Search Results (7)

Interval neutrosophic sets (INSs), characterized by truth, indeterminacy and falsity membership degrees, handle the uncertain and inconsistent information that commonly exists in real-life systems, and constitute an extension of the interval valued fuzzy set and interval valued intuitionistic fuzzy set. The existing works on similarity measures for INSs are mostly constructed by distance measures and entropies. Meanwhile, the degree of similarity is expressed as a single number, even if the interval-valued information is considered. This may lead to a loss of interval-valued information. In order to cope with these issues, in this paper, we introduce a new approach to constructing the similarity measures for INSs using fuzzy equivalencies. First, based on fuzzy equivalencies and aggregation operators, the definition of interval-valued fuzzy equivalence is generalized to interval neutrosophic values. Then, based on the framework of INSs, we propose the definition and construction method of the similarity measure using the interval neutrosophic fuzzy equivalence. The similarity degree is expressed as an interval and could retain more information than ever before. In addition, according to practical situations, one can obtain different similarities by selecting the parameters in fuzzy equivalence. Due to the increase in edge computing, it is necessary to reasonably offload the client’s resource and assign them to the edge server to balance the resource usage. The Similarity measure is conductive to select and match the client and edge server. Finally, an illustrative example verifies that the proposed method can find a reasonable client and edge server, as well as effectiveness in the edge computing application. Full article

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter. Full article

The Neutrosophic set (NS) has grasped concentration by its ability for handling indeterminate, uncertain, incomplete, and inconsistent information encountered in daily life. Recently, there have been various extensions of the NS, such as single valued neutrosophic sets (SVNSs), Interval neutrosophic sets (INSs), bipolar neutrosophic sets (BNSs), Refined Neutrosophic Sets (RNSs), and triangular fuzzy number neutrosophic set (TFNNs). This paper contains an extended overview of the concept of NS as well as several instances and extensions of this model that have been introduced in the last decade, and have had a significant impact in literature. Theoretical and mathematical properties of NS and their counterparts are discussed in this paper as well. Neutrosophic-set-driven decision making algorithms are also overviewed in detail. Full article

The interval neutrosophic set (INS) is a subclass of the neutrosophic set (NS) and a generalization of the interval-valued intuitionistic fuzzy set (IVIFS), which can be used in real engineering and scientific applications. This paper aims at developing new generalized Choquet aggregation operators for INSs, including the generalized interval neutrosophic Choquet ordered averaging (G-INCOA) operator and generalized interval neutrosophic Choquet ordered geometric (G-INCOG) operator. The main advantages of the proposed operators can be described as follows: (i) during decision-making or analyzing process, the positive interaction, negative interaction or non-interaction among attributes can be considered by the G-INCOA and G-INCOG operators; (ii) each generalized Choquet aggregation operator presents a unique comprehensive framework for INSs, which comprises a bunch of existing interval neutrosophic aggregation operators; (iii) new multi-attribute decision making (MADM) approaches for INSs are established based on these operators, and decision makers may determine the value of $\lambda$ by different MADM problems or their preferences, which makes the decision-making process more flexible; (iv) a new clustering algorithm for INSs are introduced based on the G-INCOA and G-INCOG operators, which proves that they have the potential to be applied to many new fields in the future. Full article

Recently, the TODIM has been used to solve multiple attribute decision making (MADM) problems. The single-valued neutrosophic sets (SVNSs) are useful tools to depict the uncertainty of the MADM. In this paper, we will extend the TODIM method to the MADM with the single-valued neutrosophic numbers (SVNNs). Firstly, the definition, comparison, and distance of SVNNs are briefly presented, and the steps of the classical TODIM method for MADM problems are introduced. Then, the extended classical TODIM method is proposed to deal with MADM problems with the SVNNs, and its significant characteristic is that it can fully consider the decision makers’ bounded rationality which is a real action in decision making. Furthermore, we extend the proposed model to interval neutrosophic sets (INSs). Finally, a numerical example is proposed. Full article

As a significant business activity, merger and acquisition (M&A) generally means transactions in which the ownership of companies, other business organizations or their operating units are transferred or combined. In a typical M&A procedure, M&A target selection is an important issue that tends to exert an increasingly significant impact on different business areas. Although some research works based on fuzzy methods have been explored on this issue, they can only deal with incomplete and uncertain information, but not inconsistent and indeterminate information that exists universally in the decision making process. Additionally, it is advantageous to solve M&A problems under the group decision making context. In order to handle these difficulties in M&A target selection background, we introduce a novel rough set model by combining interval neutrosophic sets (INSs) with multigranulation rough sets over two universes, called an interval neutrosophic (IN) multigranulation rough set over two universes. Then, we discuss the definition and some fundamental properties of the proposed model. Finally, we establish decision making rules and computing approaches for the proposed model in M&A target selection background, and the effectiveness of the decision making approach is demonstrated by an illustrative case analysis. Full article

As one of the promising renewable energy resources, solar-wind energy has increasingly become a regional engine in leading the economy and raising competitiveness. Selecting a solar-wind power station location can contribute to efficient utilization of resource and instruct long-term development of socio-economy. Since the selection procedure consists of several location alternatives and many influential criteria factors, the selection can be recognized as a multiple criteria decision-making (MCDM) problem. To better express multiple uncertainty information during the selection procedure, fuzzy set theory is introduced to manage that issue. Interval neutrosophic sets (INSs), which are characterized by truth-membership, indeterminacy-membership and falsity-membership functions in the interval numbers (INs) form, are feasible in modeling more uncertainty of reality. In this paper, a newly extended weighted aggregated sum product assessment (WASPAS) technique, which involves novel three procedures, is utilized to handle MCDM issues under INSs environment. Some modifications are conducted in the extended method comparing with the classical WASPAS method. The most obvious improvement of the extended method relies on that it can generate more realistic criteria weight information by an objective and subjective integrated criteria weight determination method. A case study concerning solar-wind power station location selection is implemented to demonstrate the applicability and rationality of the proposed method in practice. Its validity and feasibility are further verified by a sensitivity analysis and a comparative analysis. These analyses effectively reveal that the extended WASPAS technique can well match the reality and appropriately handle the solar-wind power station location selection problem. Full article