Interactive Multi-Attribute Decision-Making in Construction Land Reduction: An Intuitionistic Fuzzy Mahalanobis–Taguchi Approach

Covering-based generalized IF rough sets with applications to multi-attribute decision-making

Intuitionistic fuzzy values (IFVs), each of which consists of a membership degree, a non-membership degree, and a hesitancy degree, are a powerful tool to depict uncertain or fuzzy information. In many fields, such as decision making, cluster analysis, and information retrieval, etc., information aggregation is an essential process. Therefore, how to aggregate IFVs is an interesting and important research topic, which has received great attention from researchers and a lot of intuitionistic fuzzy aggregation techniques have been developed. This chapter offers a systematic introduction to the latest research results in intuitionistic fuzzy aggregation, the extended results in interval-valued intuitionistic fuzzy environments, and their applications in multi-attribute decision making.KeywordsIntuitionistic Fuzzy Values (IFVs)Interval-valued Intuitionistic Fuzzy Decision MatrixBonferroni MeanIntuitionistic Fuzzy Weighted Geometric (IFWG)Intuitionistic Fuzzy Sets (IFSs)These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Covering based intuitionistic fuzzy (IF) rough set is a generalization of granular computing and covering based rough sets. By combining covering based rough sets, IF sets and fuzzy rough sets, we introduce three classes of coverings based IF rough set models via IF$$\beta $$-neighborhoods and IF complementary $$\beta $$-neighborhood (IFC$$\beta $$-neighborhood). The corresponding axiomatic systems are investigated, respectively. In particular, the rough and precision degrees of covering based IF rough set models are discussed. The relationships among these types of coverings based IF rough set models and covering based IF rough set models proposed by Huang et al. (Knowl Based Syst 107:155–178, 2016). Based on the theoretical analysis for coverings based IF rough set models, we put forward intuitionistic fuzzy TOPSIS (IF-TOPSIS) methodology to multi-attribute decision-making (MADM) problem with the evaluation of IF information problem. An effective example is to illustrate the proposed methodology. Finally, we deal with MADM problem with the evaluation of fuzzy information based on CFRS models. By comparative analysis, we find that it is more effective to deal with MADM problem with the evaluation of IF information based on CIFRS models than the one with the evaluation of fuzzy information based on CFRS models.

Proposed new Hamming distance and entropy for interval-valued intuitionistic fuzzy sets. And then the two new measures, which are extended from the Hamming distance and entropy for intuitionistic fuzzy sets by using the continuous ordered weighted aggregation (COWA) operator, are applied in interval-valued intuitionistic fuzzy multi-attribute decision making (MADM) problems with attribute weights completely unknown. An example is illustrated to verify the effectiveness of the two measures. In fact, we can convert a MADM problem from interval-valued intuitionistic fuzzy environment to intuitionistic fuzzy environment first and then solve it by using the intuitionistic fuzzy MADM methods, which is a new strategy.

An intuitionistic fuzzy VIKOR (IF‐VIKOR) method is proposed based on a new distance measure considering the waver of intuitionistic fuzzy information. The method aggregates all individual decision‐makers’ assessment information based on intuitionistic fuzzy weighted averaging operator (IFWA), determines the weights of decision‐makers and attributes objectively using intuitionistic fuzzy entropy, calculates the group utility and individual regret by the new distance measure, and then reaches a compromise solution. It can be effectively applied to multiattribute decision‐making (MADM) problems where the weights of decision‐makers and attributes are completely unknown and the attribute values are intuitionistic fuzzy numbers (IFNs). The validity and stability of this method are verified by example analysis and sensitivity analysis, and its superiority is illustrated by the comparison with the existing method.

Imprecision and vagueness often occur in practical multi-attribute decision making (MADM) problems. Intuitionistic fuzzy (IF) sets are flexible to simulate these situations. The aim of this paper is to develop an effective method for solving MADM problems in which the attribute values are expressed with IF sets. Inspired by TOPSIS, we propose a new ranking function of IF sets, which takes into the amount and the reliability of an IF set. Hereby we develop a new MADM method. An example of the investment selection problem is examined to demonstrate applicability and feasibility of the proposed method. It is shown that the proposed method has some advantages over other methods.

