The VIKOR methodology stands out as an important multi-criteria decision-making technique. VIKOR stands for “VIekriterijumsko KOmpromisno Rangiranje”, a Serbian term for “multi-criteria optimization and compromise solution”. It has been adapted to sources of information with sundry formats. We contribute to that strand on literature with a design of a new multiple-attribute group decision-making method called the trapezoidal bipolar fuzzy VIKOR method. It consists of a suitable redesign of the VIKOR approach so that it can use information with bipolar configurations. Bipolar fuzzy sets (and numbers) establish a symmetrical trade-off between two judgmental constituents of human thinking. The agents acquire uncertain and vague information in the form of linguistic variables parameterized by trapezoidal bipolar fuzzy numbers. Trapezoidal bipolar fuzzy numbers are considered by decision-makers for assigning the preference information of alternatives with respect to different attributes. Our non-trivial adaptation necessitates several steps. The ranking function of bipolar fuzzy numbers is employed to make a simple decision matrix with real numbers as its entries. Shannon’s entropy concept is applied to evaluate the normalized weights for attributes that may be either partially or completely unknown to the decision-makers. The ordering of the alternatives is obtained by assorting the maximum group utility and the individual regret of the opponent in an ascending manner. For illustration, the proposed technique is applied to two group decision-making problems, namely, the selection of waste treatment methods and the site to plant a thermal power station. A comparison of this method with the trapezoidal bipolar fuzzy TOPSIS method is also presented.

In fuzzy set theory, t-norms and t-conorms are fundamental binary operators. Yager proposed respective parametric families of both t-norms and t-conorms. In this paper, we apply these operators for the analysis of Pythagorean fuzzy sets. For this purpose, we introduce six families of aggregation operators named Pythagorean fuzzy Yager weighted averaging aggregation, Pythagorean fuzzy Yager ordered weighted averaging aggregation, Pythagorean fuzzy Yager hybrid weighted averaging aggregation, Pythagorean fuzzy Yager weighted geometric aggregation, Pythagorean fuzzy Yager ordered weighted geometric aggregation and Pythagorean fuzzy Yager hybrid weighted geometric aggregation. These tools inherit the operational advantages of the Yager parametric families. They enable us to study two multi-attribute decision-making problems. Ultimately we can choose the best option by comparison of the aggregate outputs through score values. We show this procedure with two practical fully developed examples.

The preference ranking organization method for enrichment of evaluations (PROMETHEE) method considers a significant outranking class of multi-criteria decision analysis (MCDA), as it is easy to deal with its simple computations. In the PROMETHEE, different preference functions are used according to the type and nature of attributes or criteria that demonstrate the clearness and reliability of this method. This study provides a new version of the PROMETHEE method using bipolar fuzzy information, named the bipolar fuzzy PROMETHEE method. Bipolar fuzzy sets or numbers constitute an asymmetrical relationship between two judgmental factors of human reasoning. Vague and imprecise knowledge is characterized by bipolar fuzzy linguistic terms which are further represented in the form of trapezoidal bipolar fuzzy numbers. The trapezoidal bipolar fuzzy numbers are used by analysts to assign the preferences of alternatives on the basis of criteria. Further, a ranking function of bipolar fuzzy numbers is considered to access the crisp real preferences of alternatives. The entropy weighting information is employed to calculate the weights of attributes by considering the condition of normality. A numerical example such as the selection of green suppliers by using the bipolar fuzzy PROMETHEE is performed on the basis of the usual criterion preference function in order to explain the procedure of the proposed method. Comparable results are derived by using the combination of linear and level preference functions. The results obtained by using different types of preference functions are the same, representing the authenticity of the proposed bipolar fuzzy PROMETHEE method.

The core aim of this paper is to provide a new multiple-criteria decision making (MCDM) model, namely bipolar fuzzy ELimination and Choice Translating REality (ELECTRE) II method, by combining the bipolar fuzzy set with ELECTRE II technique. It can be used to solve the problems having bipolar uncertainty. The proposed method is established by defining the concept of bipolar fuzzy strong, median and weak concordance as well as discordance sets and indifferent set to define two types of outranking relations, namely strong outranking relation and weak outranking relation. The normalized weights of criteria, which may be partly or completely unknown for decision makers, are calculated by using an optimization technique, which is based on maximizing deviation method. A systematic iterative procedure is applied to strongly outrank as well as weakly outrank graphs to determine the ranking of favorable actions or alternatives or to choose the best possible solution. The implementation of the proposed method is presented by numerical examples such as selection of business location and to chose the best supplier. A comparative analysis of proposed ELECTRE II method is also presented with already existing multiple-attribute decision making methods, including Technique for the Order of Preference by Similarity to an Ideal Solution (TOPSIS) and ELECTRE I under bipolar fuzzy environment by solving the problem of business location.

The paradigm shift prompted by Zadeh’s fuzzy sets in 1965 did not end with the fuzzy model and logic. Extensions in various lines have produced e.g., intuitionistic fuzzy sets in 1983, complex fuzzy sets in 2002, or hesitant fuzzy sets in 2010. The researcher can avail himself of graphs of various types in order to represent concepts like networks with imprecise information, whether it is fuzzy, intuitionistic, or has more general characteristics. When the relationships in the network are symmetrical, and each member can be linked with groups of members, the natural concept for a representation is a hypergraph. In this paper we develop novel generalized hypergraphs in a wide fuzzy context, namely, complex intuitionistic fuzzy hypergraphs, complex Pythagorean fuzzy hypergraphs, and complex q-rung orthopair fuzzy hypergraphs. Further, we consider the transversals and minimal transversals of complex q-rung orthopair fuzzy hypergraphs. We present some algorithms to construct the minimal transversals and certain related concepts. As an application, we describe a collaboration network model through a complex q-rung orthopair fuzzy hypergraph. We use it to find the author having the most outstanding collaboration skills using score and choice values.

Complex Pythagorean fuzzy (CPF), a worthwhile generalization of Pythagorean fuzzy set, is a powerful tool to deal with two-dimensional or periodic information. In this paper, we develop two prioritized aggregation operators (AOs) under CPF environment, namely, complex Pythagorean fuzzy prioritized weighted averaging (CPFPWA) operator and complex Pythagorean fuzzy prioritized weighted geometric (CPFPWG) operator. We consider the prioritization relationship among criteria and decision makers (DMs) to make our result more accurate as in real decision making (DM) problems, the criteria and DMs have different priority level. Further, we discuss remarkable properties of our proposed AOs. Moreover, we promote the evolution of MCDM problem by investigating an algorithm in CPF environment with its flow chart. Finally, to check the superiority and validity of proposed operators, we compare the computed results with the different existing techniques.