scholarly journals Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Qasim Noor ◽  
Dalal Awadh Alrowaili ◽  
Tabasam Rashid ◽  
Syed Muhammad Husnine
Keyword(s):  
Decision Making ◽  
Environmental Quality ◽  
Score Function ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Uncertain Information ◽  
Fuzzy Evaluation ◽  
Specific Calculation ◽  
Environmental Quality Assessment

As a valuable tool for representing uncertain information, probabilistic hesitant fuzzy sets (PHFS) have gained considerable recognition and in-depth discussion in recent years to increase the flexibility and manifest hesitant information in decision-making problems. However, decision-makers (DMs) cannot express all preferences only through a few probabilistic terms in actual decision-making. Much critical information is hidden behind the original information provided by the DMs. Keeping that in mind, we are interested in mining deeper uncertain information from the original probabilistic hesitant fuzzy evaluation data. To achieve the target, we put forward a novel representation tool called the normal wiggly probabilistic hesitant fuzzy set (NWPHFS) to extract deeper uncertain preferences from original probabilistic information. NWPHFS retains the original evaluation information and carries and assesses the potential uncertain details for increasing the rationality of decision-making outcomes. Herein, we propose some fundamental concepts of NWPHFS, for instance, some elementary operational laws, distance measures between two NWPHFSs, and score function. We also suggest two new aggregation operators, that is, the normal wiggly probabilistic hesitant fuzzy weighted averaging (NWPHFWA) and normal wiggly probabilistic hesitant fuzzy weighted geometric (NWPHFWG). A novel mechanism is proposed here to work out multiattribute decision-making (MADM) in solving normal wiggly probabilistic decision-making problems. Through a practical example of environmental quality assessment, the specific calculation steps of this method are epitomized. Finally, we have demonstrated the feasibility and advancement of the proposed approach via a comprehensive comparative study.

scholarly journals Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 280 ◽  
Author(s):  
Harish Garg ◽  
Gagandeep Kaur
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Weight Vector ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Maximum Deviation ◽  
Dual Hesitant Fuzzy Set ◽  
Deviation Method

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

The ELECTRE I Multi-Criteria Decision-Making Method Based on Hesitant Fuzzy Sets

2015 ◽  
Vol 14 (03) ◽  
pp. 621-657 ◽  
Author(s):  
Na Chen ◽  
Zeshui Xu ◽  
Meimei Xia
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Hesitant Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Uncertain Information ◽  
Deviation Function ◽  
Outranking Relations ◽  
Electre I ◽  
Parameter Interval ◽  
The Given

Hesitant fuzzy set (HFS), which allows the membership degree of an element to a set represented by several possible values, is considered as a powerful tool to express uncertain information in the process of multi-criteria decision making (MCDM) problems. In this paper, we develop a hesitant fuzzy ELECTRE I (HF-ELECTRE I) method and apply it to solve the MCDM problem under hesitant fuzzy environments. The new method is formulated using the concepts of hesitant fuzzy concordance and hesitant fuzzy discordance which are based on the given score function and deviation function, and employed to determine the preferable alternative. Numerical examples are provided to demonstrate the application of the proposed method, and the influence of different numbers of alternatives on outranking relations is analyzed based on a derived sensitive parameter interval in which a change in the parameters has no effects on the set of the nonoutranked alternatives. The randomly generated numerical cases are also investigated in the framework of the HF-ELECTRE I method. Furthermore, the outranking relations obtained in the HF-ELECTRE I method with those derived from the aggregation operator-based approach and the ELECTRE III and ELECTRE IV methods are discussed.

A Multi-Attribute Decision-Making Method Based on SPAOWA Operator

2014 ◽  
Vol 571-572 ◽  
pp. 124-127
Author(s):  
Wan Jun Wang ◽  
Yan Yan
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Information Aggregation ◽  
Weighted Averaging ◽  
Fuzzy Decision Making ◽  
Uncertain Information ◽  
Pair Number ◽  
Multi Attribute Decision Making ◽  
Human Thinking ◽  
Set Up

The vagueness of human thinking and complexity of perception of the objective reality led to the uncertainty of decision-making. Facing with the growing mass of information, the problem of uncertain information, vague information and uncertain fuzzy decision making become increasingly important. The paper studied the multi-attribute decision-making problem raised from decision information in the form of set pair number, put forward a Set Pair Analysis Ordered Weighted Averaging (SPAOWA) operator and set up a multi-attribute decision-making method for information aggregation and ordering by score function with set pair number. Feasibility of the proposed method has been analyzed by the given examples.

