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Similarity measure is a very important topic in fuzzy set theory. Torra (2010) proposed the notion of hesitant fuzzy set(HFS), which is a generalization of the notion of Zadeh' fuzzy set. In this paper, some new similarity measures for HFSs are developed. Based on the proposed similarity measures, a method of multiple attribute decision making under hesitant fuzzy environment is also introduced. Additionally, a numerical example is given to illustrate the application of the proposed similarity measures of HFSs to decision-making.

In this paper, generalised intuitionistic fuzzy soft sets and relations on generalised intuitionistic fuzzy soft sets are defined and a few of their properties are studied. An application of generalised intuitionistic fuzzy soft sets in decision making with respect to degree of preference is investigated.

This thesis examines the use of fuzzy set theory and the analytic hierarchy process in decision making. It begins by reviewing the insight of psychologists, social scientists and computer scientists to the decision making process. The Operations Research-Systems Analysis approach is discussed followed by a presentation of the basis of fuzzy set theory and the analytic hierarchy process. Two applications of these methods are presented. The first uses fuzzy sets and a little of the analytic hierarchy process to solve an hypothetical decision problem for the commanding officer of a naval task force. The second applies the latter technique and estimated data to the problem of choosing the best alternative to provide quality air service to Mexico City. Originator supplied key words include: Decision Making, Fuzzy Sets, Analytical Hierarchy Process. (Author)

As a combination of the hesitant fuzzy set (HFS) and the single valued neutrosophic set (SVNS), the single valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real-life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership function and the falsity-hesitancy membership function, and encompass the fuzzy set (FS), intuitionistic fuzzy set (IFS), hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) and singlevalued neutrosophic set (SVNS). Correlation and correlation coefficient have been applied widely in many research domains and practical fields.

Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function.

In many areas, due to situational complexity, conceptual imprecision, or informational imperfection, management accounting is faced with a high degree of uncertainty or ambiguity. Many of these uncertainties spring from emotional and or lingual causes. Until the Fuzzy Set Theory (FST) was introduced, people learned how to model these uncertainties arising from the human mind and the environment. The present study explores the applied potentials of fuzzy sets and Genetic Algorithms (GA) in different areas of management accounting, especially logistic issues. Logistic issues in a dynamic business environment primarily involve allocating specific resources to several corresponding consumption destinations. Each resource supplies certain goods, whereas each destination demands certain quantities. In this type of issue, the goal is to identify the most economical transportation route that meets the demand without violating the supply constraints. This paper suggests using fuzzy sets to supply appropriate information regarding price, demand, and other variables. The suggestions include the calculation method of the shortest route with the least cost prices for the distribution cycle (network). Finally, as a solution for this complex problem, a GA in combination with a well-suited fuzzy function is recommended. 

This thesis examines the use of fuzzy set theory and the analytic hierarchy process in decision making. It begins by reviewing the insight of psychologists, social scientists and computer scientists to the decision making process. The Operations Research- Systems Analysis approach is discussed followed by a presentation of the basis of fuzzy set theory and the analytic hierarchy process. Two applications of these methods are presented. The first uses fuzzy sets and a little of the analytic hierarchy process to solve an hypothetical decision problem for the commanding officer of a naval task force. The second applies the latter technique and estimated data to the problem of choosing the best alternative to provide quality air service to Mexico City.

This thesis examines the use of fuzzy set theory and the analytic hierarchy process in decision making. It begins by reviewing the insight of psychologists, social scientists and computer scientists to the decision making process. The Operations Research- Systems Analysis approach is discussed followed by a presentation of the basis of fuzzy set theory and the analytic hierarchy process. Two applications of these methods are presented. The first uses fuzzy sets and a little of the analytic hierarchy process to solve an hypothetical decision problem for the commanding officer of a naval task force. The second applies the latter technique and estimated data to the problem of choosing the best alternative to provide quality air service to Mexico City.

The q-rung orthopair fuzzy set can represent a wide range of uncertainty in information. When combined with a soft set, the resulting notion of a q-rung orthopair fuzzy soft set (OFSSq ) is more effective in dealing with uncertainties as it allows for parameterization. The OFSSq is a parameterized family of q-rung orthopair fuzzy sets and a generalization of the Intuitionistic fuzzy soft set (IFSS), the Pythagorean fuzzy soft set (PFSS) and the Fermatean fuzzy soft set (FFSS). While entropy and similarity measures have been defined for these fuzzy set extensions, defining these measures for OFSSq provides generalized expressions that apply to all these special cases. This article proposes distinct expressions for entropy and similarity measures for OFSSq s. The proposed entropy measure aids in assessing uncertainty within an OFSSq , while the similarity measure identifies the degree of similarity between any two OFSSqs. This article showcases the use of the suggested entropy and similarity measures in decision making, highlighting their effectiveness. Both concepts of entropy and similarity will be applied to decision making problems related to Covid-19 pandemic, especially when some dubious inputs are present, and a quick decision must be made.

Distance measurement is an important technique for determining the similarity of two Picture Fuzzy Sets (PFSs). The article presents a novel idea of distance measure for PFSs, which is then applied to solve Multi-Criteria Decision-Making (MCDM) problems. By using the distance measure of the PFSs, the TOPSIS approach is applied to solve MCDM problems. The score function is employed to determine the best alternatives for both Picture Fuzzy Positive Ideal Solution (PFPIS) and Picture Fuzzy Negative Ideal Solutions (PFNIS). The options are ranked using the revised index technique and the relative closeness coefficient method. An illustrative numerical example is provided to demonstrate the feasibility and practicality of the proposed distance measure for PFSs.

