Abstract
Fuzzy set theory, extensively applied in abundant disciplines, has been recognized as a plausible tool in dealing with uncertain and vague information due to its prowess in mathematically manipulating the knowledge of imprecision. In fuzzy-data comparisons, exploring the general ranking measure that is capable of consistently differentiating the magnitude of fuzzy numbers has widely captivated academics’ attention. To date, numerous indices have been established; however, counterintuition, less discrimination, and/or inconsistency on their fuzzy-number rating outcomes have prohibited their comprehensive implementation. To ameliorate their manifested ranking weaknesses, this paper proposes a unified index that multiplies weighted-mean and weighted-area discriminatory components of a fuzzy number, respectively, called centroid value and attitude-incorporated left-and-right area. From theoretical proof of consistency property and comparative studies for triangular, triangular-and-trapezoidal mixed, and nonlinear fuzzy numbers, the unified index demonstrates conspicuous ranking gains in terms of intuition support, consistency, reliability, and computational simplicity capability. More importantly, the unified index possesses the consistency property for ranking fuzzy numbers and their images as well as for symmetric fuzzy numbers with an identical altitude which is a rather critical property for accurate matching and/or retrieval of information in the field of computer vision and image pattern recognition.
Highlights
It has been well recognized that uncertainty inevitably exists in several real-world phenomena due to the inherent errors or impreciseness of measurement tools, methods, and uncontrollable conditions [1, 2]
Numerous indices have been established; counterintuition, less discrimination, and/or inconsistency on their fuzzy-number rating outcomes have prohibited their comprehensive implementation. To ameliorate their manifested ranking weaknesses, this paper proposes a unified index that multiplies weighted-mean and weighted-area discriminatory components of a fuzzy number, respectively, called centroid value and attitude-incorporated left-and-right area
Since the inception of the fuzzy set theory, Soliman and Mantawy [5] showed that five major strongly connected branches have been developed, including fuzzy mathematics, fuzzy logic and artificial intelligence, fuzzy systems, uncertainty and information, and fuzzy decision-making. Their subbranches have been established; for example, fuzzy differential equations [6,7,8,9,10,11,12,13,14] and fuzzy integrodifferential equations [15,16,17,18,19,20,21,22] are of fuzzy mathematics while fuzzy-number ranking, the focus of this paper, is of fuzzy decision-making
Summary
It has been well recognized that uncertainty inevitably exists in several real-world phenomena due to the inherent errors or impreciseness of measurement tools, methods, and uncontrollable conditions [1, 2]. Based on its feasible mathematical capacity for representing the imprecise information in practice, we have observed many successful cases spreading in disparate disciplines, such as robot selection [23], supplier selection [24], logistics center allocation [25], facility location determination [26], choosing mining methods [27], manufacturing process monitoring [1, 2, 28,29,30,31], cutting force prediction [32], firm-environmental knowledge management [33, 34], green supply-chain operation [35], and weapon procurement decision [36] To find their best alternative, those decisive problems are evaluated under resource constraints and with to some extent linguistic preference of multiattribute, which is realized from users’ perspectives, as well as subjective quantification of multiple characteristics, which is assessed from decision-makers [2, 3, 37,38,39].
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