scholarly journals A Decision-making Approach for Choosing a Reliable Product under the Hesitant Fuzzy Environment via a Novel Distance Measure

2020 ◽  
Vol 45 (3) ◽  
pp. 147-159
Author(s):  
Palash Dutta ◽  
Rupjit Saikia
Keyword(s):  
Decision Making ◽  
Distance Measure ◽  
Score Function ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Mean Deviation ◽  
Manufacturing Companies ◽  
Digital Products ◽  
Executive Summary ◽  
Fuzzy Environment

Executive Summary In the contemporary time, the reliability of any product has become a big issue from the customer’s perspective due to exponentially mushrooming markets of electronics and digital gadgets. Since the use of digital equipment is tremendously increasing, as a consequence, the production and availability of products are also increasing rampantly. Due to the flooding of digital products, customers often end up in a dilemma regarding the abundant choice and subsequently, become very much dependent upon the reviews of experts and fellow customers as well. In many cases, unfortunately, it is encountered that the products are not reliable enough as suggested by the reviewers. Besides, it is often seen that the manufacturing companies provide almost similar types of features and facilities for products and customers usually end up in a dilemma The confusion gets triggered when varieties of commodities are manufactured and supplied by different manufacturers bearing almost the same features nearly at the same price. In such situations, the reviews of experts and customers already using the product become essential. The reliability of a product relies upon the reviews of the previous customers of the same product. In this article, fuzzy multi-criteria decision-making methodology has been employed to find the reliability of a product considering different features of the product based on the reviews of customers and experts. This paper presents a neo distance measure on hesitant fuzzy set which is found on the notion of score function and mean deviation. Explanatory instances are provided to reveal the distinctiveness and merit of our proposed idea on distance measure over existing distance measures. After that, the proposed distance measure is applied in the decision-making approach for taking up the best electronic products. It is evidenced that the proposed distance measure is beneficial to measure distance degree between two unequal Hesitant Fuzzy Elements (HFEs) without putting extra elements in the shorter HFE. The proposed distance measures can be utilized in the decision-making field in the near future under diverse conditions to display undetermined particulars in a much-clarified manner.

scholarly journals q-Rung Orthopair Fuzzy Rough Einstein Aggregation Information-Based EDAS Method: Applications in Robotic Agrifarming

2021 ◽  
Vol 2021 ◽  
pp. 1-27
Author(s):  
Shahzaib Ashraf ◽  
Noor Rehman ◽  
Azmat Hussain ◽  
Hussain AlSalman ◽  
Abdu H. Gumaei
Keyword(s):  
Decision Making ◽  
Real Life ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Entropy Measure ◽  
Uncertain Information ◽  
Multicriteria Group Decision Making ◽  
Decision Making Model ◽  
Numerical Case Study

The main purpose of this manuscript is to present a novel idea on the q-rung orthopair fuzzy rough set (q-ROFRS) by the hybridized notion of q-ROFRSs and rough sets (RSs) and discuss its basic operations. Furthermore, by utilizing the developed concept, a list of q-ROFR Einstein weighted averaging and geometric aggregation operators are presented which are based on algebraic and Einstein norms. Similarly, some interesting characteristics of these operators are initiated. Moreover, the concept of the entropy and distance measures is presented to utilize the decision makers’ unknown weights as well as attributes’ weight information. The EDAS (evaluation based on distance from average solution) methodology plays a crucial role in decision-making challenges, especially when the problems of multicriteria group decision-making (MCGDM) include more competing criteria. The core of this study is to develop a decision-making algorithm based on the entropy measure, aggregation information, and EDAS methodology to handle the uncertainty in real-word decision-making problems (DMPs) under q-rung orthopair fuzzy rough information. To show the superiority and applicability of the developed technique, a numerical case study of a real-life DMP in agriculture farming is considered. Findings indicate that the suggested decision-making model is much more efficient and reliable to tackle uncertain information based on q-ROFR information.

