Search Results (10)

Dynamic decision-making is the process of seeking optimal choice with multiple related attributes under the multi-time-point situation. Considering that the time-varying nature of decision information can have a specific impact on the psychology of decision makers, in this paper, a dynamic decision-making method based on the cumulative prospect theory is proposed. Combining this with infinite parameterization of fuzzy soft sets, a time series interval triangular fuzzy soft set is presented, which has characteristics of boundedness, monotonicity, and symmetry. Then, based on the new information priority principle, the exponential decay model is used to determine the time weight coefficient, and a static fuzzy soft matrix is obtained. Furthermore, a method of calculating psychological utility values is proposed, in which the threshold-reference point set is introduced to analyze the psychological “profit and loss” values. Simultaneously, the time probability of the decision-making scenario is transformed into the corresponding weight function. On the basis of prospect maximization theory and maximum entropy theory, an optimization model for determining the weight of decision parameters is established. The cumulative prospect values of the alternatives are given to achieve the best choice for the alternatives. Finally, an example showed the feasibility and effectiveness of this method. Full article

Under uncertain environments, how to characterize individual preferences more naturally and aggregate parameters better have been hot research topics in multiple attribute decision making (MADM). Fuzzy set theory provides a better mathematical tool to deal with uncertain data, which promotes substantial extended studies. In this paper, we propose a hybrid fuzzy set model by combining a linguistic interval-valued spherical fuzzy set with a soft set for MADM. The emergence of a linguistic interval-valued spherical fuzzy soft set (LIVSFSS) not only handles qualitative information and provides more freedom to decision makers, but also solves the inherent problem of insufficient parameterization tools for fuzzy set theory. To tackle the application challenges, we introduce the basic concepts and define some operations of LIVSFSS, e.g., the “complement”, the “AND”, the “OR”, the “necessity”, the “possibility” and so on. Subsequently, we prove De Morgan’s law, associative law, distribution law for operations on LIVSFSS. We further propose the linguistic weighted choice value and linguistic weighted overall choice value for MADM by taking parameter weights into account. Finally, the MADM algorithm and parameter reduction algorithm are provided based on LIVSFSS, together with examples and comparisons with some existing algorithms to illustrate the rationality and effectiveness of the proposed algorithms. Full article

Supplier selection as a multiattribute decision-making (MADM) problem has various inherent uncertainties due to a number of symmetrical variables. In order to handle such information-based uncertainties, rational models like intuitionistic fuzzy sets have already been introduced in the literature. However, a picture fuzzy set (PiFS) with four dimensions of positive, neutral, negative, and rejection is better at capturing and interpreting such kinds of ambiguous information. Additionally, fuzzy parameterization (FPara) is helpful for evaluating the degree of uncertainty in the parameters. This study aims to develop a fuzzy parameterized picture fuzzy soft set (FpPiFSS) by integrating the ideas of PiFS and FPara. This integration is more adaptable and practical since it helps decision makers manage approximation depending on their objectivity and parameterization uncertainty. With the assistance of instructive examples, some of the set-theoretic operations are examined. A decision support framework is constructed using matrix manipulation, preferential weighting, fuzzy parameterized grades based on Pythagorean means, and the approximations of decision makers. This framework proposes a reliable algorithm to evaluate four timber suppliers (initially scrutinized by perusal process) based on eight categorical parameters for real estate projects. In order to accomplish suppliers evaluation, crucial validation outcomes are taken into account, including delivery level, purchase cost, capacity, product quality, lead time, green degree, location, and flexibility. To assess the advantages, dependability, and flexibility of the recommended strategy, comparisons in terms of computation and structure are provided. Consequently, the results are found to be reliable, analog, and consistent despite the use of fuzzy parameterization and picture fuzzy setting. Full article

Fuzzy parameterized fuzzy hypersoft set ($\Delta$-set) is more flexible and reliable model as it is capable of tackling features such as the assortment of attributes into their relevant subattributes and the determination of vague nature of parameters and their subparametric-valued tuples by employing the concept of fuzzy parameterization and multiargument approximations, respectively. The existing literature on medical diagnosis paid no attention to such features. Riesz Summability (a classical concept of mathematical analysis) is meant to cope with the sequential nature of data. This study aims to integrate these features collectively by using the concepts of fuzzy parameterized fuzzy hypersoft set ($\Delta$-set) and Riesz Summability. After investigating some properties and aggregations of $\Delta$-set, two novel decision-support algorithms are proposed for medical diagnostic decision-making by using the aggregations of $\Delta$-set and Riesz mean technique. These algorithms are then validated using a case study based on real attributes and subattributes of the Cleveland dataset for heart-ailments-based diagnosis. The real values of attributes and subattributes are transformed into fuzzy values by using appropriate transformation criteria. It is proved that both algorithms yield the same and reliable results while considering hypersoft settings. In order to judge flexibility and reliability, the preferential aspects of the proposed study are assessed by its structural comparison with some related pre-developed structures. The proposed approach ensures that reliable results can be obtained by taking a smaller number of evaluating traits and their related subvalues-based tuples for the diagnosis of heart-related ailments. Full article

