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Fuzzy sets, soft sets and N-soft set are essential concepts for fuzzy modeling, decision making under uncertainty and computational intelligence. Nevertheless, all these models have some limitations imposed on the alternatives and attributes. These mathematical models were unable to handle the situations whenever decision makers need to assign non-binary evaluations to both attributes and alternatives. To overcome these problems, Riaz et al. (Symmetry 13(5):1–31, 2021) proposed the idea of M-parameterized N-soft set (MPNSS), through examining independent non-binary evaluations to both parameters and alternatives. MPNSSs are highly convenient in representation of ambiguous and uncertain data in decision analysis during ranking, rating and grading the objects. The proposed model has greater efficiency to handle the imprecision rather than existing mathematical models. Additionally, we develop multi-attribute decision-making (MADM) techniques on account of M-parameterized N-soft sets (MPNSSs), M-parameterized N-soft aggregation operators (MPNSAO) and M-parameterized N-soft weighted aggregation operators (MPNSWAO). For these objectives, we define fundamental operations on MPNSSs and their properties. Meanwhile, several related results are well proven and some algorithms for MADM are also developed. Moreover, the applications of MADM techniques corresponding to proposed algorithms are explained by illustrative material. To explain the presumption, authenticity and effectiveness of the suggested course of actions, we compared the techniques with few existing MADM methods. [ABSTRACT FROM AUTHOR]

Rough set theory introduced by Pawlak (Int J Comput Inf Sci 11:341–356, 1982), multi-set theory proposed by Blizard (Notre Dame J Form Log 30:36–65, 1989) and soft set theory introduced by Molodtsov (Comput Math Appl 37(4–5):19–31, 1999) are fundamental concepts in computational intelligence, which have a myriad of applications in modeling uncertainties and decision making under uncertainty. In this paper, the idea of soft multi-rough set (SMRS) is introduced as a hybrid model of soft set, multi-set and rough set. The SMRS provides roughness of a multi-set in terms of soft multi-approximation space. The novel concept of soft multi-rough topology (SMR-topology) is defined to discuss topological structure of SMRSs by using pairwise SMR-approximations. The proposed models of SMRS and SMR-topology are suitable for modeling uncertainties in the real-life circumstances. SMR-topology is the generalization of crisp topology, soft topology and soft rough set topology. Some fundamental properties of SMR-topology and their related results are studied. Some algorithms for are developed for multi-criteria decision making based on soft multi-sets, soft multi-rough sets and soft multi-rough topology. Based on proposed algorithms, the applications of SMRSs and SMR-topology toward diagnosis of depression and diabetes are illustrated by the numerical examples. A comparison analysis of proposed methods with some existing methods is also given to justify their reliability, feasibility and flexibility. [ABSTRACT FROM AUTHOR]

In this paper, we bring out the idea of bipolar fuzzy soft topology (BFS-topology) based on bipolar fuzzy soft set (BFS-set). BFS-topology is the generalization of the crisp topology. We discuss certain properties of BFS-topology including, BFS-closure, BFS-interior, BFS-exterior and BFS-frontier by utilizing BFS-points. We study the concept of BFS-subspace, BFS-neighbourhoods and BFS-base for BFS-topology with the help of detailed examples. Furthermore, we use BFS-topology in decision-making by applying an algorithm to deal with unpredictability. [ABSTRACT FROM AUTHOR]

The purpose of this research study is to extend the multi-attribute group decision-making (MAGDM) methods to hesitant fuzzy soft set (HFS-set), hesitant fuzzy soft topology (HFS-topology) and HFS-Hausdorff spaces in group decision-making environment, as HFS-set is more superior tool to capture vagueness, hesitancy and incompleteness in individual evaluations. In order to obtain optimal decisions in MAGDM, we present two algorithms based on hesitant fuzzy soft set and hesitant fuzzy soft topology. Lastly, we present MAGDM method by using HFS-Hausdorff space to deal with hesitancy and uncertainty. The developed methods have the ability to solve MADGM problems in which the assessment information on available alternatives, provided by the experts, is presented by hesitant fuzzy soft sets. Furthermore, the efficiency of proposed algorithms is shown by applying them to the real-world problems. We use reduct, optimum reduct, aggregate HFS-sets and weight vector according of given alternatives, priority of the attributes and customer demand for best MAGDM in the selection of car. [ABSTRACT FROM AUTHOR]