In this paper, an intuitionistic fuzzy (IF) distance measure between two triangular intuitionistic fuzzy numbers (TIFNs) is developed. The metric properties of the proposed IF distance measures are also studied. Then, based on the IF distance, an extended TOPSIS is developed to solve multi-attribute decision making (MADM) problems with the ratings of alternatives on attributes of TIFNs. In this methodology, the IF distances between each alternative and the TIFN positive ideal-solution are calculated as well as the TIFN negative ideal-solution. Then the relative closeness degrees obtained of each alternative to the TIFN positive ideal solution are TIFNs. Based on the ranking methods of TIFNs the alternatives are ranked. A numerical example is examined to the validity and practicability of the method proposed in this paper.

Intuitionistic fuzzy geometric aggregation operators in the framework of Aczel-Alsina triangular norms and their application to multiple attribute decision making

Multiattribute decision making method based on generalized OWA operators with intuitionistic fuzzy sets

The aim of this article is further extending the linear programming techniques for multidimensional analysis of preference (LINMAP) to develop a new methodology for solving multiattribute decision making (MADM) problems under Atanassov's intuitionistic fuzzy (IF) environments. The LINMAP only can deal with MADM problems in crisp environments. However, fuzziness is inherent in decision data and decision making processes. In this methodology, Atanassov's IF sets are used to describe fuzziness in decision information and decision making processes by means of an Atanassov's IF decision matrix. A Euclidean distance is proposed to measure the difference between Atanassov's IF sets. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to an Atanassov's IF positive ideal solution (IFPIS) which is unknown a prior. The Atanassov's IFPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the Atanassov's IFPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this article can deal with MADM problems under not only Atanassov's IF environments but also both fuzzy and crisp environments.

Due to the uncertainty existing in real-world, intuitionistic fuzzy sets (IFSs) are used to model uncertain information in multi-attribute group decision making (MAGDM). The intuitionistic fuzzy MAGDM problems have gained great popularity recently. But, most of the current methods depend on various aggregation operators that may provide unreasonable collective intuitionistic fuzzy values of alternatives to be ranked. To solve such problem, a new method is developed based on evidence theory and IFSs. First, the mathematical relation between IFSs and evidence theory is analyzed, followed by the transformation from intuitionistic fuzzy evaluation information to basic belief assignment in evidence theory. Then, a new intuitionistic fuzzy weighted evidential (IFWE) average operator is introduced based on the operation of evidence discounting and evidence combination rule. We also develop a possibility-based ranking method for intuitionistic fuzzy values (IFVs) to obtain the linear ordering of IFVs. The proposed evidential model uses the IFWE average operator to aggregate the decision matrix and the attribute weight that is given by each decision maker, based on which each decision maker’s aggregated decision matrix can be obtained. Based on the decision matrices of all decision makers and the weights of the decision makers, the aggregated intuitionistic fuzzy value of each alternative can be obtained by the IFWE average operator. Finally, the preference order of all alternatives can be obtained by the possibility-based ranking method. Comparative analysis based on several application examples of MAGDM demonstrates that the proposed method can overcome the drawbacks of existing methods for MAGDM in intuitionistic fuzzy environments.

A reliable and data-based teaching quality evaluation is essential for the continuous improvement of higher-education systems. However, the inherent ambiguity of assessment indicators and the subjectivity of evaluators render traditional, crisp-value models insufficient. To address this challenge, we develop a novel intuitionistic fuzzy multi-attribute decision-making framework that integrates Yager triangular norms (t-norms) with the geometric Heronian mean. Specifically, we first introduce intuitionistic fuzzy operations based on Yager t-norms and Yager t-conorms and subsequently construct two aggregation operators: the intuitionistic fuzzy geometric Heronian mean operators and the intuitionistic fuzzy weighted geometric Heronian mean operators. The idempotency, monotonicity, and boundedness properties of these operators are formally proven. Next, the intuitionistic fuzzy weighted geometric Heronian mean operators are employed to develop an approach for multi-attribute decision-making in classroom teaching quality evaluation under intuitionistic fuzzy information. Moreover, an application case study of teaching quality evaluation in an intuitionistic fuzzy environment is presented to demonstrate the practicality and effectiveness of the proposed approach. Additionally, sensitivity and comparative analyses with other techniques are carried out to further confirm the coherence and superiority of the recommended approach. The research results clearly show that our proposed method is highly effective in accurately evaluating teaching quality and can serve as a valuable tool for educational institutions in enhancing their teaching quality management.