In this article, we presented the notion of M-parameterized N-soft set (MPNSS) to assign independent non-binary evaluations to both attributes and alternatives. The MPNSS is useful for making explicit the imprecise data which appears in ranking, rating, and grading positions. The proposed model is superior to existing concepts of soft set (SS), fuzzy soft sets (FSS), and N-soft sets (NSS). The concept of M-parameterized N-soft topology (MPNS topology) is defined on MPNSS by using extended union and restricted intersection of MPNS-power whole subsets. For these objectives, we define basic operations on MPNSSs and discuss various properties of MPNS topology. Additionally, some methods for multi-attribute decision making (MADM) techniques based on MPNSSs and MPNS topology are provided. Furthermore, the TOPSIS (technique for order preference by similarity to an ideal solution) approach under MPNSSs and MPNS topology is established. The symmetry of the optimal decision is illustrated by interesting applications of proposed models and new MADM techniques are demonstrated by certain numerical illustrations and well justified by comparison analysis with some existing techniques. Full article

In the definition of the complex neutrosophic soft expert set (CNSES), parameters set is a classical set, and the parameters have the same degree of importance, which is considered as 1. This poses a limitation in modeling of some problems. This paper introduces the concept of fuzzy parameterized complex neutrosophic soft expert set (FP-CNSES) to handle this issue by assigning a degree of importance to each of the problem parameters. We further develop FP-CNSES by establishing the concept of weighted fuzzy parameterized complex neutrosophic soft expert set (WFP-CNSES) based on the idea that each expert has a relative weight. These new mathematical frameworks reduce the chance of unfairness in the decision making process. Some essential operations with their properties and relevant laws related to the notion of FP-CNSES are defined and verified. The notation of mapping on fuzzy parameterized complex neutrosophic soft expert classes is defined and some properties of fuzzy parameterized complex neutrosophic soft expert images and inverse images was investigated. FP-CNSES is used to put forth an algorithm on decision-making by converting it from complex state to real state and subsequently provided the detailed decision steps. Then, we provide the comparison of FP-CNSES to the current methods to show the ascendancy of our proposed method. Full article

Contemporary research has refined systems with complex fuzzy sets in order to improve the design and model of real-life applications. Symmetry and antisymmetry are basic characteristics of binary relations used when modeling the decision maker’s preferences. A recent focus has been the analysis of a complex data set using the properties of fuzzy concept lattice and the complex soft set. We will introduce a new concept to represent the information which utilizes the time factor, called fuzzy parameterized complex multi-fuzzy soft expert set ( $FP$ - $\mathcal{CMFSES}$ ), and investigate part of its fundamental properties. This $FP$ - $\mathcal{CMFSES}$ model allows us to validate the information provided by an expert, at a given phase of time, using the properties of complex fuzzy sets. We then construct an algorithm based on this concept by converting it from the complex state to the real state. Eventually, we implement it to a decision-making problem to demonstrate the applicability of the suggested method. A comparison among $FP$ - $\mathcal{CMFSES}$ and other existing methods is made to expose the dominance of the suggested method. Apart from that, we also propose the weighted fuzzy parameterized complex multi-fuzzy soft expert set and investigate its application to decision-making. Full article

Molodtsov originated soft set theory that was provided a general mathematical framework for handling with uncertainties in which we meet the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as neutrosophic set theory. The main object of this paper is to lay a foundation for providing a new approach of single-valued neutrosophic soft tool which is considering many problems that contain uncertainties. In present study, a new aggregation operators of single-valued neutrosophic soft numbers have so far not yet been applied for ranking of the alternatives in decision-making problems. To this propose work, single-valued neutrosophic soft weighted arithmetic averaging (SVNSWA) operator, single-valued neutrosophic soft weighted geometric averaging (SVNSWGA) operator have been used to compare two single-valued neutrosophic soft numbers (SVNSNs) for aggregating different single-valued neutrosophic soft input arguments in neutrosophic soft environment. Then, its related properties have been investigated. Finally, a practical example for Medical diagnosis problems provided to test the feasibility and applicability of the proposed work. Full article

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theories. Full article

Fuzzy sets, rough sets and soft sets are different tools for modeling problems involving uncertainty. Graph theory is another powerful tool for representing the information by means of diagrams, matrices or relations. A possible amalgamation of three different concepts rough sets, soft sets and graphs, known as soft rough graphs, is proposed by Noor et al. They introduced the notion of vertex, edge induced soft rough graphs and soft rough trees depending upon the parameterized subsets of vertex set and edge set. In this article, a new framework for studying the roughness of soft graphs in more general way is introduced. This new model is known as the modified soft rough graphs or $\mathcal{MSR}$ -graphs. The concept of the roughness membership function of vertex sets, edge sets and of a graph is also introduced. Further, it has been shown that $\mathcal{MSR}$ -graphs are more robust than soft rough graphs. Some results, which are not handled by soft rough graphs, can be handled by modified soft rough graphs. The notion of uncertainty measurement associated with $\mathcal{MSR}$ -graphs is introduced. All applications related to decision makings are only restricted to the information of individuals only, not their interactions, using this technique we are able to involve the interactions (edges) of individuals with each other that enhanced the accuracy in decisions. Full article