Bipolar irrational emotions are implicated in a broad variety of individual actions. For example, two specific elements of decision making are the benefits and adverse effects. The harmony and respectful coexistence between these two elements is viewed as a cornerstone to a healthy social setting. For bipolar fuzzy characteristics of the universe of choices that rely on a small range of degrees, a bipolar fuzzy decision making method utilizing different techniques is accessible. The idea of a simplistic bipolar fuzzy set is ineffective in supplying consistency to the details about the frequency of the rating due to minimal knowledge. In this respect, we present cubic bipolar fuzzy sets (CBFSs) as a generalization of bipolar fuzzy sets. The plan of this research is to establish an innovative multi-criteria group decision making (MCGDM) based on cubic bipolar fuzzy set (CBFS) by unifying aggregation operators under geometric mean operations. The geometric mean operators are regarded to be a helpful technique, particularly in circumstances where an expert is unable to fuse huge complex unwanted information properly at the outset of the design of the scheme. We present some basic operations for CBFSs under dual order, i.e., P -Order and R -Order. We introduce some algebraic operations on CBFSs and some of their fundamental properties for both orders. We propose P -cubic bipolar fuzzy weighted geometric (P -CBFWG) operator and R -cubic bipolar fuzzy weighted geometric (R -CBFWG) operator to aggregate cubic bipolar fuzzy data. We also discuss the useability and efficiency of these operators in MCGDM problem. In human decisions, the second important part is ranking of alternatives obtained after evaluation. In this regard, we present an improved score and accuracy function to compare the cubic bipolar fuzzy elements (CBFEs). We also discuss a set theoretic comparison of proposed set with other theories as well as method base comparison of the proposed method with some existing techniques of bipolar fuzzy domain. [ABSTRACT FROM AUTHOR]

As the volume of waste generated by human activities continues to rise, the need for effective and sustainable solid waste management methods becomes increasingly important. Traditional approaches, such as landfilling and incineration, can have negative impacts on the environment and human health. Waste management sustainability research can benefit from the use of cosine similarity, a mathematical technique that measures the similarity between two vectors. To address this issue, innovative approaches, such as the use of cubic m-polar fuzzy cosine similarity measures (CmPF), are being explored. In this scenario, the membership grade (MG) is represented by a fuzzy interval, while the non-membership grade (NMG) is stated by a fuzzy number. An m-polar fuzzy set (mPFS) allots m different numbers of MGs to each of the possibilities that assist compensate for the universal set. A CmPF similarity can deal directly with single and multipolar data in an environment that is cubical. There are numerous distinct uses for similarity measures (SMs) in a range of domains. As a result, three unique cosine similarity metrics for CmPFSs are shown in each SM. These measurements utilize the cosine angle between two vectors, a unique distance measure and the cosine function. Additionally, a TOPSIS technique based on cosine SMs has been developed for application in multi-criteria group decision-making (MCGDM) situations. An example of selecting a solid waste recycling technique is offered to demonstrate how effective the MCGDM approach to waste management can be. [ABSTRACT FROM AUTHOR]

The natural gas industry faces significant challenges in implementing industrial filtration systems that are both sustainable and maintainable. These are complex issues that necessitate a thorough and pragmatic evaluation to ensure that the technology is both effective and efficient. Due to the increasing importance of environmental sustainability and the need to reduce waste and emissions, the deployment of filtration technology must be carefully evaluated to ensure that it meets these objectives. The goal of this study is to develop a decision-making approach based on Aczel–Alsina (AA) operations, which provide a variety of advantages when dealing with real-world issues. To begin, we’ll go over some new hesitant q-rung orthopair fuzzy set operations such the Aczel–Alsina product, sum, exponent, and scalar multiplication. The suggested AOs are based on AA operations and are used to prioritize industrial filtering technologies while keeping sustainability and maintainability in mind. Several solutions are studied for managing impurities produced by Pakistan’s natural gas sector. After careful evaluation, it has been determined that the cyclo-filter technology is the most viable solution for the natural gas industry. This technology has been chosen due to its adaptability with the regional and local conditions of the study area. By utilizing this technology, policymakers can gain practical insight into process energy and environmental systems and effectively control contamination in the natural gas industry. This decision-making framework offers a new and innovative approach to address sustainability and maintainability challenges in the industry. [ABSTRACT FROM AUTHOR]