Selection of suitable biomass conservation process techniques: a versatile approach to normal wiggly interval-valued hesitant fuzzy set using multi-criteria decision making

A country that relies on developing industrialization and GDP requires a lot of energy. Biomass is emerging as one of the possible renewable energy resources that may be used to generate energy. Through the proper channels, such as chemical, biochemical, and thermochemical processes, it can be turned into electricity. In the context of India, the potential sources of biomass can be broken down into agricultural waste, tanning waste, sewage, vegetable waste, food, meat waste, and liquor waste. Each form of biomass energy so extracted has advantages and downsides, so determining which one is best is crucial to reaping the most benefits. The selection of biomass conversion methods is especially significant since it requires a careful study of multiple factors, which can be aided by fuzzy multi-criteria decision-making (MCDM) models. This paper proposes the normal wiggly interval-valued hesitant fuzzy-based decision-making trial and evaluation laboratory model (DEMATEL) and the Preference Ranking Organization METHod for Enrichment of Evaluations II (PROMETHEE) for assessing the problem of determining a workable biomass production technique. The proposed framework is used to assess the production processes under consideration based on parameters such as fuel cost, technical cost, environmental safety, and C O 2 emission levels. Bioethanol has been developed as a viable industrial option due to its low carbon footprint and environmental viability. Furthermore, the superiority of the suggested model is demonstrated by comparing the results to other current methodologies. According to comparative study, the suggested framework might be developed to handle complex scenarios with many variables.

Multiple-attribute decision making method based on power generalized maclaurin symmetric mean operators under normal wiggly hesitant fuzzy environment

A normal wiggly hesitant fuzzy set is a very useful tool to mine the potential uncertain information given by decision makers, which is considered as an extension of hesitant fuzzy set and can improve the effectiveness of decision making. Power average operator can relieve the impact on decision result of unreasonable data, and the generalized Maclaurin symmetric mean operator (GMSM) is an extension of Maclaurin symmetric mean operator with wider range of applications, which can consider the relationship among decision attributes. By integrating the advantages of them, in this paper, we develop the normal wiggly hesitant fuzzy power GMSM (NWHFPGMSM) operator and its weighted form based on the distance measure of two normal wiggly hesitant fuzzy elements, then we further discuss their properties and some special cases. Thus, a new multi-attribute decision making method based on the NWHFPGMSM operator under normal wiggly hesitant fuzzy environment is proposed. Finally, we select some examples to illustrate the effectiveness and superiority of the proposed method in this paper through comparison and analysis with other methods.

An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection

Generally, in real decision-making, all the pieces of information are used to find the optimal alternatives. However, in many cases, the decision-makers (DMs) only want “how good/bad a thing can become.” One possibility is to classify the alternatives based on minimum (tail) information instead of using all the data to select the optimal options. By considering the opportunity, we first introduce the value at risk (VaR), which is used in the financial field, and the probabilistic interval-valued hesitant fuzzy set (PIVHFS), which is the generalization of the probabilistic hesitant fuzzy set (PHFS). Second, deemed value at risk (DVaR) and reckoned value at risk (RVaR) are proposed to measure the tail information under the probabilistic interval-valued hesitant fuzzy (PIVHF) environment. We proved that RVaR is more suitable than DVaR to differentiate the PIVHFEs with example. After that, a novel complete group decision-making model with PIVHFS is put forward. This study aims to determine the most appropriate alternative using only tail information under the PIVHF environment. Finally, the proposed methods’ practicality and effectiveness are tested using a stock selection example by selecting the ideal stock for four recently enrolled stocks in China. By using the novel group decision-making model under the environment of PIVHFS, we see that the best stock is E₄ when the distributors focus on the criteria against 10% certainty degree and E₁ is the best against the degree of 20%, 30%, 40% and 50% using the DVaR method. On the other hand when RVaR method is used then the best alternative is E₄ and the worst is E₂ against the different certainty degrees. Furthermore, a comparative analysis with the existing process is presented under the PHF environment to illustrate the effectiveness of the presented approaches.

Multi-attributive border approximation area comparison (MABAC) method based on normal q-rung orthopair fuzzy environment

The normal intuitionistic fuzzy number (NIFN), which membership function and non-membership function are expressed by normal fuzzy numbers (NFNs), can better describe the normal distribution phenomenon in the real world, but it cannot deal with the situation where the sum of membership function and non-membership function is greater than 1. In order to make up for this defect, based on the idea of q-rung orthopair fuzzy numbers (q-ROFNs), we put forward the concept of normal q-rung orthopair fuzzy numbers (q-RONFNs), and its remarkable characteristic is that the sum of the qth power of membership function and the qth power of non-membership function is less than or equal to 1, so it can increase the width of expressing uncertain information for decision makers (DMs). In this paper, firstly, we give the basic definition and operational laws of q-RONFNs, propose two related operators to aggregate evaluation information from DMs, and develop an extended indifference threshold-based attribute ratio analysis (ITARA) method to calculate attribute weights. Then considering the multi-attributive border approximation area comparison (MABAC) method has strong stability, we combine MABAC with q-RONFNs, put forward the q-RONFNs-MABAC method, and give the concrete decision steps. Finally, we apply the q-RONFNs-MABAC method to solve two examples, and prove the effectiveness and practicability of our proposed method through comparative analysis.

The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making

The information measures (IMs) of complex fuzzy information are very useful tools in the areas of machine learning and decision making. In some multi-attribute group decision making (MAGDM) problems, the decision makers can make a decision mostly according to IMs such as similarity measures (SMs), distance measures (DIMs), entropy measures (EMs) and cross-entropy measures (C-EMs) in order to choose the best one. However, the relation between C-EMs and DIMs in the environment of complex fuzzy sets (CFSs) has not been developed and verified. In this manuscript, the notions of DIMs and C-EMs in the environment of CFSs are investigated and the relation between DIMs and EMs in the environment of CFSs is also discussed. The complex fuzzy discrimination measures (CFDMs), the complex fuzzy cross-entropy measures (CFC-EMs), and the symmetry complex fuzzy cross-entropy measures (SCFC-EMs) are proposed. We also examined that the C-EMs satisfied all the conditions of DIMs, and finally proved that C-EMs including CFC-EMs were also a DIMs. In last, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.