A Fractional - spread defuzzification framework for n-tuple fuzzy numbers with application to nonlinear optimization

When decision variables exhibit asymmetric and multiscale uncertainty, ranking fuzzy numbers continues to be a major difficulty in nonlinear optimization. Conventional defuzzification methods, such as centroid-based and exponential spread-sensitive models, frequently depend on single-parameter attenuation processes that might not fully capture nonlocal dispersion effects and heavy-tail behavior. We present a generalized Fractional-Spread Defuzzification (FSD) framework for arbitrary n-tuple fuzzy numbers in this paper. The suggested operator uses a fractional-order attenuation kernel controlled by two parameters that jointly control deviation penalization and dispersion sensitivity in a multiscale fashion. Essential axiomatic properties such as boundedness, normalization, translation invariance, continuity, and stability under discretization refinement are satisfied by the resulting ranking function, which forms a convex aggregation of tuple components. The mean-dominant and core - dominant ranking regimes interpolate smoothly, according to a thorough parameter-phase study. The framework’s analytical tractability and adjustable risk sensitivity are demonstrated by embedding it within a nonlinear quadratic programming model with fully fuzzy coefficients. The FSD operator produces stable and structurally sound optimization results under various dispersion settings, according to numerical results. Thus, a versatile and theoretically sound extension of spreadsensitive defuzzification for nonlinear fuzzy optimization is established by the suggested methodology.