{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,29]],"date-time":"2023-08-29T05:05:42Z","timestamp":1693285542744},"reference-count":55,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Info. Tech. Dec. Mak."],"published-print":{"date-parts":[[2015,11]]},"abstract":"<jats:p> Z Utility Theory refers to a class of nonlinear utility functions for solving Risk and Multiple Criteria Decision-Making problems. Z utility functions are hybrids of additive and nonadditive (nonlinear) functions. This paper addresses the concepts and assessment methods for the additive part of Z-utility functions for multiple criteria problems that satisfy the efficiency (nondominancy) principle. We provide a decision paradigm and guidelines on how to approach, formulate, and solve decision-making problems. We, also, overview the modeling of decision process based on four types of decision-making styles. For multi-criteria problems, a new definition of convex efficiency is introduced. Also polyhedral efficiency is developed for presenting multi-criteria efficiency (nondominancy) graphically. New double helix quasi-linear value functions for multi-criteria are developed. Two types of double helix value functions for solving bi-criteria (Advantages versus Disadvantages) and also risk problems are introduced: Food\u2013Fun curves for expected values and Fight-Flight curves for expected risk values. Ordinal\/Cardinal Approach (OCA) for assessment of additive utility functions is developed. Simple consistency tests to determine whether the assessed utility function satisfies ordinal and\/or cardinal properties are provided. We show that OCA can also be used to solve outranking problems. We provide a critique of Analytic Hierarchy Process (AHP) for assessing additive value functions and show that the developed Ordinal\/Cardinal Approach overcomes the shortcomings of AHP. We also develop a unified\/integrated approach for simultaneous assessment of nonlinear value and additive (multi-criteria) utility functions. These results in an additive utility function that can be concave, convex, or hybrid concave\/convex based on the nonlinear value function. Finally, we show an interactive paired comparisons approach for solving nonadditive and nonlinear utility functions for bi-criteria decision-making problems. Several illustrative examples are provided. The paper provides reliable and robust approaches for modeling the utility preferences of heterogeneous economic agents in macro and micro-economics. <\/jats:p>","DOI":"10.1142\/s0219622014500412","type":"journal-article","created":{"date-parts":[[2013,12,14]],"date-time":"2013-12-14T03:29:13Z","timestamp":1386991753000},"page":"1353-1400","source":"Crossref","is-referenced-by-count":2,"title":["Double Helix Value Functions, Ordinal\/Cardinal Approach, Additive Utility Functions, Multiple Criteria, Decision Paradigm, Process, and Types (Z Theory I)"],"prefix":"10.1142","volume":"14","author":[{"given":"Behnam","family":"Malakooti","sequence":"first","affiliation":[{"name":"Systems Engineering, Electrical Engineering and Computer Science Department, Case Western Reserve University, Cleveland, Ohio 44106, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,1,10]]},"reference":[{"key":"S0219622014500412BIB001","volume-title":"Operations and Production with Multiple Objectives","author":"Malakooti B.","year":"2014"},{"key":"S0219622014500412BIB002","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1070.0838"},{"key":"S0219622014500412BIB003","volume-title":"Supply Chain Engineering: Models and Applications","author":"Ravindran A. 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