An Extended LINMAP Method for Multi-Attribute Group Decision Making under Interval-Valued Intuitionistic Fuzzy Environment (original) (raw)
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Expert Systems with Applications, 2012
This article proposes a framework to handle multiattribute group decision making problems with incomplete pairwise comparison preference over decision alternatives where qualitative and quantitative attribute values are furnished as linguistic variables and crisp numbers, respectively. Attribute assessments are then converted to intervalvalued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in the evaluation process. Group consistency and inconsistency indices are introduced for incomplete pairwise comparison preference relations on alternatives provided by the decision-makers (DMs). By minimizing the group inconsistency index under certain constraints, an auxiliary linear programming model is developed to obtain unified attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS). Attribute weights are subsequently employed to calculate distances between alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method.
2008
Based on the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy numbers, and the information about attribute weights is partially known. A numerical example is used to illustrate the applicability of the proposed approach.
Fuzzy Optimization and Decision Making, 2011
The aim of this paper is to extend the VIKOR method for multiple attribute group decision making in interval-valued intuitionistic fuzzy environment, in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number, and the information about attribute weights is partially known, which is an important research field in decision science and operation research. First, we use the interval-valued intuitionistic fuzzy hybrid geometric operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. We use the different distances to calculate the particular measure of closeness of each alternative to the interval-valued intuitionistic positive-ideal solution. According to values of the particular measure, we rank the alternatives and then select the most
Multiple attribute group decision making using interval-valued intuitionistic fuzzy soft matrix
2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2014
A noticeable progress has been found in decision making problems since the introduction of soft set theory by Molodtsov in 1999. It is found that classical soft sets are not suitable to deal with imprecise parameters whereas fuzzy soft sets (FSS) are proved to be useful. Use of intuitionistic fuzzy soft sets (IFSS) is more effective in environment where arguments are presented using membership and nonmembership values. In this paper we propose an algorithmic approach for multiple attribute group decision making problems using interval-valued intuitionistic fuzzy soft matrix
Expert Systems with Applications, 2011
This article proposes an approach to handle multi-attribute decision making (MADM) problems under the interval-valued intuitionistic fuzzy environment, in which both assessments of alternatives on attributes (hereafter, referred to as attribute values) and attribute weights are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). The notion of relative closeness is extended to interval values to accommodate IVIFN decision data, and fractional programming models are developed based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to determine a relative closeness interval where attribute weights are independently determined for each alternative. By employing a series of optimization models, a quadratic program is established for obtaining a unified attribute weight vector, whereby the individual IVIFN attribute values are aggregated into relative closeness intervals to the ideal solution for final ranking. An illustrative supplier selection problem is employed to demonstrate how to apply the proposed procedure.
IEEE, 2021
The presented work is an extensive study of the existing non-linear programming (NLP) methods in an uncertain environment of an interval-valued intuitionistic fuzzy soft set (IVIFSS) for solving multi-attribute decision-making (MADM) problems. IVIFSS is an intriguing extension of a fuzzy set (FS) involving both interval-valued intuitionistic fuzzy set (IVIFS) (which considers interval-value of both membership and non-membership elements of an intuitionistic fuzzy set (IFS)) and soft set (SS) (which gives importance to each parameter in an alternative). A comprehensive study projects that the existing NLP method in accordance with the technique for order preference by similarity to ideal solution (TOPSIS) for solving interval-valued intuitionistic fuzzy soft multi-attribute decision-making (IVIFSMADM) problems (decision-making (DM) problems in which assessment of rating of each alternative, over each character is rendered by an IVIFSS) is posing some limitations due to some mathematical incorrect assumptions and hence incorporating ambiguous results in real-life applications. Henceforth, an attempt has been made to properly understand the root cause of the posed shortcoming and suggested a new NLP method for solving IVIFSMADM problems, and also to validate this proposed NLP method a real-life problem is solved successfully.
Applied Mathematical Modelling, 2011
TOPSIS Multiple attribute group decision making (MAGDM) Interval-valued intuitionistic fuzzy decision matrix Interval-valued intuitionistic fuzzy number (IVIFN) Interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator a b s t r a c t TOPSIS is one of the well-known methods for multiple attribute decision making (MADM). In this paper, we extend the TOPSIS method to solve multiple attribute group decision making (MAGDM) problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision-makers is presented as intervalvalued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFNs), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective intervalvalued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and construct the weighted collective interval-valued intuitionistic fuzzy decision matrix, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. Based on different distance definitions, we calculate the relative closeness of each alternative to the interval-valued intuitionistic positive-ideal solution and rank the alternatives according to the relative closeness to the interval-valued intuitionistic positive-ideal solution and select the most desirable one(s). Finally, an example is used to illustrate the applicability of the proposed approach.
Advancements in Multi-Criteria Decision Making Based on Interval-Valued Intuitionistic Fuzzy Set
2013
Multi-criteria decision-making (MCDM) problem is the process of finding the best option from all of the feasible alternatives where all the alternatives can be evaluated according to a number of criteria or attribute. Since human judgments including preferences are often vague and cannot estimate his preference with an exact numerical value. Multi-criteria decision-making problems usually consist of uncertain and imprecise data and information. To deal with vagueness/imprecision Atanassov‟s intuitionistic fuzzy set [1] has found to be highly useful and they are successfully applied to the field of multi criteria decision making problems. Later on, integrating interval valued fuzzy sets with IFSs; Atanassov introduced the concept of interval valued intuitionistic fuzzy sets (IVIFSs) [2]. As a generalization of an intuitionistic fuzzy set, it is more flexible for IVIFSs to deal with uncertain and fuzzy problems. There are many situations in multi attribute decision making where IVIFS ...
Applied Intelligence, 2017
Interval-valued intuitionistic fuzzy (IVIF) soft set is one of the useful extensions of the fuzzy soft set which efficiently deals with the uncertain data for the decisionmaking processes. In this paper, an attempt has been made to present a nonlinear-programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve multi-attribute decision-making problems. In this approach, both ratings of alternatives on attributes and weights of attributes are represented by IVIF sets. Based on the available information, NP models are constructed on the basis of the concepts of the relativecloseness coefficient and the weighted distance. Some NP models are further deduced to calculate relative-closeness of sets of alternatives which can be used to generate the ranking order of the alternatives. A real example is taken to demonstrate the applicability and validity of the proposed methodology.