In this work, we present definition of intuitionistic fuzzy parameterized (IFP) intuitionistic fuzzy soft set and its operations. Then we define IFP-aggregation operator to form IFP-intuitionistic fuzzy soft-decision-making method which allows constructing more efficient decision processes.
The superiority and inferiority ranking (SIR) method is a generation of the well-known PROMETHEE method, which can be more efficient to deal with multi-criterion decision making (MCDM) problem. Intuitionistic fuzzy sets (IFSs), as an important extension of fuzzy sets (IFs), include both membership functions and non-membership functions and can be used to, more precisely describe uncertain information. In real world, decision situations are usually under uncertain environment and involve multiple individuals who have their own points of view on handing of decision problems. In order to solve un…
In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough) equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions were generalized by Tripathy, Mitra and Ojha ([13]), who introduced the concepts of approximate (rough) equivalences of sets. Rough equivalences capture equality of sets at a higher level than rough equalities. More properties of these concepts were established in [14]. Combining the conditions for the two types of approximate equalities, two more approximate equaliti…
Research Center for Electronics and Information Technology(电子与信息技术研究中心);Valahia University(瓦拉几亚大学)
The paper presents an extension of Shannon fuzzy entropy for intuitionistic fuzzy one. Firstly, we presented a new formula for calculating the distance and similarity of intuitionistic fuzzy information. Then, we constructed measures for information features like score, certainty and uncertainty. Also, a new concept was introduced, namely escort fuzzy information. Then, using the escort fuzzy information, Shannon's formula for intuitionistic fuzzy information was obtained. It should be underlined that Shannon's entropy for intuitionistic fuzzy information verifies the four defining conditions …
Southwest Petroleum University(西南石油大学);Zhuhai College of Jilin University(吉林大学珠海学院);Shandong University of Finance and Economics(山东财经大学);City University of Hong Kong(香港城市大学);Shandong University(山东大学)
We prove that the space of intuitionistic fuzzy values (IFVs) with a linear order based on a score function and an accuracy function has the same algebraic structure as the one induced by a linear order based on a similarity function and an accuracy function. By introducing a new operator for IFVs via the linear order based on a score function and an accuracy function, we show that such an operator is a strong negation on IFVs. Moreover, we observe that the space of IFVs is a complete lattice and a Kleene algebra with the new operator. We also demonstrate that the topological space of IFVs wit…
Feasible strategies for conflict resolution within intuitionistic fuzzy preference-based conflict situations
School of Mathematics and Statistics, Changsha University of Science and Technology(长沙理工大学数学与统计学学院);Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology(湖南省工程数学建模与分析重点实验室,长沙理工大学);Department of Computer Science, University of Manitoba(曼尼托湾大学计算机科学系)
In this book we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic logics), plithogenic probability (as generalization of classical, imprecise, and neutrosophic probabilities), and plithogenic statistics (as generalization of classical, and neutrosophic statistics). Plithogenic Set is a set whose elements are characterized by one or more attributes, and each attribute may have many values. An attribute value v has a corresponding (fuzzy, …
Nanjing University(南京大学);University of Derby(德比大学)
Researchers are increasingly focusing on intelligent games as a hot research area.The article proposes an algorithm that combines the multi-attribute management and reinforcement learning methods, and that combined their effect on wargaming, it solves the problem of the agent's low rate of winning against specific rules and its inability to quickly converge during intelligent wargame training.At the same time, this paper studied a multi-attribute decision making and reinforcement learning algorithm in a wargame simulation environment, and obtained data on red and blue conflict.Calculate the we…
The Interval-valued intuitionistic fuzzy sets (IVIFSs) based on the intuitionistic fuzzy sets combines the classical decision method is in its research and application is attracting attention. After comparative analysis, there are multiple classical methods with IVIFSs information have been applied into many practical issues. In this paper, we extended the classical EDAS method based on cumulative prospect theory (CPT) considering the decision makers (DMs) psychological factor under IVIFSs. Taking the fuzzy and uncertain character of the IVIFSs and the psychological preference into considerati…
Indian Institute of Technology Roorkee(印度理工学院鲁尔基分校)