Aggregation of intuitionistic fuzzy information is a hot topic in Atanassov's intuitionistic fuzzy set theory, which has attracted much interest from researchers in recent years. In this paper, a series of new aggregation operators and weighted averaging operators are proposed for aggregating intuitionistic fuzzy information. First, some basic laws for operations on intuitionistic fuzzy values are presented together with their properties. Then, we propose intuitionistic fuzzy weighted arithmetic averaging operator and intuitionistic fuzzy weighted geometric averaging operator to aggregate intuitionistic fuzzy information. Inspired by the idea of ordered weighted averaging and hybrid weighted averaging, we further develop intuitionistic fuzzy ordered weighted arithmetic averaging operator, intuitionistic fuzzy ordered weighted geometric averaging operator, intuitionistic fuzzy hybrid weighted arithmetic averaging (IFHWAA) operator, and intuitionistic fuzzy hybrid weighted geometric averaging (IFHWGA) operator. It is proved that all proposed weighted averaging operators have the properties of idempotency, boundary, monotonicity, and commutativity. Finally, we propose new methods based on IFHWAA and IFHWGA operators, respectively, to solve multi-attribute group decision making under intuitionistic fuzzy environment. Some examples are applied to illustrate the performance of the proposed methods. The experimental results show the effectiveness and advantages of the developed method by comparing with the other methods.

The aim of this paper is to present a novel approach for deriving weights of the decision criteria or alternatives in multi-attribute decision making (MADM) under intuitionistic fuzzy (IF) environment. In order to tackle the uncertainty and imprecision of the practical situations, decision makers’ pair-wise comparison judgments are represented by intuitionistic fuzzy numbers (IFNs). The assessment of the priorities from these IF pair-wise comparison judgments is formulated as an IF decision making problem where goals are described in intuitionistic fuzzy sense. Then by resolving hesitancy via a parameter, IF goals are transformed into fuzzy goals. Finally, aggregation of fuzzy goals and application of the max - min principle lead us to a nonlinear optimization problem whose solution gives the desired crisp priorities. Unlike the other prioritization methods, the proposed approach generates crisp priorities from IF pair-wise comparison matrix. Thus, the proposed approach eliminates the additional r...

The n-intuitionistic polygonal fuzzy set (n-IPFS), combined by the intuitionistic fuzzy and polygonal fuzzy sets, is an extended form of the triangular intuitionistic fuzzy set (TIFS) and the trapezoidal intuitionistic fuzzy set (TrIFS). The aim of this paper is to develop some new aggregation operators for n-IPFSs and apply them to multi-attribute group decision making (MAGDM) problems. First, the operational properties and the score function of n-IPFSs are defined. Then, three kinds of n-intuitionistic polygonal fuzzy aggregation operators are investigated including n-intuitionistic polygonal fuzzy weighted averaging (n-IPFWA) operator, n-intuitionistic polygonal fuzzy ordered weighted averaging (n-IPFOWA) operator and n-intuitionistic polygonal fuzzy hybrid aggregation (n-IPFHA) operator. Finally, we propose an improved technique for order preference by similarity to an ideal solution (TOPSIS) approach with n-IPFSs and unknown attributes weights. The attributes weights are obtained by combining the entropy weights and the subjective weights, and the entropy weights are calculated based on the score function of n-IPFS. The spatial closeness reflected by the Hamming distance and the grey relationship with the positive/negative solution are both considered in getting the relative closeness degree to rank the alternatives. The example analysis of a location selection is given to verify the practicality and the effectiveness of the proposed approach in this paper.