Development of neutrosophic cubic hesitant fuzzy exponential aggregation operators with application in environmental protection problems.

The population growth and urbanization has caused an exponential increase in waste material. The proper disposal of waste is a challenging problem nowadays. The proper disposal site selection with typical sets and operators may not yield fruitful results. To handle such problems, the exponential aggregation operators based on neutrosophic cubic hesitant fuzzy sets are proposed. For appropriate decisions in a decision-making problem, it is important to have a handy environment and aggregation operators. Many multi attribute decision making methods often ignore the uncertainty and hence yields the results which are not reliable. The neutrosophic cubic hesitant fuzzy set can efficiently handle the complex information in a decision-making problem, as it combines the advantages of neutrosophic cubic set and hesitant fuzzy set. In this paper first we establish exponential operational laws in neutrosophic cubic hesitant fuzzy sets, in which the exponents are neutrosophic cubic hesitant fuzzy numbers and bases are positive real numbers. In order to use neutrosophic cubic hesitant fuzzy sets in decision making, we are developing exponential aggregation operators and investigate their properties in the current study. In many multi expert decision-making methods there are different decision matrices but same weighting vector for attributes. The results of a multi expert decision-making problem becomes more reliable if every decision expert has its own decision matrix along with his own weighting vector for attributes. In this study, we are developing multi expert decision-making method that uses different weights for an attribute corresponding to different experts. At the end we present two applications of exponential aggregation operators in environmental protection multi attribute decision making problems.

Extended fuzzy N-Soft PROMETHEE method and its application in robot butler selection.

This paper extends the literature on fuzzy PROMETHEE, a well-known multi-criteria group decision-making technique. The PROMETHEE technique ranks alternatives by specifying an allowable preference function that measures their deviations from other alternatives in the presence of conflicting criteria. Its ambiguous variation helps to make an appropriate decision or choose the best option in the presence of some ambiguity. Here, we focus on the more general uncertainty in human decision-making, as we allow N-grading in fuzzy parametric descriptions. In this setting, we propose a suitable fuzzy N-soft PROMETHEE technique. We recommend using an Analytic Hierarchy Process to test the feasibility of standard weights before application. Then the fuzzy N-soft PROMETHEE method is explained. It ranks the alternatives after some steps summarized in a detailed flowchart. Furthermore, its practicality and feasibility are demonstrated through an application that selects the best robot housekeepers. The comparison between the fuzzy PROMETHEE method and the technique proposed in this work demonstrates the confidence and accuracy of the latter method.

Novel multiple criteria decision-making analysis under m-polar fuzzy aggregation operators with application.

Aggregation is a very efficient indispensable tool in which several input values are transformed into a single output value that further supports dealing with different decision-making situations. Additionally, note that the theory of m-polar fuzzy (mF) sets is proposed to tackle multipolar information in decision-making problems. To date, several aggregation tools have been widely investigated to tackle multiple criteria decision-making (MCDM) problems in an m-polar fuzzy environment, including m-polar fuzzy Dombi and Hamacher aggregation operators (AOs). However, the aggregation tool to deal with m-polar information under Yager's operations (that is, Yager's t-norm and t-conorm) is missing in the literature. Due to these reasons, this study is devoted to investigating some novel averaging and geometric AOs in an mF information environment through the use of Yager's operations. Our proposed AOs are named as the mF Yager weighted averaging (mFYWA) operator, mF Yager ordered weighted averaging operator, mF Yager hybrid averaging operator, mF Yager weighted geometric (mFYWG) operator, mF Yager ordered weighted geometric operator and mF Yager hybrid geometric operator. The initiated averaging and geometric AOs are explained via illustrative examples and some of their basic properties, including boundedness, monotonicity, idempotency and commutativity are also studied. Further, to deal with different MCDM situations containing mF information, an innovative algorithm for MCDM is established under the under the condition of mFYWA and mFYWG operators. After that, a real-life application (that is, selecting a suitable site for an oil refinery) is explored under the conditions of developed AOs. Moreover, the initiated mF Yager AOs are compared with existing mF Hamacher and Dombi AOs through a numerical example. Finally, the effectiveness and reliability of the presented AOs are checked with the help of some existing validity tests.