Data Envelopment Analysis (DEA) is a technique used to measure the efficiency of decision-making units (DMUs). In order to measure the efficiency of DMUs, the essential requirement is input-output data. Data is usually collected by humans, machines, or both. Due to human/machine errors, there are chances of having some missing values or inaccuracy, such as vagueness/uncertainty/hesitation in the collected data. In this situation, it will be difficult to measure the efficiencies of DMUs accurately. To overcome these shortcomings, a method is presented that can deal with missing values and inacc…
Southwest Petroleum University(西南石油大学);Zhuhai College of Jilin University(吉林大学珠海学院);Karadeniz Technical University(卡拉德尼兹技术大学);Shandong University of Finance and Economics(山东财经大学)
This study is inspired by those of Huang et al. (Soft Comput. 25, 2513--2520, 2021) and Wang et al. (Inf. Sci. 179, 3026--3040, 2009) in which some ranking techniques for interval-valued intuitionistic fuzzy numbers (IVIFNs) were introduced. In this study, we prove that the space of all IVIFNs with the relation in the method for comparing any two IVIFNs based on a score function and three types of entropy functions is a complete chain and obtain that this relation is an admissible order. Moreover, we demonstrate that IVIFNs are complete chains to the relation in the comparison method for IVIFN…
In this paper one presents new similarity, cardinality and entropy measures for bipolar fuzzy set and for its particular forms like intuitionistic, paraconsistent and fuzzy set. All these are constructed in the framework of multi-valued representations and are based on a penta-valued logic that uses the following logical values: true, false, unknown, contradictory and ambiguous. Also a new distance for bounded real interval was defined.
Graduate Technological Educational Institute of Western Greece(西希腊高等技术教育学院)
The present paper comes across the main steps that laid from Zadeh's fuzziness ana Atanassov's intuitionistic fuzzy sets to Smarandache's indeterminacy and to Molodstov's soft sets. Two hybrid methods for assessment and decision making respectively under fuzzy conditions are also presented through suitable examples that use soft sets and real intervals as tools. The decision making method improves an earlier method of Maji et al. Further, it is described how the concept of topological space, the most general category of mathematical spaces, can be extended to fuzzy structures and how to genera…
Tongji University(同济大学);Changsha University of Science and Technology(长沙理工大学)
Pythagorean fuzzy sets provide stronger ability than intuitionistic fuzzy sets to model uncertainty information and knowledge, but little effort has been paid to conflict analysis of Pythagorean fuzzy information systems. In this paper, we present three types of positive, central, and negative alliances with different thresholds, and employ examples to illustrate how to construct the positive, central, and negative alliances. Then we study conflict analysis of Pythagorean fuzzy information systems based on Bayesian minimum risk theory. Finally, we investigate group conflict analysis of Pythago…
This paper presents two variants of penta-valued representation for neutrosophic entropy. The first is an extension of Kaufmann's formula and the second is an extension of Kosko's formula. Based on the primary three-valued information represented by the degree of truth, degree of falsity and degree of neutrality there are built some penta-valued representations that better highlights some specific features of neutrosophic entropy. Thus, we highlight five features of neutrosophic uncertainty such as ambiguity, ignorance, contradiction, neutrality and saturation. These five features are suppleme…
School of Computing Sciences and Engineering, VIT University(VIT大学计算科学与工程学院)
Emergences of computers and information technological revolution made tremendous changes in the real world and provides a different dimension for the intelligent data analysis. Well formed fact, the information at right time and at right place deploy a better knowledge.However, the challenge arises when larger volume of inconsistent data is given for decision making and knowledge extraction. To handle such imprecise data certain mathematical tools of greater importance has developed by researches in recent past namely fuzzy set, intuitionistic fuzzy set, rough Set, formal concept analysis and …
A Matrix-based Distance of Pythagorean Fuzzy Set and its Application in Medical Diagnosis
Key Laboratory of High Confidence Software Technologies (Peking University)(高可信软件技术重点实验室(北京大学));School of Computer Science, Peking University(北京大学计算机学院);University of Macau(澳门大学)
Medical diagnosis process vary in the degree to which they attempt to deal with different complicating aspects of diagnosis such as relative importance of symptoms, varied symptom pattern and the relation between diseases them selves. Based on decision theory, in the past many mathematical models such as crisp set, probability distribution, fuzzy set, intuitionistic fuzzy set were developed to deal with complicating aspects of diagnosis. But, many such models are failed to include important aspects of the expert decisions. Therefore, an effort has been made to process inconsistencies in data b…