Interval-valued Fuzzy Research Articles

Separation Axioms of Interval-Valued Fuzzy Soft Topology via Quasi-Neighborhood Structure

In this study, we present the concept of the interval-valued fuzzy soft point and then introduce the notions of its neighborhood and quasi-neighborhood in interval-valued fuzzy soft topological spaces. Separation axioms in an interval-valued fuzzy soft topology, so-called q- T i for i = 0 , 1 , 2 , 3 , 4 , are introduced, and some of their basic properties are also studied.

Multiple attribute group decision‐making based on order‐α divergence and entropy measures under q‐rung orthopair fuzzy environment

The q-rung orthopair fuzzy set (qROPFS), proposed by Yager, is a more effective and proficient tool to represent uncertain or vague information in real-life situations. Divergence and entropy are two important measures, which have been extensively studied in different information environments, including fuzzy, intuitionistic fuzzy, interval-valued fuzzy, and Pythagorean fuzzy. In the present communication, we study the divergence and entropy measures under the q-rung orthopair fuzzy environment. First, the work defines two new order-α divergence measures for qROPFSs to quantify the information of discrimination between two qROPFSs. We also examine several mathematical properties associated with order-α qROPF divergence measures in detail. Second, the paper introduces two new parametric entropy functions called “order-α qROPF entropy measures” to measure the degree of fuzziness associated with a qROPFS. We show that the proposed order-α divergence and entropy measures include several existing divergence and entropy measures as their particular cases. Further, the paper develops a new decision-making approach to solve multiple attribute group decision-making problems under the qROPF environment where the information about the attribute weights is completely unknown or partially known. Finally, an example of selecting the best enterprise resource planning system is provided to illustrate the decision-making steps and effectiveness of the proposed approach.

On m-Polar Interval-valued Fuzzy Graph and its Application

In this paper, the concept of the -polar fuzzy graph (-PFG) and interval-valued fuzzy graph (IVFG) is integrated and introduced an unprecedented kind of fuzzy graph designated as -polar interval-valued fuzzy graph (-PIVFG). Complement of the -PIVFG is defined and the failure of this definition in some cases are highlighted. Various examples are cited and then redefined the notation of complement such that it applies to all -PIVFGs. The other algebraic properties such as isomorphism, weak isomorphism, co-weak isomorphism of the -PIVFG are investigated. Moreover, some basic results on the isomorphic property of -PIVFG are proved. Finally, an application of -PIVFG is explored. Abbreviations: The following abbreviations are employed in this study: FS: Fuzzy set; FG: Fuzzy graph; IVFS: Interval-valued fuzzy sets; IVFG: Interval-valued fuzzy graph; -PFS: -polar fuzzy sets; -PFG: -polar fuzzy graph; -PIVFS: -polar interval-valued fuzzy sets; -PIVFG: -polar interval-valued fuzzy graph.

Evaluation of Investment Opportunities With Interval-Valued Fuzzy Topsis Method

Abstract The purpose of this study is extended the TOPSIS method based on interval-valued fuzzy set in decision analysis. After the introduction of TOPSIS method by Hwang and Yoon in 1981, this method has been extensively used in decision-making, rankings also in optimal choice. Due to this fact that uncertainty in decision-making and linguistic variables has been caused to develop some new approaches based on fuzzy-logic theory. Indeed, it is difficult to achieve the numerical measures of the relative importance of attributes and the effects of alternatives on the attributes in some cases. In this paper to reduce the estimation error due to any uncertainty, a method has been developed based on interval-valued fuzzy set. In the suggested TOPSIS method, we use Shannon entropy for weighting the criteria and apply the Euclid distance to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s) can be selected in the decision-making process.

Computation of Support and Confidence for Interval-Valued Fuzzy Association Rules

The aim of this paper is to provide an algorithm for the computation of support and confidence of the association rules on interval-valued fuzzy sets. Each element of the interval-valued fuzzy set has a membership degree defined as an interval. In other words, the membership intervals may be interpreted as partial knowledge when the precise value is not known. The computations of the support and the confidence are discussed with respect to the three most common triangular norms (minimum, product and Łukasiewicz), which act as conjunction in support and confidence definitions.