A new multi-objective optimization ratio analysis plus full multiplication form method for the selection of an appropriate mining method based on 2-tuple spherical fuzzy linguistic sets.

The selection of an appropriate mining method is considered as an important tool in the mining design process. The adoption of a mining method can be regarded as a complex multi-attribute group decision-making (MAGDM) problem as it may contain uncertainty and vagueness. The main goal of this paper is to propose an extended multi-objective optimization ratio analysis plus full multiplication form (MULTIMOORA) method that is based on a 2-tuple spherical fuzzy linguistic set (2TSFLS). The MULTIMOORA method under 2TSFL conditinos has been developled as a novel approach to deal with uncertainty in decision-making problems. The proposed work shows that 2TSFLSs contain collaborated features of spherical fuzzy sets (SFSs) and 2-tuple linguistic term sets (2TLTSs) and, hence, can be considered as a rapid and efficient tool to represent the experts' judgments. Thus, the broader structure of SFSs, the ability of 2TLTSs to represent linguistic assessments, and the efficiency of the MULTIMOORA approach have motivated us to present this work. To attain our desired results, we built a normalized Hamming distance measure and score function for 2TSFLSs. We demonstrate the applicability and realism of the proposed method with the help of a numerical example, that is, the selection of a suitable mining method for the Kaiyang phosphate mine. Then, the results of the proposed work are compared with the results of existing methods to better reflect the strength and effectiveness of the proposed work. Finally, we conclude that the proposed MULTIMOORA method within a 2TSFLS framework is quite efficient and comprehensive to deal with the arising MAGDM problems.

A new group decision-making framework based on 2-tuple linguistic complex q-rung picture fuzzy sets.

The need for multi-attribute decision-making brings more and more complexity, and this type of decision-making extends to an ever wider range of areas of life. A recent model that captures many components of decision-making frameworks is the complex $ q $-rung picture fuzzy set (C$ q $-RPFS), a generalization of complex fuzzy sets and $ q $-rung picture fuzzy sets. From a different standpoint, linguistic terms are very useful to evaluate qualitative information without specialized knowledge. Inspired by the ease of use of the linguistic evaluations by means of 2-tuple linguistic term sets, and the broad scope of applications of C$ q $-RPFSs, in this paper we introduce the novel structure called 2-tuple linguistic complex $ q $-rung picture fuzzy sets (2TLC$ q $-RPFSs). We argue that this model prevails to represent the two-dimensional information over the boundary of C$ q $-RPFSs, thanks to the additional features of 2-tuple linguistic terms. Subsequently, some 2TLC$ q $-RPF aggregation operators are proposed. Fundamental cases include the 2TLC$ q $-RPF weighted averaging/geometric operators. Other sophisticated aggregation operators that we propose are based on the Hamacher operator. In addition, we investigate some essential properties of the new operators. These tools are the building blocks of a multi-attribute decision making strategy for problems posed in the 2TLC$ q $-RPFS setting. Furthermore, a numerical instance that selects an optimal machine is given to guarantee the applicability and effectiveness of the proposed approach. Finally, we conduct a comparison with other existing approaches.

Group decision-making analysis with complex spherical fuzzy N-soft sets.

