A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information

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

A Multi-criteria Picture Fuzzy Decision-making Model for Green Supplier Selection based on Fractional Programming

Due to the increasing complexity in green supplier selection, there would be some important issues for expressing inherent uncertainty or imprecision of decision makers’ cognitive information in decision making process. As an extension of intuitionistic fuzzy sets (IFSs) and neutrosophic sets (NSs), picture fuzzy sets (PFSs) can better model and represent the hesitancy and uncertainty of decision makers’ preference information. In this study, an attempt has been made to present a multi-criteria picture fuzzy decision-making model for green supplier selection based on fractional programming. In this approach, the ratings of alternatives and weights of criteria are represented by PFSs and IFSs, respectively. Based on the available information, some pairs of fractional programming models are derived from the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and the proposed biparametric picture fuzzy distance measure to determine the relative closeness coefficient intervals of green suppliers, which are aggregated for the criteria to generate the ranking order of all green suppliers by computing their optimal degrees of membership based on the ranking method of interval numbers. Finally, an example is conducted to validate the effectiveness of the proposed multi-criteria decision making (MCMD) method

Developing an integrated AHP and Intuitionistic FuzzyTOPSIS methodology

U ovom se istraživanju daje pregled analitičkog hijerarhijskog postupka (AHP) i intuicijskih FuzzyTOPSIS (IFT) metoda. Rad se bavi procjenom metodologije zasnovane na AHP-IFT gdje se nesigurnosti opisuju lingvističkim vrijednostima. Najprije se problem izbora dobavljača formulira primjenom AHP, a zatim se koristi za određivanje težina kriterija. Kasnije se IFT koristi za postizanje rangiranja među alternativama temeljenim na mišljenju donositelja odluka (DMs). Ovaj model omogućuje točnu i laku klasifikaciju svojstava dobavljača prema tome kako su rangirani u hibridnom modelu. Daje se numerički primjer kako bi se objasnio glavni dobiveni rezultat u radu.This research gives an overview of the Analytic Hierarchy Process (AHP) and Intuitionistic FuzzyTOPSIS (IFT) methods. This study deals with an evaluation methodology based on the AHP-IFT where the uncertainties are handled with linguistic values. First, the supplier selection problem is formulated using AHP and, then, it is used to determine the weights of the criteria. Later, IFT is used to obtain full- ranking among alternatives based on opinion of the Decision Makers (DMs). The present model provides an accurate and easy classification in supplier attributes by those that have been prioritized in the hybrid model. A numerical example is given to clarify the main developed result in this paper

Developing an integrated AHP and Intuitionistic FuzzyTOPSIS methodology

U ovom se istraživanju daje pregled analitičkog hijerarhijskog postupka (AHP) i intuicijskih FuzzyTOPSIS (IFT) metoda. Rad se bavi procjenom metodologije zasnovane na AHP-IFT gdje se nesigurnosti opisuju lingvističkim vrijednostima. Najprije se problem izbora dobavljača formulira primjenom AHP, a zatim se koristi za određivanje težina kriterija. Kasnije se IFT koristi za postizanje rangiranja među alternativama temeljenim na mišljenju donositelja odluka (DMs). Ovaj model omogućuje točnu i laku klasifikaciju svojstava dobavljača prema tome kako su rangirani u hibridnom modelu. Daje se numerički primjer kako bi se objasnio glavni dobiveni rezultat u radu.This research gives an overview of the Analytic Hierarchy Process (AHP) and Intuitionistic FuzzyTOPSIS (IFT) methods. This study deals with an evaluation methodology based on the AHP-IFT where the uncertainties are handled with linguistic values. First, the supplier selection problem is formulated using AHP and, then, it is used to determine the weights of the criteria. Later, IFT is used to obtain full- ranking among alternatives based on opinion of the Decision Makers (DMs). The present model provides an accurate and easy classification in supplier attributes by those that have been prioritized in the hybrid model. A numerical example is given to clarify the main developed result in this paper

Intuitionistic fuzzy-based TOPSIS method for multi-criterion optimization problem: a novel compromise methodology

