𝔹𝔻$. In order to discuss efficiency and validity of the proposed MCDM approaches, we apply the authenticity test for ranking of feasible alternatives and optimal decision by TOPSIS and ELECTRE-I. The comparison analysis of proposed MCDM approaches with existing techniques is also given.

In this article, micro and nano titania (TiO₂) filled A384 alloy composites are fabricated by stir casting technique with varying filler content from 0–8 wt.% respectively and then we study their physical, mechanical, thermal and erosive wear characteristics respectively. Effect of impact velocity (25–70 m/sec) and impingement angle (30°–90°) on erosion wear behavior of micro and nano TiO₂ filled A384 alloy has also been studied. Finally, an optimization technique was implemented in order to develop a correlation between the physical, mechanical and erosion rate of TiO₂ filled A384 alloy composites by using technique order preference by similarity to ideal solution (TOPSIS).

This study determines the suitable general circulation models (GCMs) for the prediction of future precipitation of Upper Godavari sub-basin, India. Five performance indicators (PIs) namely correlation coefficient (CC), normalized root mean square deviation (NRMSD), absolute normalized mean biased deviation (ANMBD), skill score (SS), Nash Sutcliffe efficiency (NSE), and three different combinations (Case 1: all performance indicators, Case 2: CC, SS and ANMBD, and Case 3: CC, SS, and NRMSD) were considered to evaluate the performance of 38 GCM models for the study area. The observed precipitation data for 12 grid points covering the Upper Godavari sub-basin along with eight districts of Maharashtra were used for the selection of the suitable GCMs. The weights of the indicators were determined by the entropy method. Compromise programming (CP) and the technique for order preference to the similarity to ideal solution (TOPSIS) methods were used for ranking the GCMs. The group decision-making approach was employed to make a collective decision about the rank of 38 GCMS considering all the grid points. In view of all the three combinations of PIs, the study suggests that the effect of the performance indicator NSE on the ranking of GCM models is the most significant (weights for the grid points varying in the range 22.75%–78%) followed by ANMBD, CC, NRMSD, and SS. Including the maximum number of PIs and considering their combinations is found to be much helpful to enhance the credibility of the ranking of GCMs. From the group decision-making approach, it was observed that the ensemble of MPI-ESM-P, CNRM-CM5-2, and CNRM-CM5 is suitable for the prediction of precipitation for the study area.