This paper develops the ELiminating Et Choice Translating REality (ELECTRE) method under the generalized environment of complex spherical fuzzy $ N $-soft sets ($ CSFN\mathcal{S}_{f}Ss $) that have distinctive and empirical edge of non-binary parametrization and also indeed overcome the limitations and flaws of existing ELECTRE I methods. We propose an innovatory decision-making technique, namely, $ CSFN\mathcal{S}_{f} $-ELECTRE I method where the data and information are in modern modes. The proposed $ CSFN\mathcal{S}_{f} $-ELECTRE I method enjoys all the distinct and modern attributes of uncertain information which mainly comprises of parameterizations, neutral perspective, multi-valuation and two-dimensional representations. We support the proposed work by a flowchart along with an algorithm and then utilize it to solve the MAGDM problem under $ CSFN\mathcal{S}_{f} $ environment. This novel technique employs the principles of $ CSFN\mathcal{S}_{f} $ concordance and $ CSFN\mathcal{S}_{f} $ discordance sets which are established on score and accuracy functions and engrossed to enjoin the most superior alternative. Ultimately, the decision graph and aggregated outranking Boolean matrix are formulated by merging the outcomes of $ CSFN\mathcal{S}_{f} $ concordance and $ CSFN\mathcal{S}_{f} $ discordance indices which are evaluated through score function and distance measures, respectively. Moreover, linear-ranking order is evaluated which provides linear ordering of decision alternatives. A prime MAGDM problem of poverty alleviation is addressed from socio-economic field that approve the flexibility of the intended approach. We perform a sustaining comparison with another approach (CSF-ELECTRE I approach) to assure the productivity and potency of the proposed methodology. We also provide an allegorical line graph of this comparison that demonstrate the admissibility of the resulting outcomes.

A new MAGDM method with 2-tuple linguistic bipolar fuzzy Heronian mean operators.

In this article, we introduce the 2-tuple linguistic bipolar fuzzy set (2TLBFS), a new strategy for dealing with uncertainty that incorporates a 2-tuple linguistic term into bipolar fuzzy set. The 2TLBFS is a better way to deal with uncertain and imprecise information in the decision-making environment. We elaborate the operational rules, based on which, the 2-tuple linguistic bipolar fuzzy weighted averaging (2TLBFWA) operator and the 2-tuple linguistic bipolar fuzzy weighted geometric (2TLBFWG) operator are presented to fuse the 2TLBF numbers (2TLBFNs). The Heronian mean (HM) operator, which can reflect the internal correlation between attributes and their influence on decision results, is integrated into the 2TLBF environment to analyze the effect of the correlation between decision factors on decision results. Initially, the generalized 2-tuple linguistic bipolar fuzzy Heronian mean (G2TLBFHM) operator and generalized 2-tuple linguistic bipolar fuzzy weighted Heronian mean (G2TLBFWHM) operator are proposed and properties are explained. Further, 2-tuple linguistic bipolar fuzzy geometric Heronian mean (2TLBFGHM) operator and 2-tuple linguistic bipolar weighted geometric Heronian mean (2TLBFWGHM) operator are proposed along with some of their desirable properties. Then, an approach to multi-attribute group decision-making (MAGDM) based on the proposed aggregation operators under the 2TLBF framework is developed. At last, a numerical illustration is provided for the selection of the best photovoltaic cell to demonstrate the use of the generated technique and exhibit its adequacy.

Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator.

This study presents a new analytical method to extract the fuzzy solution of the fuzzy initial value problem (FIVP) of fourth-order fuzzy ordinary differential equations (FODEs) using the Laplace operator under the strongly generalized Hukuhara differentiability (SGH-differentiability). To this end, firstly the fourth-order derivative of the fuzzy valued function (FVF) according to the type of the SGH-differentiability is introduced, and then the relationships between the fourth-order derivative of the FVF and its Laplace transform are established. Furthermore, considering the types of differentiabilities and switching points, some fundamental theorems related to the Laplace transform of the fourth-order derivative of the FVF are stated and proved in detail and a method to solve FIVP by the fuzzy Laplace transform is presented in detail. An application of our proposed method in Resistance-Inductance circuit (RL circuit) is presented. Finally, FIVP's solution is graphically analyzed to visualize and support theoretical results.