scholarly journals An innovative picture fuzzy distance measure and novel multi-attribute decision-making method

2021 ◽  
Author(s):  
Abdul Haseeb Ganie ◽  
Surender Singh
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Real Data ◽  
Distance Measures ◽  
Classification Problems ◽  
Data Set ◽  
The Real ◽  
Picture Fuzzy Set ◽  
Multi Attribute Decision Making

AbstractPicture fuzzy set (PFS) is a direct generalization of the fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). The concept of PFS is suitable to model the situations that involve more answers of the type yes, no, abstain, and refuse. In this study, we introduce a novel picture fuzzy (PF) distance measure on the basis of direct operation on the functions of membership, non-membership, neutrality, refusal, and the upper bound of the function of membership of two PFSs. We contrast the proposed PF distance measure with the existing PF distance measures and discuss the advantages in the pattern classification problems. The application of fuzzy and non-standard fuzzy models in the real data is very challenging as real data is always found in crisp form. Here, we also derive some conversion formulae to apply proposed method in the real data set. Moreover, we introduce a new multi-attribute decision-making (MADM) method using the proposed PF distance measure. In addition, we justify necessity of the newly proposed MADM method using appropriate counterintuitive examples. Finally, we contrast the performance of the proposed MADM method with the classical MADM methods in the PF environment.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1147-1160
Author(s):  
Yali Cheng ◽  
Yonghong Li ◽  
Jie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Linguistic Intuitionistic Fuzzy Sets ◽  
Linguistic Scale Function ◽  
Different Response

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

Some Measures of Picture Fuzzy Sets and Their Application

2017 ◽  
Vol 3 (2) ◽  
pp. 35
Author(s):  
Nguyen Van Dinh ◽  
Nguyen Xuan Thao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Dissimilarity Measure ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
The Difference ◽  
Picture Fuzzy Sets

To measure the difference of two fuzzy sets (FSs) / intuitionistic sets (IFSs), we can use the distance measure and dissimilarity measure between fuzzy sets/intuitionistic fuzzy set. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide  the formulas for determining these values. We also present an application of dissimilarity measures in the sample recognition problems, can also be considered a decision-making problem.

Several Generalized Interval-Valued 2-Tuple Linguistic Interval Distance Measures and Their Application

2017 ◽  
Vol 25 (05) ◽  
pp. 759-786 ◽  
Author(s):  
Fanyong Meng ◽  
Yige Yuan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Distance Measure ◽  
Decision Makers ◽  
Distance Measures ◽  
Linguistic Variables ◽  
Weighting Vector ◽  
Interval Distance ◽  
Multi Attribute Decision Making ◽  
Optimal Weighting ◽  
Interval Valued

Interval-valued linguistic variables are efficient tools to express the decision makers’ uncertain qualitative judgments. Considering the application of interval-valued linguistic variables, this paper proposes an interval distance measure, which is then used to define interval-valued linguistic interval distance measures by combining the 2-tuple linguistic representation model. To reflect the interactions between elements in a set, three correlative interval distance measures on intervalvalued linguistic variables are proposed. Meanwhile, several models designed to obtain the optimal weighting vector are constructed. After that, an approach to pattern recognition and to multi-attribute decision making with interval-valued linguistic information is developed. Meanwhile, associated examples are offered to demonstrate the concrete application of the proposed procedure.

scholarly journals Some Similarity Measures for Interval-Valued Picture Fuzzy Sets and Their Applications in Decision Making

Information ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 369 ◽  
Author(s):  
Peide Liu ◽  
Muhammad Munir ◽  
Tahir Mahmood ◽  
Kifayat Ullah
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets ◽  
Interval Valued

Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples.

scholarly journals Multi-Attribute Decision-Making Based on Preference Perspective with Interval Neutrosophic Sets in Venture Capital

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 257 ◽  
Author(s):  
Yanran Hong ◽  
Dongsheng Xu ◽  
Kaili Xiang ◽  
Han Qiao ◽  
Xiangxiang Cui ◽  
...  
Keyword(s):  
Decision Making ◽  
Venture Capital ◽  
Euclidean Distance ◽  
Distance Measure ◽  
Distance Measures ◽  
Neutrosophic Sets ◽  
Todim Method ◽  
Multi Attribute Decision Making ◽  
Parameter Interval ◽  
Interval Neutrosophic Sets

Fuzzy information in venture capital can be well expressed by neutrosophic numbers, and TODIM method is an effective tool for multi-attribute decision-making. The distance measure is an essential step in TODIM method. The keystone of this paper is to define several new distance measures, in particular the improved interval neutrosophic Euclidean distance, and these measures are applied in the TODIM method for multi-attribute decision-making. Firstly, the normalized generalized interval neutrosophic Hausdorff distance is defined and proved to be valid in this paper. Secondly, we define a weighted parameter interval neutrosophic distance and discuss whether different weight parameters affect the decision result based on TODIM method. Thirdly, considering the preference perspective of decision-makers in behavioral economics, we define the improved interval neutrosophic Euclidean distance with the known parameter of risk preference. Finally, an application example is given to compare the effects of different parameters on the result and discuss the feasibility of these two distance measures in TODIM method.

