Intuitionistic fuzzy control of twin rotor multiple input multiple output systems

A note on direct product of complex intuitionistic fuzzy subfield

This paper presents the concepts of a complex intuitionistic fuzzy subfield (CIFSF) and the direct product of a complex intuitionistic fuzzy subfield which is generalized from the concept of a complex fuzzy subfield by adding the notion of intuitionistic fuzzy into a complex fuzzy subfield. The main contribution and originality of this research are adding the non-membership term to the definition of a complex fuzzy subfield that assigns for any element a complex-valued grade. We expand the complex fuzzy subfield and obtain a new structure called CIFSF. This new concept is innovative in that it may attain a wider range of values for both membership and non-membership functions where these functions are expanded to the unit disc in the complex plane. Furthermore, we discuss that the direct product of two CIFSFs is CIFSF, and some related properties are investigated. In addition, we present the definition of necessity and possibility operators on the direct product of CIFSF, and some associated theorems are given. Finally, we propose the level subsets of the direct product of two complex intuitionistic fuzzy subsets of a field and prove that the level subset of the direct product of two CIFSFs is a subfield and discuss some related results.

A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

This paper presents an optimization method to solve a multi-objective model of a bi-level linear programming problem with intuitionistic fuzzy coefficients. The idea is based on TOPSIS (technique for order preference by similarity to ideal solution) method. TOPSIS method is a multiple criteria method that identifies a satisfactory solution from a given set of alternatives based on the minimization of distance from an ideal point and maximization of distance from the nadir point simultaneously. A new model of multi-objective bi-level programming problem in an intuitionistic fuzzy environment has been considered. The problem is first reduced to a conventional multi-objective bi-level linear programming problem using accuracy function. Then the modified TOPSIS method is proposed to solve the problem at both the leader and the follower level where various linear/non-linear membership functions are used to represent the flexibility in the approach of decision-makers (DMs). The problem is solved hierarchically, i.e., first the problem at the leader level is solved and then the feasible region is extended by relaxing the decision variables controlled by the leader. The feasible region is extended to obtain a satisfactory solution for the DMs at both levels. Finally, the application of the proposed approach in the production planning of a company has been presented. An illustrative numerical example is also given to explain the methodology defined in this paper.

Solar energy plant project selection with AHP decision-making method based on hesitant fuzzy linguistic evaluation

Increased energy demand is expected to be met by reliable and continuous energy sources. Renewable energy which is obtained from nature and can continuously reload itself from natural sources is a new generation energy type. The sun, which is the main source of renewable energies and produces heat and electricity by direct and indirect methods, is an important renewable energy source. The installation of solar energy systems takes place under the basic technical, economic and political factors. Alternative solar energy plant projects are evaluated linguistically under the main criteria based on the knowledge and experience of the experts. Hesitant fuzzy linguistic terms are used to incorporate the uncertain and hesitant expressions into the decision-making process. The decision-making process that takes place with hesitant linguistic expressions in multiple sub-criteria is based on the AHP model. The inclusion of hesitant statements in the decision-making process with the AHP model enables more realistic choices among the alternatives. System technology (0.18), energy policy (0.15) and energy price change (0.13) appear as the most important factors in the pairwise comparison of the factors based on hesitant fuzzy linguistic evaluations. The results coincide with the need for high efficiency in solar energy systems, the importance of governmental supportive policies and the effects of price competition in the energy sector. Also, the closeness of the overall priority values of all projects (0.189, 0.23, 0.287, 0.135, 0.158) indicates that the decision makers take into account the effective factors.

Recommendation decision-making algorithm for sharing accommodation using probabilistic hesitant fuzzy sets and bipartite network projection

In recent years, with the uninterrupted development of sharing accommodation, it not only caters to the diversified accommodation of tourists, but also takes an active role in expanding employment and entrepreneurship channels, enhancing the income of urban and rural residents, and promoting the revitalization of rural areas. However, with the continuous expansion of the scale of sharing accommodation, it is fairly complicated for users to search appropriate services or information. The decision-making problems become more and more complicated. Hence, a probabilistic hesitant fuzzy recommendation decision-making algorithm based on bipartite network projection is proposed in this paper. First of all, combining the users’ decision-making information and the experts’ evaluation information, a bipartite graph connecting users and alternatives is established. Then, the satisfaction degree of probabilistic hesitant fuzzy element is defined. Besides, the recommended alternative is obtained by the allocation of resources. Finally, a numerical case of Airbnb users is given to illustrate the feasibility and effectiveness of the proposed method.