APPLICATION OF INTERVAL VALUED FUZZY SET AND SOFT SET

Molodtsov was a father of soft set approach. We can’t easily settle the membership degree in some practical application. So it must be much better to describe interval-valued data instead of explaining membership degree. In this paper, we introduce the latest approach of the interval-valued fuzzy soft set by combining the interval-valued fuzzy set and soft set models. This approach successfully follows distributive, associative and DeMorgan’s laws as well. In the end, a decision problem is solved by this approach.

Interval Subsethood Measures with Respect to Uncertainty for the Interval-Valued Fuzzy Setting

In this paper, the problem of measuring the degree of subsethood in the interval-valued fuzzy setting is addressed. Taking into account the widths of the intervals, two types of interval subsethood measures are proposed. Additionally, their relation and main properties are studied. These developments are made both with respect to the regular partial order of intervals and with respect to admissible orders. Finally, some construction methods of the introduced interval subsethood measures with the use interval-valued aggregation functions are examined.

Edge Detection based in Interval-Valued Fuzzy Mathematical Morphology and Aggregation Functions K

Edge Detection based in Interval-Valued Fuzzy Mathematical Morphology and Aggregation Functions K

Interval Valued Fuzzy Soft Sets and Fuzzy Connectives

The Article, We Learning A Few Operations Of Interval Valued Fuzzy Soft Sets Of Connectives And Give Elementary Properties Of Interval Valued Fuzzy Soft Sets Of Principal Disjunctive Normal Form And Principal Conjunctive Normal Form. 2000 Ams Subject Classification: 03f55, 08a72, 20n25. Keywords: Interval Valued Fuzzy Subset, Interval Valued Fuzzy Soft Set, And Principal Conjunctive Normal Form And Principal Disjunctive Normal Form Interval Valued Fuzzy Soft Set ‘’ ‘’ Operator And ‘’ ’’ Operator.

Outsourcing modelling using a novel interval-valued fuzzy quantitative strategic planning matrix (QSPM) and multiple criteria decision-making (MCDMs)

Outsourcing drives companies to focus on: their capabilities, advantages of external resources, and decreasing overall operational costs. Selecting appropriate alliances, which are aligned with the company's strategies, establishes a situation through which the firms can enhance their technical capabilities and achieve new technologies. However, two critical issues in outsourcing modeling should be addressed: how to find strategic indicators for building successful alliances, and how to select these partners. Besides, as the imprecise and vague information (due to a lack of data) existing in the outsourcing models cannot be neglected, the application of fuzzy interval sets could efficiently address the complexity of these problems.To deal with these issues, this paper proposes a two-step interval-based framework for the problem. At the beginning, and for the first time, the novel integration of an interval valued fuzzy (IVF) version of strength-weakness-opportunity-threats (SWOT) technique and the quantitative strategic planning matrix (QSPM) with Gap analysis is designed to find the most effective strategies for the alliance evaluation, and to weight them. In the next step, four interval-valued version of multiple criteria decision-making methods (IVF-MCDMs) are implemented to evaluate the strategic partners.Finally, the results are aggregated with the help of the utility interval approach, and a sensitivity analysis is implemented to assess the robustness of the proposed methodology. To illustrate the efficiency of the proposed approach, a real partner selection problem at a holding car manufacturing factory in Iran is presented.

Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making

AbstractAs an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given, and an numerical example is provided to demonstrate that the developed approach is both valid and practical.

Improved Fuzzy Bayesian Network-Based Risk Analysis With Interval-Valued Fuzzy Sets and D–S Evidence Theory

