Within Multi-Criteria Decision Analysis (MCDA), the TOPSIS method and its fuzzy extensions, fuzzy TOPSIS (FTOPSIS) models, are widespread ones for solving multi-criteria decision problems. At the same time, FTOPSIS models, as a rule, are implemented based on approximate computations with the use of triangular and trapezoidal fuzzy numbers. This paper introduces a novel approach to fuzzy extension of TOPSIS with the use of fuzzy criteria values and fuzzy weight coefficients of the general type and implementing functions of fuzzy numbers based on standard fuzzy arithmetic and transformation methods. Within FTOPSIS, for ranking of fuzzy numbers/alternatives the concept of Fuzzy Multi-criteria Acceptability Analysis (FMAA) is implemented. The use of FMAA within Fuzzy MCDA(FMCDA) represents a systematical implementation of the concept of fuzzy decision analysis that "the decision taken in the fuzzy environment must be inherently fuzzy". FTOPSIS-FMAA model not only allows ranking the set of alternatives, but also provides the confidence measure for the rank obtained by this model. This approach also considers the overestimation problem, which arises within FMCDA and FTOPSIS-FMAA implementation. A case study on a multi-criteria housing development decision problem is introduced and explored by several FTOPSIS-FMAA models. Finally, a comparison of different FTOPSIS-FMAA models is implemented with the use of Monte Carlo simulation.