The decision-making process is characterized by some doubt or hesitation due to the existence of uncertainty among some objectives or criteria. In this sense, it is quite difficult for decision maker(s) to reach the precise/exact solutions for these objectives. In this study, a novel approach based on integrating the technique for order preference by similarity to ideal solution (TOPSIS) with the intuitionistic fuzzy set (IFS), named TOPSIS-IFS, for solving a multi-criterion optimization problem (MCOP) is proposed. In this context, the TOPSIS-IFS operates with two phases to reach the best compromise solution (BCS). First, the TOPSIS approach aims to characterize the conflicting natures among objectives by reducing these objectives into only two objectives. Second, IFS is incorporated to obtain the solution model under the concept of indeterminacy degree by defining two membership functions for each objective (i.e., satisfaction degree, dissatisfaction degree). The IFS can provide an effective framework that reflects the reality contained in any decision-making process. The proposed TOPSIS-IFS approach is validated by carrying out an illustrative example. The obtained solution by the approach is superior to those existing in the literature. Also, the TOPSIS-IFS approach has been investigated through solving the multi-objective transportation problem (MOTP) as a practical problem. Furthermore, impacts of IFS parameters are analyzed based on Taguchi method to demonstrate their effects on the BCS. Finally, this integration depicts a new philosophy in the mathematical programming field due to its interesting principles

A complex proportional assessment method for group decision making in an interval-valued intuitionistic fuzzy environment

Multi-criteria decision making is an implicational field that concerns with selecting or designing the best scenarios among a finite set of scenarios based on a finite set of criteria. Different methods and techniques for handling this issue have been proposed. Complex proportional assessment is an analytical tool for solving multi-criteria decision making problems. Originally, the COPRAS method has been developed for decision making under a deterministic environment. Since uncertainty is an unavoidable property of decision making due to a lack of knowledge, this paper suggests an extended form of the COPRAS method used for group decision making problems in an uncertain environment where such uncertainty is captured through a generalized form of fuzzy sets - the so called interval valued intuitionistic fuzzy sets. An algorithmic scheme for the COPRAS-IVIF method has been introduced thus examining its application with reference to two numerical examples. It seems that the recommended framework of COPRAS-IVIF can be satisfactorily implemented in decision making problems under ambiguous and ill-defined conditions

Multiattribute Decision Making Based on Entropy under Interval-Valued Intuitionistic Fuzzy Environment

Multiattribute decision making (MADM) is one of the central problems in artificial intelligence, specifically in management fields. In most cases, this problem arises from uncertainty both in the data derived from the decision maker and the actions performed in the environment. Fuzzy set and high-order fuzzy sets were proven to be effective approaches in solving decision-making problems with uncertainty. Therefore, in this paper, we investigate the MADM problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy (IVIF) set (IVIFS). We first propose a new definition of IVIF entropy and some calculation methods for IVIF entropy. Furthermore, we propose an entropy-based decision-making method to solve IVIF MADM problems with completely unknown attribute weights. Particular emphasis is put on assessing the attribute weights based on IVIF entropy. Instead of the traditional methods, which use divergence among attributes or the probabilistic discrimination of attributes to obtain attribute weights, we utilize the IVIF entropy to assess the attribute weights based on the credibility of the decisionmaking matrix for solving the problem. Finally, a supplier selection example is given to demonstrate the feasibility and validity of the proposed MADM method

Group Decision Making Using Comparative Linguistic Expression Based on Hesitant Intuitionistic Fuzzy Sets

We introduce a method for aggregation of experts’ opinions given in the form of comparative linguistic expression. An algorithmic form of technique for order preference is proposed for group decision making. A simple example is given by using this method for the selection of the best alternative as well as ranking the alternatives from the best to the worst

An approach to multiple attribute group decision making with interval intuitionistic trapezoidal fuzzy information

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of interval intuitionistic trapezoidal fuzzy numbers. Firstly, some operational laws of interval intuitionistic trapezoidal fuzzy numbers are introduced. Then some new aggregation operators including interval intuitionistic trapezoidal fuzzy ordered weighted geometric (IITFOWG) operator and interval intuitionistic trapezoidal fuzzy hybrid geometric (IITFHG) operator are proposed and some desirable properties of these operators are studied, such as commutativity, idempotency and monotonicity. An IITFWG and IITFHG operators-based approach is developed to solve the MAGDM problems in which both the attribute weights and the expert weights take the form of real numbers and attribute values take the form of interval intuitionistic trapezoidal fuzzy numbers. Finally, some illustrative examples are given to verify the developed approach and to demonstrate its practicality and effectiveness