scholarly journals Novel Parameterized Distance Measures on Hesitant Fuzzy Sets with Credibility Degree and Their Application in Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 557 ◽  
Author(s):  
Jiaru Li ◽  
Fangwei Zhang ◽  
Qiang Li ◽  
Jing Sun ◽  
Janney Yee ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Cardinal Number ◽  
Decision Makers ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
The Subject ◽  
The Relationship

The subject of this study is to explore the role of cardinality of hesitant fuzzy element (HFE) in distance measures on hesitant fuzzy sets (HFSs). Firstly, three parameters, i.e., credibility factor, conservative factor, and a risk factor are introduced, thereafter, a series of novel distance measures on HFSs are proposed using these three parameters. These newly proposed distance measures handle the relationship between the cardinal number and the element values of hesitant fuzzy set well, and are suitable to combine subjective and objective decision-making information. When using these functions, decision makers with different risk preferences are allowed to give different values for these three parameters. In particular, this study transfers the hesitance degree index to a credibility of the values in HFEs, which is consistent with people’s intuition. Finally, the practicability of the newly proposed distance measures is verified by two examples.

scholarly journals A method for decision making with the OWA operator

2012 ◽  
Vol 9 (1) ◽  
pp. 357-380 ◽  
Author(s):  
José Merigó ◽  
Anna Gil-Lafuente
Keyword(s):  
Decision Making ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Minimum Level ◽  
Ordered Weighted Averaging ◽  
Special Cases ◽  
Wide Range ◽  
Decision Making Problem ◽  
Parameterized Family

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

scholarly journals Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Harish Garg ◽  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Sultan Aljahdali
Keyword(s):  
Decision Making ◽  
Solution Method ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Distance Measures ◽  
Uncertain Information ◽  
Cosine Similarity Measures ◽  
Complex Valued ◽  
Interval Valued ◽  
The Ideal

The purpose of this paper is to present a new method to solve the decision-making algorithm based on the cosine similarity and distance measures by utilizing the uncertain and vague information. A complex interval-valued q-rung orthopair fuzzy set (CIVQROFS) is a reliable and competent technique for handling the uncertain information with the help of the complex-valued membership grades. To address the degree of discrimination between the pairs of the sets, cosine similarity measures (CSMs) and distance measures (DMs) are an accomplished technique. Driven by these, in this manuscript, we defined some CSMs and DMs for the pairs of CIVQROFSs and investigated their several properties. Choosing that the CSMs do not justify the axiom of the similarity measure (SM), then we investigate a technique to developing other CIVQROFSs-based SMs using the explored CSMs and Euclidean DMs, and it fulfills the axiom of the SMs. In addition, we find the cosine DMs (CDMs) by considering the inter-relationship between the SM and DMs; then, we have modified the procedure for the rank of partiality by similarity to the ideal solution method for the CDMs under investigation, which can deal with the associated decision-making problems not only individually from the argument of the opinion of geometry but also the fact of the opinion of algebra. Finally, we provide a numerical example to demonstrate the practicality and effectiveness of the proposed procedure, which is also in line with existing procedures. Graphical representations of the measures developed are also used in this manuscript.

scholarly journals Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment

2015 ◽  
Vol 24 (1) ◽  
pp. 23-36 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Fuzzy Environment ◽  
Cosine Measure ◽  
Multiple Attribute

AbstractOn the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator and investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems

2018 ◽  
Vol 29 (1) ◽  
pp. 154-171 ◽  
Author(s):  
Muhammad Sajjad Ali Khan ◽  
Saleem Abdullah ◽  
Asad Ali ◽  
Khaista Rahman
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Information Aggregation ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Fuzzy Environment ◽  
Multidimensional Evaluation

Abstract In this paper, we introduce the concept of the Pythagorean hesitant fuzzy set (PHFS), which is the generalization of the intuitionistic hesitant fuzzy set under the restriction that the square sum of its membership degrees is ≤1. In decision making with PHFSs, aggregation operators play a key role because they can be used to synthesize multidimensional evaluation values represented as Pythagorean hesitant fuzzy values into collective values. Under PHFS environments, Pythagorean hesitant fuzzy ordered weighted averaging and Pythagorean fuzzy ordered weighted geometric operators are used to aggregate the Pythagorean hesitant fuzzy values. The main advantage of these operators is that they provide more accurate and valuable results. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean hesitant fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, we compare the proposed approach to the existing methods.

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