scholarly journals The Consistency between Cross-Entropy and Distance Measures in Fuzzy Sets

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 386 ◽  
Author(s):  
Yameng Wang ◽  
Han Yang ◽  
Keyun Qin
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Minimum Principle ◽  
Cross Entropy ◽  
Distance Measures ◽  
Uncertain Information ◽  
Neutrosophic Sets ◽  
Information Measures ◽  
The One

The processing of uncertain information is increasingly becoming a hot topic in the artificial intelligence field, and the information measures of uncertainty information processing are also becoming of importance. In the process of decision-making, decision-makers make decisions mostly according to information measures such as similarity, distance, entropy, and cross-entropy in order to choose the best one. However, we found that many researchers apply cross-entropy to multi-attribute decision-making according to the minimum principle, which is in accordance with the principle of distance measures. Thus, among all the choices, we finally chose the one with the smallest cross-entropy (distance) from the ideal one. However, the relation between cross-entropy and distance measures in fuzzy sets or neutrosophic sets has not yet been verified. In this paper, we mainly consider the relation between the discrimination measure of fuzzy sets and distance measures, where we found that the fuzzy discrimination satisfied all the conditions of distance measure; that is to say, the fuzzy discrimination was found to be consistent with distance measures. We also found that the cross-entropy, which improved when it was based on the fuzzy discrimination, satisfied all the conditions of distance measure, and we finally proved that cross-entropy, including fuzzy cross-entropy and neutrosophic cross-entropy, was also a distance measure.

The cross-entropy and improved distance measures for complex q-rung orthopair hesitant fuzzy sets and their applications in multi-criteria decision-making

2021 ◽  
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Cross Entropy ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Pythagorean Fuzzy Set ◽  
The Real

AbstractThe complex q-rung orthopair fuzzy set (Cq-ROFS) is the extension of complex Pythagorean fuzzy set (CPFS) in which the sum of the q-power of the real part (imaginary part) of the support for and the q-power of the real part (imaginary part) of the support against is limited by one; however, it is difficult to express the hesitant information. In this study, the conception of complex q-rung orthopair hesitant fuzzy set (Cq-ROHFS) by combining the Cq-ROFS and hesitant fuzzy set (HFS) is proposed, and its properties are discussed, obviously, Cq-ROHFS can reflect the uncertainties in structure and in detailed evaluations. Further, some distance measures (DMs) and cross-entropy measures (CEMs) are developed based on complex multiple fuzzy sets. Moreover, these proposed measures are utilized to solve a multi-criteria decision-making problem based on TOPSIS (technique for order preference by similarity to ideal solution) method. Then, the advantages and superiority of the proposed measures are explained by the experimental results and comparisons with some existing methods.

scholarly journals Q-Rung Probabilistic Dual Hesitant Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1574
Author(s):  
Li Li ◽  
Hegong Lei ◽  
Jun Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
High Efficiency ◽  
Distance Measure ◽  
Comparison Method ◽  
Hesitant Fuzzy Sets ◽  
Probabilistic Information ◽  
Fuzzy Madm ◽  
Multi Attribute Decision Making ◽  
Multiple Membership

The probabilistic dual hesitant fuzzy sets (PDHFSs), which are able to consider multiple membership and non-membership degrees as well as their probabilistic information, provide decision experts a flexible manner to evaluate attribute values in complicated realistic multi-attribute decision-making (MADM) situations. However, recently developed MADM approaches on the basis of PDHFSs still have a number of shortcomings in both evaluation information expression and attribute values integration. Hence, our aim is to evade these drawbacks by proposing a new decision-making method. To realize this purpose, first of all a new fuzzy information representation manner is introduced, called q-rung probabilistic dual hesitant fuzzy sets (q-RPDHFSs), by capturing the probability of each element in q-rung dual hesitant fuzzy sets. The most attractive character of q-RPDHFSs is that they give decision experts incomparable degree of freedom so that attribute values of each alternative can be appropriately depicted. To make the utilization of q-RPDHFSs more convenient, we continue to introduce basic operational rules, comparison method and distance measure of q-RPDHFSs. When considering to integrate attribute values in q-rung probabilistic dual hesitant fuzzy MADM problems, we propose a series of novel operators based on the power average and Muirhead mean. As displayed in the main text, the new operators exhibit good performance and high efficiency in information fusion process. At last, a new MADM method with q-RPDHFSs and its main steps are demonstrated in detail. Its performance in resolving practical decision-making situations is studied by examples analysis.

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