The new concept of fuzzy interval matrices has been introduced in this book for the first time.
The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem. Further, the authors have introduced in this book multiexpert models using these three new types of interval matrices. The new multi expert models dealt in this book are FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IBBAMs, nIBAMs, FAIMs, FAnIMS, etc. Illustrative examples are given so that the reader can follow these concepts easily. This book has three chapters. The first chapter is introductory in nature and makes the book a self-contained one. Chapter two introduces the concept of fuzzy interval matrices. Also the notion of fuzzy interval matrices, neutrosophic interval matrices and fuzzy neutrosophic interval matrices, can find applications to Markov chains and Leontief economic models. Chapter three gives the application of fuzzy interval matrices and neutrosophic interval matrices to real-world problems by constructing the models already mentioned. Further these models are mainly useful when the data is an unsupervised one and when one needs a multi-expert model. The new concept of fuzzy interval matrices and neutrosophic interval matrices will find their applications in engineering, medical, industrial, social and psychological problems. We have given a long list of references to help the interested reader.
In this paper we prove that Neutrosophic Set (NS) is an extension of Intuitionistic Fuzzy Set (IFS) no matter if the sum of single-valued neutrosophic components is < 1, or > 1, or = 1. For the case when the sum of components is 1 (as in IFS), after applying the neutrosophic aggregation operators one gets a different result from that of applying the intuitionistic fuzzy operators, since the intuitionistic fuzzy operators ignore the indeterminacy, while the neutrosophic aggregation operators take into consideration the indeterminacy at the same level as truth-membership and falsehood-nonmembers…
Interval valued bipolar fuzzy weighted neutrosophic set(IVBFWN-set) is a new generalization of fuzzy set, bipolar fuzzy set, neutrosophic set and bipolar neutrosophic set so that it can handle uncertain information more flexibly in the process of decision making. Therefore, in this paper, we propose concept of IVBFWN-set and its operations. Also we give the IVBFWN-set average operator and IVBFWN-set geometric operator to aggregate the IVBFWN-sets, which can be considered as the generalizations of some existing ones under fuzzy, neutrosophic environments and so on. Finally, a decision making al…
Multi-criteria decision making method based on similarity measures under single valued neutrosophic refined and interval neutrosophic refined environments
Analysis of Social Aspects of Migrant Labourers Living With HIV/AIDS Using Fuzzy Theory and Neutrosophic Cognitive Maps: With Special Reference to Rural Tamil Nadu in India
一般来说，任何现实世界的问题并不总是可解的，因为不仅存在一定比例的不确定性，而且存在一定比例的不确定性。使用模糊逻辑分析了不确定性的存在。在这本书中，不确定性的数量正在使用逻辑分析。这些模型大多使用矩阵的概念。矩阵有一定的局限性;当模型具有时间依赖性，并且同时研究任何两个专家的意见时，我们不能在每个阶段对两个专家的意见进行比较。双矩阵的新概念肯定会满足这些需求。双矩阵AB = A1 U A2，其中A1和A2是任意阶的不同矩阵。这本书介绍了双矩阵的概念，并研究了几个概念，如贝根值，贝根向量，特征双多项式，双变换，双算子和双对角化。在此基础上，我们引入并探讨了模糊双矩阵、模糊双矩阵、模糊模糊双矩阵等概念，这些概念将在模糊逻辑和模糊逻辑中得到应用。
In this paper we prove that the Single-Valued (and respectively Interval-Valued, as well as Subset-Valued) Score, Accuracy, and Certainty Functions determine a total order on the set of neutrosophic triplets (T, I, F). This total order is needed in the neutrosophic decision-making applications.
In this paper the notion of quasicoincidence of a fuzzy interval valued with an interval valued fuzzy set, which generalizes the concept of quasicoincidence of a fuzzy point in a fuzzy set is concentrated.
In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure, interior and neighbourhood are introduced here and established some important results.
A characterization of flat ideals in the unit interval with the canonical fuzzy order is obtained with the help of the ordinal sum decomposition of continuous t-norms. This characterization will be useful in the study of topological and domain theoretic properties of fuzzy orders.
The main aim of this paper is to introduced the operations "Union" and "Intersection," and four operators $O_1, O_2, O_3, O_4 $ on interval-valued hesitant fuzzy soft sets and discuss some of their properties.
This article is meant to give a lucid and widely accessible, self-contained account of a novel way of performing arithmetic operations on fuzzy intervals. Based on two formulae of generalized inversion (the first in close analogy to the inversion of cumulative distribution functions in probability and statistics, and subsequent re-inversion which in this form seems to be new in the literature) the technique could prove to be of some importance for the practical handling of fuzzy intervals whose characterizing functions are discontinuous and/or not strictly monotonic, e.g. piecewise constant. N…
In this paper, combined with the degradation and monotonicity of parameters of Hamacher operation and the advantages of the correlation between input parameters of Heronian operators, IVq-ROFHHMWA and IVq-ROFHHMGA operators, which are the fusion of Hamacher and Heronian, are proposed, and their properties are studied. Finally, a group decision-making method based on IVq-ROFHHMWA operator is proposed. The implementation and comparative analysis results show that the operator and group decision-making methods proposed in this paper are effective and feasible.
In this paper, it is proved that, for the truth value algebra of interval-valued fuzzy sets, the distributive laws do not imply the monotonicity condition for the set inclusion operation. Then, a lattice-ordered $t_{r}$-norm, which is not the convolution of $t$-norms on $[0, 1]$, is obtained. These results negatively answer two open problems posed by Walker and Walker in [15].
Rosenfeld defined a fuzzy subgroup of group $G$ as a fuzzy subset of $G$ with two special conditions attached\cite{Rosenfeld1971Fuzzysubgroups}. In this paper, we introduce the fuzzy $t$-norms and vague $t$-norms. The unit interval with a $t$-norm or a $t$-conorm is a special monoid, so we mainly talk about fuzzy subsets of monoids and vague monoids. Firstly, we generalize some properties of $t$-norm to fuzzy $t$-subnorm, so that we can analyze and classify the fuzzy $t$-norms. Further, we explore specific research on these properties of the vague $t$-norm. In addition, the concept of lattice …
The novelty of this paper is to construct the explicit combinatorial formula for the number of all distinct fuzzy matrices of finite order, which leads us to invent a new sequence. In order to achieve this new sequence, we analyze the behavioral study of equivalence classes on the set of all fuzzy matrices of a given order under a suitable natural equivalence relation. In addition this paper characterizes the properties of non-equivalent classes of fuzzy matrices of order n with elements having degrees of membership values anywhere in the closed unit interval [0,1]. Further, this paper also de…
