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The objective of this paper is to develop Pythagorean fuzzy (PF) multi‐objective optimization by ratio analysis (PF‐MOORA) plus full MULTIplicative form (PF‐MULTIMOORA) method for solving multicriteria decision making (MCDM) problems with completely unknown information of criteria weights. In the model formulation process, a new distance measure is defined to quantify the difference between PF sets by combining Hamming distance and Hausdorff metric. This distance measure is, subsequently, implemented in entropy weight model for determining unknown weights of criteria, and also in reference point approach for obtaining preference indices of alternatives. To overcome the deficiencies occurred in existing MULTIMOORA method, like multiple comparisons, circular reasoning, and so on, an aggregation‐based approach is recommended in the proposed PF‐MULTIMOORA. To demonstrate the feasibility and practicality of the proposed method, an example concerning strategy prioritization of a tiles manufacturing company is presented. In the strategy evaluation process, at first, the judgement values provided by the decision maker are expressed in linguistic terms, and then those are converted into PF numbers through a PF weighting scale. The sensitivity of the proposed model is validated by changing of weights of criteria which impact on the ranks of the strategies. To show robustness of the developed method, the result attained by applying PF‐MULTIMOORA is compared with existing techniques, not only in crisp and fuzzy quantitative strategic planning matrix context, but also using four other MCDM methods, namely, modified PF‐MOORA, as a particular case of the proposed PF‐MULTIMOORA technique, PF weighted sum, PF‐TOPSIS and PF‐VIKOR. [ABSTRACT FROM AUTHOR]

The concept of distance between Pythagorean fuzzy sets (PFSs) has been proven to be relevant in the applications of PFSs as seen in the literature. The main purpose of this paper is to show that Zhang and Xu's distance measure between PFSs fails the conditions of distance measure; hence, it is not an appropriate distance measure for PFSs. Some numerical examples are used to validate this stance. In order to remedy this shortcoming, Zhang and Xu's distance measure for PFSs is normalised/modified to cater for the limitation by employing the technique used to normalise both Hamming and Euclidean distances between intuitionistic fuzzy sets by Szmidt and Kacprzyk. The modified Zhang and Xu's distance measure for PFSs satisfies the conditions of the axiomatic definition of distance measure for PFSs; hence, it is an appropriate/reliable distance measure for PFSs. Finally, the modified Zhang and Xu's distance measure for PFSs is applied to pattern recognition problems of classification of building materials and mineral fields. [ABSTRACT FROM AUTHOR]

It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their drawbacks and pursue more accuracy and effectiveness, in this paper, we propose a new inclusion relation of IFSs and a new definition called strict distance measure. Based on this new relation, an analysis is given to point out that the common shortcoming of Hamming distance measure and Euclidean distance measure is the mishandling of hesitancy degree. Therefore, the role of hesitancy degree in distance measure is studied deeply and then three strict distance measures are put forward to overcome the above shortcoming. In addition, a novel definition called the characteristic function of distance measure is defined to describe the character of strict distance measure. On this basis, a theorem is presented to illustrate the inevitability of the occurrence of unrecognized result in pattern recognition problems in some special cases. This theorem also shows that the problem cannot be entirely attributed to distance measures. In view of this condition, we provide an appropriate solution. Compared with other existing distance measures in some examples, the superiorities of our improved distance measures are demonstrated to be more effective and more significant. [ABSTRACT FROM AUTHOR]

A Pythagorean fuzzy soft set is a parameterized family of Pythagorean fuzzy sets and a generalization of intuitionistic fuzzy soft sets. In this paper, the notions of entropy and distance measures are defined for the Pythagorean fuzzy soft sets (PFSSs). Since, the already existing techniques for finding entropy and distance measures are not working for PFSSs, it is necessary to introduce these techniques in the contest of PFSSs. This work proposes a characterization of the Pythagorean fuzzy soft entropy. Also, the expressions for the standard distance measures like Hamming distance and Euclidean distance are obtained. Further, the applications of PFSSs in decision making problem and pattern recognition problem are discussed. Finally, comparative studies with other existing equations are also carried out. [ABSTRACT FROM AUTHOR]

In this paper, a new version of distance measure for hesitant fuzzy linguistic term sets is developed. The new version of distance measure provides an objective way to handle the diverse dimensions of two HFLTSs, i.e., without shortening the HFLTS to be a linguistic interval or extending the shorter one by adding linguistic terms. The Hamming distance, the Euclidean distance and the corresponding forms are put forward. By the relationship between the distance measure and the similarity measure, some parallel similarity measures are also investigated. As applications of the proposed measures, the issues of pattern recognition, clustering analysis and multi-criteria decision making are considered. [ABSTRACT FROM AUTHOR]

This paper proposes a generalized distance measure and its similarity measures between single valued neutrosophic multisets (SVNMs). Then, the similarity measures are applied to a medical diagnosis problem with incomplete, indeterminate and inconsistent information. This diagnosis method can deal with the diagnosis problem with indeterminate and inconsistent information which cannot be handled by the diagnosis method based on intuitionistic fuzzy multisets (IFMs). [ABSTRACT FROM AUTHOR]

Interval neutrosophic fuzzy decision making is an important part of decision making under uncertainty, which is based on preference order. In this study, a new multi-valued interval neutrosophic fuzzy multiple attribute decision making method has been developed by integrating the DEMATEL (decision making trial and evaluation laboratory) method and the TOPSIS (the technique for order preference by similarity to an ideal solution) method. Evaluation values are given in the form of multi-valued interval neutrosophic fuzzy values. By using DEMATEL, dependencies among attributes can be modeled, and attribute weights are determined. The normalized Euclidean distance and the normalized Hamming distance between multi-valued interval neutrosophic fuzzy values are defined. Alternatives are ranked by using the TOPSIS method based on the distance measures. The truck selection problem in the logistics industry is presented to illustrate the feasibility and practical advantages of the proposed method. Some comparisons of the new method with other methods are also made. [ABSTRACT FROM AUTHOR]