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Fuzzy addition is one of the operations widely used in the application of fuzzy systems. The analytical and closed form expressions of the fuzzy additions of the generalized fuzzy numbers and the interval type 2 fuzzy numbers (IT2FS) are developed. The generalized fuzzy numbers is a non-flat and subnormal fuzzy number with different left and right shape functions. Classical fuzzy operations based on the minimum t-norm could lead to uncontrollable fuzziness. Fuzzy addition based on generalized t-norm can better control ambiguity. In order to control the ambiguity of fuzzy addition, this paper is to develop a general type 1 fuzzy set and interval type 2 fuzzy set (IT2FS) additions based on t-norm. The closed forms of the generalized IT2FS additions based on some popular t-norms are formulated. The specific analytical and closed form expressions based on Archimedean t-norms: e.g. drastic, Łukasiewicz, product and the families of Schweizer-Sklar and Yager t-norms are derived. The IT2FS are widely used to characterize the natural words, e.g. the decision making linguistic judgments, the fuzzy real time control systems with linguistic rules. Furthermore, based on the analytical T1FS additions results, the application to the linguistic multiple criteria decision making aggregation of the IT2FS additions based on t-norms is introduced. A comparative MCDM numerical example is demonstrated for the verification of the developed closed form expressions. [ABSTRACT FROM AUTHOR]

This paper develops an integrated methodology for multiple criteria and multiple experts decision making problems using type 2 fuzzy sets (T2FS) as the linguistic judgments. The experts or decision maker's opinions are in linguistics forms. The proposed approach is the extension of the analytic hierarchy process (AHP) method for multiple experts. The pairwise or relative comparisons of decision linguistic judgments are characterized by interval type 2 fuzzy sets (IT2FS). The integrated methodology consists of the following stages: 1. Construct IT2FS pairwise comparison matrix (PCM), 2. Elicit IT2FS weights and rates, 3. Normalize the IT2FS weights and rates, 4. Synthesize the IT2FS weights and rates, 5. Calculate the global IT2FS rates, 6. Determine the final decision priority. At the outset of the decision making the IT2FS PCM for a set of criteria is created. The quadratic programming models are constructed to elicit the absolute IT2FS weights of the criteria in the sense of minimizing the least squares logarithmic regression functions. A normalization procedure is introduced for the IT2FS vector to obtain the well-defined and normalized IT2FS weights. Two approaches, the linear programming model and the IT2 fuzzy weighted average (FWA), are developed to synthesize and aggregate the local rates and weights. Thus, the overall global IT2FS rates for the alternatives are obtained. The final decision then can be concluded by the priority of the overall IT2FS rates of the alternatives. The proposed approach is applied to New Product Development (NPD) project screening. NPD is largely uncertain, because of competition accompanied with modern technology and market changes. It always leads to failure of New Product Development. The final project screening decision is obtained from the overall global IT2FS rates of the projects with respect to the screening criteria. [ABSTRACT FROM AUTHOR]

• The interval type 2 fuzzy Bonferroni mean Ordered Weighted Averaging is developed. • Seven Bonferroni mean quantifier Ordered Weighted Averaging models are formulated. • The optimal weights are solved from the mixed integer linear programming models. • The models are applied to various linguistic decision making aggregation schemes. In this paper, the new aggregation models for the interrelated multi-criteria decision making (MCDM) problems based on the quantifier guided ordered weighted averaging (QGOWA) and Bonferroni mean (BM) operator with interval type 2 fuzzy sets (IT2FS) are developed. In most MCDM problems, the decision criteria might not be totally independent. For some MCDM methodologies that are not considering the interrelationship of the criteria, the decision results suggested are meaningless. The BM operator can express the interrelationship of the input arguments, which serves as a mean type aggregator. Yager introduced the OWA operator which is associated with the orness level (attitudinal character) by means of the quantifiers. Different quantifier functions are associated with the respective different orness levels. This is referred to as the QGOWA operator. Besides, the real world MCDM problems are mostly under uncertain environments. To address such MCDM problems, the linguistic criteria weights and the alternative rates are better characterized by IT2FS. The major contributions of this paper are to propose the interrelation MCDM aggregation models with various extensions, to construct the mixed integer linear programming models for obtaining the optimal QGOWA BM IT2FS weights, and to formulate a new interrelation MCDM paradigm. The developed aggregation models are: (1). Ordinary MCDM aggregation; (2). BM with OWA weights; (3). BM with OWA weights and personal importance; (4). BM with QGOWA weights; (5). BM with QGOWA weights and personal importance; (6). BM with QGOWA weights and attitudinal characters; (7). BM with QGOWA weights, attitudinal characters and personal importance. A new MCDM aggregation methodology with application based on the developed models is introduced. The application results from the MCDM aggregation methodology demonstrate that the final decision prioritization are actually affected by the various orness levels predetermined by the decision experts. [ABSTRACT FROM AUTHOR]