A novel risk analysis approach is developed by merging interval-valued fuzzy sets (IVFSs), improved Dempster–Shafer (D–S) evidence theory, and fuzzy Bayesian networks (BNs), acting as a systematic decision support approach for safety insurance for the entire life cycle of a complex system under uncertainty. Aiming to alleviate the problem of insufficient and imprecise data collected from the complicated environment, the expert judgment in linguistic expressions is employed to describe the risk levels for all risk factors, which are represented by IVFSs using Gaussian membership function to fully consider such fuzziness and uncertainty. In regard to interval fusion and highly conflicting data, an improved combination rule based on the D–S evidence theory is developed. Then, fuzzy prior probability for each risk factor can be generated from fused intervals and fed into a fuzzy BN model for fuzzy-based Bayesian inference, including predictive, sensitivity, and diagnosis analysis. Furthermore, a case study is used to demonstrate the feasibility of the proposed risk analysis. A comparison of risk analysis based upon the hybrid improved D–S, classical D–S, and arithmetic average method is illustrated to show the outstanding performance of the developed approach in fusing multisource information with ubiquitous uncertainty and conflicts in an efficient manner, leading to more reliable risk evaluation. It is concluded that the proposed risk analysis provides a deep insight on risk control, especially for complex project environment, which enables to not only reduce the likelihood of failure ahead of time but also mitigate risk magnitudes to some degree after the occurrence of a failure.

On BL-Algebras and its Interval Counterpart

Interval Fuzzy Logic and Interval-valued Fuzzy Sets have been widely investigated. Some Fuzzy Logics were algebraically modelled by Peter Hájek as BL-algebras. What is the algebraic counterpart for the interval setting? It is known from literature that there is a incompatibility between some algebraic structures and its interval counterpart. This paper shows that such incompatibility is also present in the level of BL-algebras. Here we show both: (1) the impossiblity of match imprecision and the correctness of the underlying BLimplication and (2) some facts about the intervalization of BL-algebras.

A Preferential Interval-Valued Fuzzy C-Means Algorithm for Remotely Sensed Imagery Classification

Remotely sensed imagery classification have a large amount of uncertainty related to the intraclass heterogeneity and the interclass ambiguity of objects. Fuzzy set theory can address the uncertainty effectively, while interval-valued model can improve the separability of samples. Therefore, we propose a novel interval-valued fuzzy c-means algorithm, which integrates the interval-valued model and preferential adaptive method. It preferentially adjusts the interval width according to MSE (mean-square-error) and boundary factor for determining the optimal set of features for the data. In this paper, it is proved that the method can make the intraclass MSE and boundary factor always proportional to the separability of objects, so that it can dynamically adjust the interval-valued separability by controlling the interval width. Experimental data consisting of SPOT5 (10-m spatial resolution) satellite data for three case study areas in China are used to test this algorithm. Compared with other state-of-the-art fuzzy classification methods, our algorithm demonstrates the markedly improved overall accuracy and Kappa coefficients.

On Interval-Valued Fuzzy on Ideal Sets

Fuzzy sets, formalized by Zadeh in 1965, generalizes the classical idea of sets. The idea itself was generalized in 1975 when Zadeh introduced the interval-valued fuzzy sets. In this paper, we generalize further the above concepts by introducing interval-valued fuzzy on ideal sets, where an ideal is a nonempty collection of sets with a property describing the notion of smallness. We develop its basic concepts and properties and consider how one can create mappings of interval-valued fuzzy on ideal sets from mappings of ordinary sets. We then consider topology and continuity with respect to these sets.

A NEW ANALYTICAL METHODOLOGY TO HANDLE TIME-COST TRADE-OFF PROBLEM WITH CONSIDERING QUALITY LOSS COST UNDER INTERVAL-VALUED FUZZY UNCERTAINTY

This paper proposes a new framework in addressing time-cost trade-off problem (TCTP) under uncertainty. First critical path analysis is carried out based on developing a new interval-valued fuzzy (IVF)-program evaluation and review technique (PERT) approach. Then, non-conformance risks that influence on execution quality of activities are identified and evaluated based on a new approach that considers probability of risk along with impacts on time, cost, and performance. Then, a new mathematical model under IVF uncertainty is presented to decrease project total time while considering time, cost and quality loss cost that is determined in form of rework or modification cost. Finally, the approach categorizes the activities in three groups based on their level of criticality. Outcome of this methodology is a scheduling that addresses time, cost and quality trade-offs in addition to categorizing activities in different groups based on being on the critical path. Therefore, the project manager not only gets a scheduling based on the TCTP with considering quality loss cost but also has a knowledge of activities that require extra attentions. To show the steps of this methodology, an existing application from the literature is adopted and solved.