Distance measurement is an important technique for determining the similarity of two Picture Fuzzy Sets (PFSs). The article presents a novel idea of distance measure for PFSs, which is then applied to solve Multi-Criteria Decision-Making (MCDM) problems. By using the distance measure of the PFSs, the TOPSIS approach is applied to solve MCDM problems. The score function is employed to determine the best alternatives for both Picture Fuzzy Positive Ideal Solution (PFPIS) and Picture Fuzzy Negative Ideal Solutions (PFNIS). The options are ranked using the revised index technique and the relative closeness coefficient method. An illustrative numerical example is provided to demonstrate the feasibility and practicality of the proposed distance measure for PFSs.

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In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define exdended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm to solve decision making problems by using bipolar fuzzy soft set.

In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define exdended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm to solve decision making problems by using bipolar fuzzy soft set.

The Dempster-Shafer theory of evidence is applied to a multiattribute decision making problem whereby the decision maker (DM) must compromise with available alternatives, none of which exactly satisfies his ideal. The decision mechanism is constrained by the uncertainty inherent in the determination of the relative importance of each attribute element and the classification of existing alternatives. The classification of alternatives is addressed through expert evaluation of the degree to which each element is contained in each available alternative. The relative importance of each attribute element is determined through pairwise comparisons of the elements by the decision maker and implementation of a ratio scale quantification method. Then the 'belief' and 'plausibility' that an alternative will satisfy the decision maker's ideal are calculated and combined to rank order the available alternatives. Application to the problem of selecting computer software is given.

In this article, we define some types of distances between two intuitionistic fuzzy soft (IFS) sets and proposed similarity measures of two IFS-sets. We then construct a decision method which is applied to a medical diagnosis problem that is based on similarity measures of IFS-sets. Finally we give two simple example to show the possibility of using this method for diagnosis of diseases which could be improved by incorporating clinical results and other competing diagnosis.

In this study, we first introduce the fuzzy sets, soft sets, fuzzy soft sets and their related properties. We then present the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) that is one of classical Multiple Attribute Decision Making (MADM) methods. We also present the Grey Relation Method. In the main part of this study, we extend the TOPSIS method on the fuzzy soft set theory to construct a decision making method to deal with problems that contain uncertainties. To make it we combine the TOPSIS and The Grey Relational Analysis (GRA) under fuzzy soft sets. We finally give an illustrative application for drug selection.

Uncertainty may be caused by the ambiguity in the terms used to describe a specific situation. It may also be caused by skepticism of rules used to describe a course of action or by missing and/or erroneous data. To deal with uncertainty, techniques other than classical logic need to be developed. Although, statistics may be the best tool available for handling likelihood, it is not always adequate for dealing with knowledge acquisition under uncertainty. Inadequacies caused by estimating probabilities in statistical processes can be alleviated through use of the Dempster-Shafer theory of evidence. Fuzzy set theory is another tool used to deal with uncertainty where ambiguous terms are present. Other methods include rough sets, the theory of endorsements and nonmonotonic logic. J. Grzymala-Busse has defined the concept of lower and upper approximation of a (crisp) set and has used that concept to extract rules from a set of examples. We will define the fuzzy analogs of lower and upper approximations and use these to obtain certain and possible rules from a set of examples where the data is fuzzy. Central to these concepts will be the idea of the degree to which a fuzzy set A is contained in another fuzzy set B, and the degree of intersection of a set A with set B. These concepts will also give meaning to the statement; A implies B. The two meanings will be: (1) if x is certainly in A then it is certainly in B, and (2) if x is possibly in A then it is possibly in B. Next, classification will be looked at and it will be shown that if a classification will be looked at and it will be shown that if a classification is well externally definable then it is well internally definable, and if it is poorly externally definable then it is poorly internally definable, thus generalizing a result of Grzymala-Busse. Finally, some ideas of how to define consensus and group options to form clusters of rules will be given.

Uncertainty may be caused by the ambiguity in the terms used to describe a specific situation. It may also be caused by skepticism of rules used to describe a course of action or by missing and/or erroneous data. To deal with uncertainty, techniques other than classical logic need to be developed. Although, statistics may be the best tool available for handling likelihood, it is not always adequate for dealing with knowledge acquisition under uncertainty. Inadequacies caused by estimating probabilities in statistical processes can be alleviated through use of the Dempster-Shafer theory of evidence. Fuzzy set theory is another tool used to deal with uncertainty where ambiguous terms are present. Other methods include rough sets, the theory of endorsements and nonmonotonic logic. J. Grzymala-Busse has defined the concept of lower and upper approximation of a (crisp) set and has used that concept to extract rules from a set of examples. We will define the fuzzy analogs of lower and upper approximations and use these to obtain certain and possible rules from a set of examples where the data is fuzzy. Central to these concepts will be the idea of the degree to which a fuzzy set A is contained in another fuzzy set B, and the degree of intersection of a set A with set B. These concepts will also give meaning to the statement; A implies B. The two meanings will be: (1) if x is certainly in A then it is certainly in B, and (2) if x is possibly in A then it is possibly in B. Next, classification will be looked at and it will be shown that if a classification will be looked at and it will be shown that if a classification is well externally definable then it is well internally definable, and if it is poorly externally definable then it is poorly internally definable, thus generalizing a result of Grzymala-Busse. Finally, some ideas of how to define consensus and group options to form clusters of rules will be given.