In this Chapter, we imagine a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view.

Multiple criteria decision making

All the extensions of ordinary fuzzy sets with three dimensional membership functions such as intuitionistic fuzzy sets (IFS), intuitionistic fuzzy sets of second type (IFS2), and neutrosophic fuzzy sets (NFS) aim at defining the judgments of decision makers/ experts with a more detailed description. Introduction of generalized three dimensional spherical fuzzy sets (SFS) including some essential differences from the other fuzzy sets is presented in this paper. The new type of fuzzy sets is based on the spherical fuzzy distances which have been already defined in the literature. Arithmetic operations involving addition, subtraction and multiplication are presented together with their proofs. Aggregation operators, score and accuracy functions are developed. The multi-criteria decision making method TOPSIS is extended to spherical fuzzy TOPSIS and an illustrative example is presented. Additionally, a comparative analysis with intuitionistic fuzzy TOPSIS (IF-TOPSIS) is given.

Spherical fuzzy sets and spherical fuzzy TOPSIS method

Survey on fuzzy TOPSIS state-of-the-art between 2007 and 2017

Information fusion for intuitionistic fuzzy decision making

This study surveys the ordered weighted averaging OWA operator literature using a citation network analysis. The main goals are the historical reconstruction of scientific development of the OWA field, the identification of the dominant direction of knowledge accumulation that emerged since the publication of the first OWA paper, and to discover the most active lines of research. The results suggest, as expected, that Yager's paperIEEE Trans. Systems Man Cybernet, 181, 183-190, 1988 is the most influential paper and the starting point of all other research using OWA. Starting from his contribution, other lines of research developed and we describe them.

/pdf/ordered-weighted-averaging-operators-1988-2014-a-citation-kwxqol5m5y.pdf

Ordered Weighted Averaging Operators 1988-2014: A Citation-Based Literature Survey

This paper investigates the dynamic intuitionistic fuzzy multi-attribute group decision making (DIF-MAGDM) problems, in which all the attribute values provided by multiple decision makers (DMs) at different periods take the form of intuitionistic fuzzy numbers (IFNs), and develops an interactive method to solve the DIF-MAGDM problems. The developed method first aggregates the individual intuitionistic fuzzy decision matrices at different periods into an individual collective intuitionistic fuzzy decision matrix for each decision maker by using the dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator, and then employs intuitionistic fuzzy TOPSIS method to calculate the individual relative closeness coefficient of each alternative for each decision maker and obtain the individual ranking of alternatives. After doing so, the method utilizes the hybrid weighted averaging (HWA) operator to aggregate all the individual relative closeness coefficients into the collective relative closeness coefficient of each alternative and obtain the aggregate ranking of alternatives, by which the optimal alternative can be selected. In addition, the spearman correlation coefficient for both the aggregate ranking and individual ranking of alternatives is calculated to measure the consensus level of the group preferences. Finally, a numerical example is used to illustrate the developed method.

An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making

With respect to multi-attribute group decision making (MAGDM) problems in which both the attribute weights and the decision makers (DMs) weights take the form of real numbers, attribute values provided by the DMs take the form of intuitionistic fuzzy numbers, a new group decision making method is developed. Some operational laws, score function and accuracy function of intuitionistic fuzzy numbers are introduced at first. Then a new aggregation operator called induced generalized intuitionistic fuzzy ordered weighted averaging (IG-IFOWA) operator is proposed, which extend the induced generalized ordered weighted averaging (IGOWA) operator introduced by Merigo and Gil-Lafuente [Merigo, J. M., & Gil-Lafuente, A. M. (2009). The induced generalized OWA operator. Information Sciences, 179, 729-741] to accommodate the environment in which the given arguments are intuitionistic fuzzy sets that are characterized by a membership function and a non-membership function. Some desirable properties of the IG-IFOWA operator are studied, such as commutativity, idempotency, monotonicity and boundary. And then, an approach based on the IG-IFOWA and IFWA (intuitionistic fuzzy weighted averaging) operators is developed to solve MAGDM problems with intuitionistic fuzzy information. Finally, a numerical example is used to illustrate the developed approach.

Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making

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An interactive method for dynamic intuitionistic fuzzy multi-attribute group decision making

Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making