From Fuzzy Sets to Interval-Valued and Atanassov Intuitionistic Fuzzy Sets: A Unified View of Different Axiomatic Measures

This paper examines a broad collection of axiomatic definitions from various and diverse contexts within the domain of fuzzy sets (FS) to evaluate their respective extensions to the case of interval-valued fuzzy (IVF) sets and intuitionistic fuzzy (IF) sets from a purely formal point of view. We conclude that a large number of such extensions follow similar formal procedures. This fact allows us to formulate a general procedure that encompasses all the reviewed extensions as particular cases of it. The new general formulation allows us to identify three different procedures to derive the corresponding extension to the field of IVF or IF sets from a specific real-valued measure in the context of FSs. These three processes agglutinate a multitude of particular constructions found in the literature.

A Fuzzy ANP-Based GRA Approach to Evaluate ERP Packages

One of the major problems that most companies face with during the implementation of an ERP system is to determine the best satisfying ERP software based on their needs and expectations. Because an improperly selected ERP software might lead to time loss and increased costs, and in the long run, a loss of market share. Therefore, the ERP evaluation process for companies becomes to a vital point. On the other hand, evaluating ERP software alternatives under a set of criteria leads us to a multiple-criteria decision making (MCDM) problem, and needs to use proper MCDM methods. In the current literature, a number of the MCDM methods have been proposed to solve these kinds of problems, both of which are the analytic network process (ANP) of Saaty, and grey relational analysis (GRA) which has been widely used in solving MCDM selection problems in various fields. Moreover, in this article, the authors used the fuzzy extension of the ANP method to reflect the uncertainty and ambiguity of decision maker(s) into problem in order to reach more reliable solution. As the fuzzy ANP method was used to calculate the priority weights of the evaluation criteria, the GRA method with fuzzy interval-values was employed to rank a set of the possible ERP software alternatives. The proposed approach was also validated in a case study to show its applicability to potential readers and practitioners.

An extended multi-attribute group decision approach for selection of outsourcing services activities for information technology under risks

In recent years, selection of outsourcing services activities for information technology (IT) which are defined under some outsourcing projects is a challenge for companies under competitive and uncertain environments. To address the issue, assessment techniques via group decision-making could be provided to appropriately appraise the candidates regarding the incomplete information and existing complexity. This study proposes a new integrated group assessment approach based on interval-valued hesitant fuzzy (IVHF) environment to select the best outsourcing projects regarding risks and incomplete information. The proposed approach is established via some procedures to determine experts' weights, criteria weights and candidates' rankings. The interval-valued hesitant fuzzy-collective wisdom weighting (IVHF-CWW) method is presented to compute the weight of each expert/decision maker (DM). Moreover, the interval-valued hesitant fuzzy-preference weighting (IVHF-PW) technique is presented to determine weights of evaluation criteria. Furthermore, the IVHF-utility index approach is elaborated to rank the candidate outsourcing projects. Finally, a practical study is provided to check the feasibility and validity of the proposed interval-valued hesitant fuzzy-integrated group decision-making (IVHF-IGDM) approach.

Interval-Valued Fuzzy Cooperative Games Based on the Least Square Excess and Its Application to the Profit Allocation of the Road Freight Coalition

This paper is mainly committed to constructing a new model for solving interval-valued fuzzy cooperative games based on the least square excess. We propose the interval-valued least square excess solution according to the solution concept of the least square prenucleolus and the least square nucleolus for solving crisp cooperative games. In order to obtain the corresponding optimal analytical solution, one mathematic programming model is constructed. The least square excess solution can be used to determine plays’ payoffs directly. Considering the fuzziness and uncertainty existing in the process of the road freight coalition, we establish the interval-valued fuzzy utility function of the road freight coalition that can properly reflect the real situation in view of the green logistics. The illustratively calculated results show that the least square excess solution proposed in this paper is effectual and ascendant, and satisfied many important and useful properties of cooperative games, such as symmetry and uniqueness. As for the problems of interval-valued cooperative games, the model proposed in this paper can be applied appropriately to obtain the players’ interval-valued payoffs.