Abstract—Fighter aircraft selection is one of the most critical strategies for defense multiple criteria decision-making analysis to increase the decisive power of air defense and its superior power in the defense strategy. Vague set theory is an adequate approach for modeling vagueness, uncertainty, and imprecision in decision- making problems. This study integrates vague set theory and the technique for order of preference by similarity to ideal solution (TOPSIS) to support fighter aircraft selection. The proposed method is applied in the selection of fighter aircraft for the Air Force. In the proposed approach, the ratings of alternatives and the importance weights of criteria for fighter aircraft selection are represented by the vague set theory. Finally, an illustrative example for fighter aircraft selection is given to demonstrate the applicability and effectiveness of the proposed approach. The fighter aircraft candidates were selected under six criteria including costability, payloadability, maneuverability, speedability, stealthility, and survivability. Analysis results show that the best fighter aircraft is selected with the highest closeness coefficient value. The proposed method can also be applied to solve other multiple criteria decision analysis problems. Keywords—fighter aircraft selection, vague set theory, fuzzy set theory, neutrosophic set theory, multiple criteria decision making analysis, MCDMA, TOPSIS. I. INTRODUCTION ULTIPLE criteria decision making analysis (MCDMA) is an established branch of decision making theory[1-57]. MCDMA is a branch of a general class of operations research models that deal with decision problems in the presence of a set of often conflicting decision criteria. The MCDMA approach requires choosing among decision alternatives defined according to their characteristics. MCDMA problems are assumed to have a predetermined, limited number of decision alternatives. Thus, solving an MCDMA problem involves sorting, ranking, and selection processes. Therefore, multiple criteria decision-making problem is a type of problem in which all alternatives in the selection set can be evaluated according to a set of evaluation criteria. An MCDMA problem can be briefly expressed in matrix format as   1 ,..., ,1 I a a a i I =   are possible alternatives that decision makers should choose,   1 ,..., ,1 j g g g j J =   are the criteria by which alternative performance is measured, ij x is the rating of alternative i a relative to the j g criterion, and   1 ,..., ,1 j j J    =   , j  is the weight of the j g criterion. C. Ardil is with the National Aviation Academy, Baku, Azerbaijan. https://orcid.org/0000-0003-2457-7261 MCDMA approaches can be generally viewed as alternative methods for combining information from a problem's decision matrix with additional information from the decision-maker to determine a final ranking or selection among alternatives. Apart from the information contained in the decision matrix, all but the simplest MCDMA techniques require additional information from the decision-maker to arrive at a final ranking or selection. MCDMA problems and the evaluation processes often involve subjective evaluations and result in qualitatively imprecise data. Mathematical, engineering or management decisions are often made through available data and information, which is often vague, imprecise, and uncertain in nature. The decision-making process in engineering schemes, developed during the concept design phase is one of these typical situations, which often needs some method to deal with uncertain data and information that is difficult to define. During the design phase, designers often offer many alternatives. However, the subjective characteristics of the alternatives are often uncertain and need to be evaluated with insufficient knowledge and judgment of the decision maker. In ordinary set theory, the values of elements in a set are only two possibilities: present or absent in the set. The ordinary set theory cannot handle ambiguity and uncertainty. Fuzzy sets [58-60], intuitionistic sets [61-62], vague sets [63- 70], and neutrosophic sets [71-73] are considered generalizations of ordinary set theory to treat vagueness and uncertainty. A sentence is vague if and only if the sentence is neither absolutely true nor absolutely false. Fuzzy logic, is a form of multiple-valued logic which deals with imprecise information as a way of processing data by allowing partial set membership rather than definite set membership. Fuzzy logic is a computational approach based on degrees of truth rather than the usual true or false (1 or 0) Boolean logic. In fuzzy logic, the value (degrees) for linguistic variables can be between 0 and 1. When linguistic variables are used, these degrees can be handled with special functions called membership functions. Fuzzy logic represents the degrees of truth. In fuzzy set theory, a single membership value is assigned to each x ∈ U element in the universe of discourse. The single membership value contains both the evidence for and against x [53]. It cannot deal with two evidences individually, or even at the same duration. To solve this problem, the concept of vague set was introduced [53], and it allows interval-based membership function over point-based membership function. It is a further generalization of the fuzzy set theory. Vague set theory Vague Multiple Criteria Decision Making Analysis Method for Fighter Aircraft Selection C. Ardil M World Academy of Science, Engineering and Technology International Journal of Aerospace and Mechanical Engineering Vol:16, No:5, 2022 133 International Scholarly and Scientific Research & Innovation 16(5) 2022 ISNI:0000000091950263 Open Science Index, Aerospace and Mechanical Engineering Vol:16, No:5, 2022 publications.waset.org/10012555/pdf